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The theoretical prediction of the early seventies about the existence in a solid of a new state of "quantum spin liquids" is now finding real experimental confirmation. "Spin-liquid" compounds have a specific frustrated lattice consisting of triangles, at the vertices of which there are magnetic atoms that do not allow establishing long-range order. Due to quantum fluctuations and strong correlations between spins, frustrated magnets remain disordered even near absolute zero. 

This work presents results of an experimental study of the electronic system of a highly frustrated quasi-two-dimensional organic metal κ- (ET) 2Hg (SCN) 2Cl by the Shubnikov-de Haas quantum oscillation method. At temperatures above 30 K, this compound behaves like a metal with a half-filled band with strong electron-electron correlations. In the region of T = 30 K, a Mott metal-insulator transition is observed in the compound, and at low temperatures the system passes into the state of a quantum spin liquid (N.M. Hassan, and all, npj Quantum Materials 5, 15, 2020).

Organic conductors are fairly  soft materials, and application of pressure can significantly change the conduction band and affect their physical properties. The application of a hydrostatic pressure of 0.7 kbar suppresses the metal-insulator transition and restores the metallic state of κ- (ET) 2Hg (SCN) 2Cl. This enables studying the behavior of the interlayer magnetoresistance at helium temperatures. The field dependence of the magnetoresistance shows an unlimited growth according to a power law, which is a rare phenomenon for organic conductors and may indicate the presence of the polaron mechanism in interlayer transport. The spectrum of the detected oscillations of the magnetoresistance facilitates better understanding of the shape and dimensions of the Fermi surface and to estimate the parameters of the electron system.



Field dependence of the interlayer longitudinal magnetoresistance in κ- (ET) 2Hg (SCN) 2Cl at T = 0.47 K and p = 0.7 kbar. Inset 1: Fourier spectrum of magnetoresistance oscillations. Inset 2: schematic representation of the Fermi surface.

R.B. Lyubovskii, S.I. Pesotskii, V.N. Zverev, E.I. Zhilyaeva, S.A. Torunova, R.N. Lyubovskaya
JETP Letters 112, issue 9 (2020)

With the recent progress in observing new “locally incompressible” fractional quantum Hall states (FQHE), at the forefront of physics of two-dimensional systems (2DES's), there arises a necessity to develop  experimental approaches for the direct monitoring of bulk FQHE states. Since the transport characteristics of the FQHE insulators are not very informative (only the edge channels spatially separated from the bulk states contribute to conductivity), we employ optical techniques that can provide the required information. One of the confirmed experimental techniques for studying bulk electronic states in the QHE and FQHE regimes is the resonant reflection. However, the resonant reflection technique, because of  its high complexity, is not suitable for routine studies of FQHE states. Application of the nonresonant reflection for the same purpose is impossible for an uncontrolled photo-induced contribution to the experimental results. Up to now, all attempts to employ the photoluminescence technique for analysis of the FQHE states have not lead to reasonable results, despite the fact that in the QHE regime, nonresonant photoluminescence is one of the most powerful tools for studying bulk states. The reason for the incorrect use of this experimental technique became obvious only recently. In the nonresonant photoluminescence, the contribution to the signal is produced not only by two-particle excited states of 2DES, for which the conditions of “hidden symmetry” are satisfied but also by three-particle states, for which there are no symmetry restrictions on the spectral characteristics of the photoluminescence signal. The photoluminescence signal of three-particle complexes in the FQHE regime can have a complex structure with several spectral components due to the nontrivial dispersion of two-particle complexes (magnetoexcitons), from which three-particle complexes are constructed. In the presented work, we employ the resonant photoluminescence for studying FQHE state 1/3, with which we have got rid of unwanted photoluminescence of three-particle complexes. In this case, no violation of the “hidden symmetry” is observed, however, the amplitude of the resonant photoluminescence signal from the FQHE 1/3 state modifies so dramatically, that this modification can serve as an experimental marker of the 1/3 state. On the other hand, such a change in the amplitude of the resonant photoluminescence response indicates  the formation of a nonequilibrium coherent spin-excitation ensemble in 2DES, which is believed to consist of the quasi-particles with fractional charges.


L.V. Kulik et al.
JETP Letters 112,  Issue 8 (2020)

Titanium dioxide (TiO2) is actively used in the modern world: as an E171 additive in the food industry, in the fabrication of paints and varnishes, solar panels, gas sensors, etc.
For many practically significant applications, especially for the food industry, it is important to determine the composition of TiO2 powders (the proportion of nanoparticles that have toxic properties in the powder). Spectroscopic methods are promising for studying the composition of TiO2 powders; however, the optical properties of titanium dioxide remain not fully understood. For this reason, the mechanisms of radiative recombination of the anatase titanium dioxide, which are responsible for intense emission lines in the visible and near-infrared range are being actively discussed. Various authors associate TiO2 luminescence with various mechanisms: from the recombination of autolocalized excitons to the mechanism in which an electron bound to a donor impurity recombines on a hole bound to an acceptor impurity (the so-called luminescence of distant donor-acceptor pairs).
In this work, a simple model is proposed that allows one to identify the power-law decays of the luminescrence signal in TiO2 micropowders with the emission of donor-acceptor pairs located in the volume of microcrystals. Based on this model, the change in the power-law decay of the luminescence signal of donor-acceptor pairs in nanopowders is described within the framework of nonradiative recombination associated with the surface. The presented experimental results are promissing for fullu optical detection of toxic TiO2 nanoparticles in the well known E171 food aditive.



a) Luminescence decay for so-called green luminescence band at 2.3 eV, measured for a micropowder (grey curve), and its approximation by a power-law t-x dependence with x = 0.8 (red dashed line). b) Luminescence signal decay of the same band, measured for the toxic nanopowder (grey curve), and approximation of its fragments by power dependences with x = 0.5 (yellow dashed line) and x = 1.44 (red dashed line).

V.S. Krivobok et al.
JETP Letters 112, issue 8 (2020)

The planar phase of superfluid 3He has two Dirac points in the quasiparticle spectrum – the Berry phase monopoles. The quasiparticles with fixed spin behave as Weyl fermions. While in the chiral superfluid  $^3He$-A the spin-up and spin-down fermions
have the same chirality, in the planar phase these fermions have opposite chiralities forming massless Dirac fermions. As in 3He-A, the Dirac fermions experience effective gravity and gauge field produced by the deformation of the superfluid order parameter.
In both superfluid phases the primary variables, which give rise to the effective metric acting on Weyl and Dirac particles, are the vielbein fields. As distinct from the 4 x 4 matrix in the conventional tetrad gravity and in the effective gravity emerging in  $^3He$-A, the vielbein field in the planar phase has mixed dimensions: it is the 4 x 5 matrix.
The planar phase has the analog of Dirac magnetic monopole in the real space. In this monopole, the Dirac strings of different chirality compensate each other. In the presence of the monopole the effective metric describes the conical spacetime
produced by the global monopole in general relativity. But instead of the solid angle deficit, the effective spacetime in the planar phase has the solid angle excess, which corresponds to the repulsive gravity, G < 0.


 G.E. Volovik 

JETP  Letters 112, issue 9  (2020) 


The question of the influence of potential disorder on superconductivity has a rich research history dating back to the celebrated Anderson theorem about the insensitivity of the superconducting critical temperature to the disorder strength. However, a large body of empirical evidence indicates that the transition temperature is typically suppressed with disorder, which is in particular prominent for superconducting films of a mesoscopic thickness. This effect is conventionally attributed to disorder-related enhancement of Coulomb repulsion, which provides a negative contribution to the Cooper coupling, thus suppressing superconductivity.

Quantitative study of this effect in the assumption of a two-dimensional diffusive nature of electron motion was done in 1980ies by a number of authors. The first-order correction was later generalized by Finkel'stein, who derived a non-perturbative expression for the critical temperature degradation as a function of the sheet resistance of the film. The latter has become a widespread tool for fitting experimental data.

In this work, based on the theoretical treatment accompanied by the analysis of experimental data, it is argued that for the substantial fraction of superconducting films the main contribution to the critical temperature suppression stems from the region of three-dimensional ballistics rather than two-dimensional diffusion. The ballistic effects are governed by the parameter $k_F l$ (where $k_F$ is Fermi momentum and $l$ is the mean free path), which is a measure of the proximity to the three-dimensional Anderson localization.

Suppression of the critical temperature is given by the integral over the momentum $q$ carried by the electron-electron interaction. The figure is a sketch of the corresponding integrand. The integral is logarithmic in the region of two-dimensional diffusion, $q < 1/d$ ($d$ is the film thickness). It linearly diverges in the three-dimensional region $q>1/d$, extending from the diffusion to the ballistic region with a different numerical coefficient. Therefore the main contribution comes from the upper cutoff at $q \sim k_F$.


Antonenko D.S., Skvotsov M.A.
JETP Letters 112, issue 7 (2020)

Balancing an inverted pendulum subject to a given time-dependent horizontal force is a famous mathematical challenge known as the Whitney problem. For any initial and final position of the pendulum in the upper half-plane, there exists a trajectory that remains in the upper half-plane at the entire time interval. Remarkably, a non-falling solution to the Whitney problem is unique.

Assuming that the horizontal force is a random process, a formal mathematical problem of the existence of a non-falling trajectory gets translated into the context of stochastic dynamics, with the main goal of describing statistical properties of such a non-falling trajectory. Quite unexpectedly, the latter formulation has many notable connections with other mathematical physics problems: control theory, Burgers turbulence, theory of minimizers, rear events in stochastic differential equations, disordered superconductivity, etc.

A new analytical method for describing statistics of the never-falling trajectory on an infinite time interval has been recently developed by the authors of this Letter, in the framework of a supersymmetric field-theoretical approach to stochastic dynamics. In this Letter, the technique is generalized to finite time intervals and different-time correlation functions on the non-falling trajectory. In particular, it allows determining the Lyapunov exponent, which governs decay of memory correlations on the non-falling trajectory.


Examples of non-falling trajectories for the pendulum equation of motion obtained for two time intervals and the same horizontal force (a), (b). Shown are 25 such trajectories with five initial and five final positions in the upper half-plane. The memory of the boundary is lost exponentially with the rate determined by the Lyapunov exponent. (c) An inverted pendulum under the action of a horizontal force.


Stepanov N.A., Skvotsov M.A.
JETP Letters 112, issue 6 (2020)

The Standard Model unequivocally predicts parity violation in high energy hadronic interactions of polarized hadrons. However, the experimental confirmation of this prediction is still elusive. One of the possible observables is the parity violating single-spin asymmetry in scattering of the longitudinally polarized protons and deuterons. High intensity polarized beams will be available at NICA facility under construction at JINR, Dubna. The reported estimates of asymmetries in polarized proton-deuteron scattering are an extension of systematic analysis [1,2] of possibilities of experiments at NICA. Experimental observation of asymmetries in the total cross sections, expected to be well below 10-7 , is extremely challenging, and it is suggested to take advantage of substantial enhancement of asymmetry in elastic scattering. In the case of polarized deuterons, similar enhancement is shown to persist in the deuteron dissociation channel.

[1]  I.A. Koop, A.I. Milstein, N.N. Nikolaev, A.S. Popov, S.G. Salnikov, P.Yu. Shatunov, Yu.M. Shatunov, Strategies for Probing P-Parity Violation in Nuclear Collisions at the NICA
       Accelerator Facility, Physics of Particles and Nuclei Letters, 17(2), 154-159 (2020)
       [2]  A.I. Milshtein, N.N. Nikolaev, S.G. Salnikov,  Parity Violation in Proton–Proton Scattering at High Energies, JETP Letters, 111(4), 197-200 (2020)

A.I. Milshtein, N.N. Nikolaev, S.G. Salnikov,  Parity Violation in Proton–Proton Scattering at High Energies

JETP Letters 112, issue 6 (2020)

Bilayer graphene nanoribbons (BGNR) are quasi one dimensional materials which have a wide variety of properties depending on their width, geometry of edges, defects and external influences, such as mechanical deformations or electric and magnetic fields. Combination of nanoribbons with various properties can open wide prospects of their use as two dimensional electronic devices.

This work aims to investigate electronic transport in BGNR with a pore by means of the wave packet dynamics method. Wave packet (WP) is injected from metallic electrode to the BGNR and interacts with atomic structure of nanoribbon and with nonopore. The results of these calculations are the time dependent wave functions. Two types of system were considered where the electrode is connected with: (i) both layers, and (ii) with only one layer. Time dependent currents through the BGNR cross-sections were obtained, both ahead of and behind the hole. It was shown that the presence of nanopore is important for the WP propagation: it complicates the pattern of WP spreading and leads to localized states formation on the pore (Fig.1). For type (ii) connection to electrode, the nanopore plays a role of the signal separator. Currents flow after passing the nanopore are significantly different in each layer.

The propagation of the wave packet is influenced by many parameters of the nanoribbon, such as its width, hole geometry, defects, type of connection to electrode etc. This study may be the first prerequisite for potential use of such objects as elements of electronic circuits


Figure 1. Wave packet probability density in the bilayer graphene nanoribbon with a hole, in the layer connected to the electrode (left), and in the layer unconnected (right) at t = 4.2 fs

V.A. Demin, D.G. Kvashnin, P. Vancso, G. Mark, L.A. Chernozatonskii
JETP Letters 112, issue 5 (2020)


The process of spontaneous parametric down-conversion (SPDC) is a significant source of biphotons. Biphoton is a pair of quantum – correlated photons. Due to the high degree of correlation, biphotons are used in many areas such as quantum processing, quantum tomography, spectroscopy, etc. Recently, the generation of optical - terahertz biphotons under strongly frequency-non-degenerate parametric down-conversion has attracted more attention.
The paper proposes an approach that allows using the same detector with a limited dynamic range for the registration of terahertz radiation under parametric down-conversion (PDC) at a different parametric gain. This approach is based on the change of the wavelength of the optical pump and can be used to achieve the spontaneous PDC to obtain optical – terahertz biphotons with a high degree of correlation. By doubling the frequency of a pulsed laser source, we experimentally demonstrated a decrease of the parametric gain more than fivefold in the minimum value, at which terahertz (idler) radiation can be detected against the background of detector noises. The terahertz radiation generated by the PDC was detected under the record low parametric gain conditions.



The experimental setup for the generation a terahertz - optical biphotons and idler radiation detecting terahertz frequency power at the PR in two modes at the pump wavelength $\lambda_p$ = 1046.7nm and $\lambda_p$  = 523.35 nm


V.D. Sultanov, K.A. Kuznetsov, A.A. Leontyev and G.Kh. Kitaeva
JETP Letters 112, issue 5 (2020)


In 1984, a new type of superfluidity was discovered at the Kapitza Institute for Physical Problems - spin superfluidity [1]. In this effect, magnetization is carried on a long distance by the superfluid current of magnons - elementary quasiparticles of magnetization in the Bose condensed state. This phenomenon was discovered in superfluid 3He at temperatures below 2mK. Magnetic analogs of all superfluid effects such as the Josephson effect, quantum vortices, second sound, critical speed, etc. were experimentally demonstrated.  However, the application of these effects was difficult because of the very low temperature of superfluid 3He. The basis of spin superfluidity is the Bose condensation of magnons and its stability upon the spatial superflow. The latter is provided by the repulsion interaction between magnons.  A similar repulsive interaction between magnons also exists in yttrium iron garnet (YIG) films, magnetized perpendicular to the plane. In this letter, we have demonstrated a spatial magnon supercurrent similar to that observed in 3He. Remarkably, the effect was found at room temperature!

The YIG film was placed in a magnetic field gradient. Magnetic resonance was excited in the region of strip 1 when the pumping frequency corresponded to the perpendicular field (B). With a decrease in the field, a magnon BEC was formed, which filled the entire space with a field less than that corresponding to the resonance field. In field (A), the magnon BEC reached the region of strip 2 and induced in it a radiation signal. Thus, it was shown that the magnon supercurrent transports the precessing magnetization from region B to region A.

[1] G. E. Volovik, J. Low Temp. Phys., 153,  266  (2008) .


P. M. Vetoshko, G. A. Knyazev, A. N. Kuzmichev, A. A. Cholin,  V. I. Belotelov, Yu. M. Bunkov

  JETP Letters 112, issue 5 (2020).


The development of the ultrafast magnetooptics during the last 15 years results in a new fundamental knowledge on the ultrafast interaction of light and magnetic materials and also in a very important practically possibility to increase the speed of writing/reading processes in computers by a factor of 105-106. Several groups in the world have found long-living magnetic oscillations after femtosecond laser pump, for example in FeBO3 [1]. Within a phenomenological approach, this effect has been explained as the inverse Faraday effect. In our paper we demonstrate such oscillations within the microscopic model of the magnetic insulator with two possible multielectron terms at each cation site. The terms have different spin values and form local polarons due to electron-phonon interactions with vibrations of local anions. We assume that the femtosecond pumping by the very fast charge-transfer excitations results in a switching of the initial high spin term of cation into the exited low spin term, and the dynamics of the excited state is studied within the master equation for the reduced density matrix. In the figure we demonstrate the dynamics of 3 material parameters: the concentration of high spin terms (blue line), sublattice magnetization (red line), and variation of the cation-oxygen bond length (black line). The time scale is given in ps. One can see the generation of vibrons during the relaxation. After 1 ps all parameters reach their equilibrium values typical for the high spin state, and the magnetization demonstrates long-living oscillations.


1.       A.M. Kalashnikova, A.V.Kimel, R.V.Pisarev, V.N.Gridnev, A.Kirilyuk, Th. Rasing, Phys. Rev. Lett. 99, 167205 (2007). https://doi.org/10.1103/PhysRevLett.99.167205


Yu.S. Orlov, S.V. Nikolaev, S.G. Ovchinnikov and A.I. Nesterov
JETP Letters 112, issue 4 (2020)



HgTe quantum wells proved to be the most interesting and fundamental objects of modern condense matter physics due to their unique property of realization of five kinds of two-dimensional (2D) electron systems depending on the well thickness: a 2D insulator with the direct gap, a single valley 2D Weyl semimetal, a 2D topological insulator, a 2D semimetal and a 2D metal. In fact, the indicated property comes from relativistic effects that play a key role in the formation of the HgTe energy spectrum. In our work the results of the experimental study of photo- and thermoelectric effects in 2D topological insulators and 2D semimetals are reported. The most deep and important effect predicted in few theoretical papers and found in our studies is the circular photogalvanic effect in the 2D topological insulator. Figure shows the geometry of the experiment. Circularly polarized terahertz radiation illuminates the surface of the HgTe-based 2D topological insulator and generates a chiral spin photocurrent along the edge of the quantum well.  This photocurrent is generated just due to the topological helical nature of edge states of the 2D topological insulator. Circular irradiation breaks equilibrium between chiral currents of opposite directions and transforms the equilibrium helical state into non-equilibrium chiral one.


Z.D. Kvon, M.L. Savchenko, D.A.Kozlov

JETP Letters 112, issue 3 (2020)

It was shown recently that such a well-known quasi-one-dimensional conductor as (TaSe$_4)_2$I is a Weyl semimetal. Do the properties associated with the topological non-triviality of this material survive in the Peierls state when the Weyl points disappear because of the Peierls gap opening? In this letter, we  present the results of such an investigation performed on (TaSe$_4)_2$I crystals. Longitudinal magnetoresistance of studied samples in all known modes of charge-density wave motion (pinned, creeping, sliding and the ''Fröhlich superconductivity'' ) is small, positive and thus reveals no signature of the chiral anomaly. In order to check a possible contribution of charge density wave defects (dislocations, solitons), similar measurements were undertaken in focused ion beam shaped samples. In such samples, charge-density wave current motion is spatially nonuniform and accompanied by nucleation of numerous charge-density wave defects. A weak localization-like non-parabolic longitudinal magnetoresistance is found to appear in relatively small magnetic fields $B\lesssim 4$ T in the nonlinear conduction regime in the temperature range 70-120 K, whereas weak antilocalization-like behavior dominates at lower temperatures in such samples.  Possible role of the charge-density wave defects is analyzed. Our results differ significantly from ones obtained earlier and raise the question concerning conditions for observation of the chiral anomaly in Weyl semimetals in the Peierls state.

Image of a focused-ion beam pro led sample (W-type sample)


a) Temperature evolution of the longitudinal magnetoresistance in CDW sliding regime. (b-c) Evolution of the negative magnetoresistance contribution with temperature (b) and the electric field (c). W-type sample.



I.A. Cohn, S.G. Zybtsev, A.P. Orlov and S.V. Zaitsev-Zotov
JETP Letters 112, issue 3 (2020)


The potential energy of a particle in external field is uniquely expressed through the wave function of the ground state provided it has a discrete energy level. This property, based on the oscillation theorem, allows one to investigate a wide class of model potentials by setting the explicit wave functions of the ground state. Some of these model potentials have physical realizations. For many such realizations the ground-state energy is pinned at zero and does not change with variation of one or several parameters describing the potential.

Using the proposed inverse-problem method we study several classes of potentials in one, two or three dimensions: the potentials with a barrier and one discrete energy level, the crater-like potentials with possible application in string theory, the instanton-type potentials with two local minima. A vivid manifestation of the effectiveness of the proposed method is its application to the solution of nonlinear Schrodinger equation. We show that the energy of a stationary two-soliton solution of this equation coincides with the energy of one-soliton solution. This means that the decay of a soliton into two solitons happens without the change of energy, the latter is even independent on the distance between the solitons.


The one and  two-soliton solutions of the Schrodinger equation (dashed lines) with corresponding potentials (solid lines). They have the same energy E=-1, denoted by the solid green line. This plot illustrates the independence of this energy level on the number of solitons and on the distance between them, as obtained using the proposed method.



A.M.Dyugaev and P. D. Grigoriev 
JETP Letters 112, issue3 (2020)

The Goos-Hanchen (GH) effect is the lateral shift of the totally internally reflected light beam with respect to its specular point. The potential applications of the GH effect include chemical and biological sensors, as well as all-optical switching, which motivates numerous studies aiming at achieving higher GH shift values and providing control over them.
    Recently, it has been shown that when a quasi-localized eigenmode is resonantly excited in the medium, the spatial shift of the reflected beam may become comparable with its width, which has been referred to as a ’giant’ GH effect. In the current study, we consider the scattering of an incident TE-polarized light beam on a layered dielectric structure (see Fig. 1), which enables the lateral propagation of the localized eigenmode and allows for the giant GH shift, analogous to the plasmonic mechanism of a giant GH effect. On the other hand, in the considered setup, unlike the plasmonic system, the GH shift takes place not only for the reflected beam, but also for the transmitted one, thus providing additional functionalities.

Left panel: Planar dielectric structure considered in this work. The permittivities of the background and guiding layer are higher than the permittivity of the cladding layers, which play the role of a tunnel barrier between the guiding core and the background.
 Right panel: GH shift $\Delta x_{tr}$ for the transmitted radiation as a function of parameters $a$ and $\alpha$. Reversing the sign of $\alpha$ (which corresponds to changing focusing lens to defocusing one) leads to the reversal of the $\Delta x_{tr}$ sign.

In our letter, we show that the GH shift of the reflected and transmitted radiation can be easily controlled by  spatial modulation of the phase front of the incident light beam. Figure 1 (right panel) shows the dependence of the GH shift for the transmitted light on the incidentbeam parameters (namely, the beam width $a$ and the curvature of the phase front $\alpha$, supposing that the impinging beam has a Gaussian form $E_{inc} = \exp ( -0.5x^2/a^2 - 0.5i\alpha x^2)$). As it seen, square-law modulation of the phase front, which can be achieved by focusing/defocusing lensing, considerably changes the GH shift and can even reverse its sign, which is impossible for the beams with the flat phase front.

A. A. Zharov,  N. A. Zharova, and A. A. Zharov
JETP Letters 112, issue 3 (2020)


The detection of long-lived magnetoexciton levels in the QHE regime attracts interest for studying the formation of the so-called non-stationary condensate, that is, a system driven from equilibrium by an external force.  The appearance of a highly coherent state is caused by accumulation of a large number of magnetoexcitons with integer spin in a small region of the phase space.

 This work is devoted to the study of the extraordinary behavior of the Raman's anti-Stokes scattering signal in ZnO based 2DES with strong correlation.   At low temperatures (T ~ 0.35 K), this spectral line has an anomalously high intensity. It is shown that its origin may be associated with the appearance of long-lived magnetoexciton levels. Potentially, such levels can cause the formation of non-stationary condensate.


 Figure 1. Raman spectrum showing Stokes and anti-Stokes scattering signals. Note that the anti-Stokes scattering signal has a gigantic intensity, ten orders of magnitude greater than that expected at such a low temperature (T ~ 0.35 K).



 B.D.Kaisin, A.B.Van'kov, I.V.Kukushkin

JETP Letters 112, issue 1 (2020)


A wealth of fundamental physical phenomena as well as related applications suffer from inherently weak light-matter interactions during involved physical processes. Prime examples include – hardly related at the first glance - Raman scattering of light and detection of far-infrared and THz electromagnetic waves. While the former process has a deeply fundamental limitation of the scattering cross-section, the drawbacks of the latter application arise from the low sensitivity of even state-of-art detectors operating at room temperature conditions.

A widely recognized approach for amplification of Raman signal is a surface-enhancement Raman scattering (SERS) which nevertheless is mostly limited to optical frequencies ranging from UV to the red part of the visible region. The upcoming Letter continues the research of SERS-like effects with metal-dielectric metasurfaces possesing 3D sub-micron features. An exceptionally strong local enhancement of a laser light field (wavelength 1064 nm) is demonstrated along with optimal structure design. The findings not only pave the way for future applications in biosensing but also serve as a bridge for extending the field enhancement approach into the region of far-infrared and THz frequencies.



V.I. Kukushkin et al.

JETP Letters 112, issue 1 (2020).

In three-dimensional systems magnetic susceptibility of itinerant electrons is determined by competition of two eects: Landau diamagnetism and Pauli paramagnetism, both being band-structure dependent and modied by electron-electron interactions. In
order to determine whichever of them wins, a precise magnetometry is required. In two-dimensional (2D) systems magnetic measurements are challenging due to small number of carriers and inevitable contribution of the substrate. Gated two-dimensional systems allow for measurements of the magnetization derivative with respect to the carrier density [Prus et al. Phys. Rev. B 67, 205407 (2003)]. We conducted such measurements in a 2D system in narrow HgTe quantum wells, with electron spectrum consisting of gapped Dirac carriers accompanied by valleys of heavy holes. We found that paramagnetism wins for both types of carriers (Dirac and heavy holes). These ndings should motivate development of a theory for itinerant electron magnetism in systems with strong spin-orbit coupling.


A.Yu. Kuntsevich, Y.V. Tupikov, S.A. Dvoretskii,N.N. Mikhailov, M Reznikov,

JETP Letters111, issue 11 (2020)

For the edge states in two-dimensional electronic systems to be realized, a spin-orbit interaction, as well as an inverted band structure must occur. In this case, the effects of covalent mixing lead to a strong entanglement of the valence band states and the conduction band states. The inversion condition noted above also plays an important role in the formation of an excitonic insulator (EI), when the spontaneous occurrence of an excitonic order parameter (EOP) is accompanied by the generation of a hybridization interaction between the states of the valence band and the conduction band. Therefore, there is also a significant confusion of the states of these bands in the EI. Correspondingly, one can expect that the edge states can also occur in the EI in case the spin-orbit interaction will be taken into account.

Using the model of the energy structure of the HgTe quantum well, the effect of intersite Coulomb interaction on the energy spectrum was studied. In the case when only density-density Coulomb interaction has been taken into account, there were three phases with s -, d - and p - type of the EOP symmetry. Metastable p-phase was topologically nontrivial. The ground state had s-type of symmetry, for which there were no edge states.

When the exchange part of Coulomb interaction is considered, a mixed s+d-phase becomes the ground state of the EI. In this case, EOP is described by a superposition of s - and d– basis functions. An important feature of the mixed s+d - phase of EI implies that the
topological invariant has zero value, nevertheless the edge states are realized for the open system.

Dispersion relation of the excitonic insulator with the spin-orbit interaction. The excitonic order parameter has s+d symmetry. It is significant that there are two middle branches of the dispersion relation, plotted in green (red). In the vicinity of the crossing, the two middle eigenstates have energies deep inside the bulk gap, and so their wave functions are concentrated at the edges. These wave functions describe edge states of s+d- EI with spin-orbit interaction.

V.V. Val’kov

JETP Letters 111, issue11 (2020)


In quantum cryptography, in addition to attacks on transmitted quantum states, it is possible to detect states in the side channels of information leakage. Without taking into account information leakage via side channels, it is impossible to seriously talk about the secrecy of keys in real quantum cryptography systems. A quantum-mechanical method is proposed for taking into account the leakage of key information through side channels — detection of electromagnetic side radiation, active sensing of a phase modulator at a transmitting station, and back reemission of avalanche detectors on the receiving side. The method takes into account joint collective measurements of quantum states in all channels of information leakage and works at any intensity and structure of states in side channels.

The choice of special basis functions of an prolate spheroid allows one to ''sew'' a quantum and classical description of signals in side channels. A connection has been established between the leak of information and the Holevo fundamental value, and a transparent and intuitively clear interpretation on the physical level of the results has been given.

Figure 1a) shows the dependences of the length of the secret key for various ratios of the average number of photons in the state $k$ noise dispersion $\frac{\overline{M}}{\sigma_M}$, где $\overline{M}=\frac{M_{1}-M_{0}}{2}$. In the classical case, instead of the number of photons, the signal energy in the frequency band ($ E_s $) is used, similarly signal dispersion is expressed in terms of the noise intensity in the frequency band. In this case, there is a correspondence $\hbar\Omega \overline{M} \rightarrow E_s $ and $ \hbar \Omega \sigma \rightarrow \frac {N_ {noise}}{2} $. In this notation, the key length becomes the function $ \ell \left (\frac{E_s}{N_{noise}} \right) $.

It can be seen from Fig. 1a) that even without an attack on informational quantum states with a large signal-to-noise ratio, there is a good distinguishability of states (for example, curve 1 ($ \frac{\overline{M}}{\sigma_M} = 0.5 $, $ \left (\frac{E_s}{N_{noise}} \right) $)) even with a small number of photons in the side state $ \overline{M}\approx 5 $, the key length tends to zero. The eavesdropper, detecting states only in the side channel, and without making errors on the receiving side, will know the whole key. With a small signal-to-noise ratio (curve 4 of Fig. 1a)) - poor distinguishability of states allows one to obtain a key even with a large average number of photons ($ \overline{M}> 20 $) in a side state.

a) The length of the secret key when detecting only the side radiation of the transmitting station as a function of the average number of photons $\overline{M}$ for different signal-to-noise ratios $\frac{\overline{M}}{\sigma_M}$ $\left(\frac{E_s}{N_{noise}}\right)$ -- the average number of photons to the dispersion. Parameter $\frac{\overline{M}}{\sigma_M}$ $\left(\frac{E_s}{N_{noise}}\right)$ for curves 1--4 next: 1 -- 0.5; 2 -- 0.2; 3 -- 0.1; 4 -- 0.05.
b) The length of the secret key when attacking information States and actively probing the phase modulator on transmitting station. The $\mu_P$ parameter for curves 1--4: 1 -- 0.001, 2 -- 0.05, 3 -- 0.1, 4 -- 0.25.


JETP Letters 111, issue 11 (2020)



In 1959 Aharonov and Bohm [1] proposed series of experiments that demonstrate the physical significance of electromagnetic potentials. In classical electrodynamics, these quantities play the role of mathematical auxiliary quantities whereas the electric and magnetic fields have a physical sense solely. In quantum mechanics, potentials possess a primary role. To observe the Aharonov - Bohm effect (AB), it is necessary to have regions free of electromagnetic field but with non-zero potential. Unipolar pulses, in contrast to conventional bipolar multi-cycle pulses, have non vanishing electric area S_E≡∫E(t)dt ( E(t) is the electric field strength, t is the time) [2]. This means that unipolar pulse in vacuum changes the value of the vector potential A. Thus, a unipolar light pulse allows observation of the optical AB effect.

The experimental setup of the “electronic interferometer” proposed in [1] is shown in Fig.1. The plane electron wave 1 is divided by splitter 2 into the two packets, which after the refraction in prisms 3 and 4, pass through two spatially separated regions (shoulders of the electron interferometer). Then packets are directed by prisms 5 and 6 to the screen 7.

In our optical variant, a unipolar pulse 8 passes in one of the arms of interferometer before the appearance of the electronic packet. The radiation pulse is ahead of the packet and does not intersect it. Thus the packet will have to interact with a constant vector potential, which was created by unipolar pulse and the wave function of the electrons should change the phase. In this case, on the screen 7 one will observe the shift of the interference fringes relative to their position in the absence of the pulse.

Besides the fundamental interest to AB effect, its optical analogue, in our opinion, can be used for the measurement of electric area of unipolar pulses.


Fig.1. Scheme of the proposed experiment to observe the Aharonov-Bohm effect with unipolar optical pulse, which is the source of vector potential.

1. Y. Aharonov, D. Bohm, Physical Review 115, 485 (1959).
2. N. N. Rosanov, R. M. Arkhipov, M.V. Arkhipov, Phys. Usp. 61, 1227 (2018).

M.V. Arkhipov, R.M. Arkhipov, N.N. Rosanov

JETP Letters 111, issue 12 (2020)


Remarkable effect of microwave irradiation of two-dimensional electron systems is the appearance of giant magnetoresistance oscillations with the resistance tending to zero in the main minima. There are different approaches proposed to explain this effect, which predict similar resistance oscillations both in the shape and position. Their applicability is still debated. One of them is based on the non-equilibrium electron  energy distribution under the radiation. We have employed a different from magneto-transport experimental technique which is sensitive namely to such a distribution. The measurements are carried out with samples of field-effect transistors (FETs) with a channel comprising two 2D electron layers (subbands) located at different distances from the gate. Non-equilibrium occupation of electronic states leads to microwave induced electron redistribution between the layers which causes ac current between the gate and channel when the microwave power is modulated. Theoretical analysis shows that the redistribution oscillates as a function of magnetic field and is described by a product of two harmonic functions with frequencies determined by commensurability of either the subband energy separation or photon energy with the cyclotron splitting. Such oscillation pattern with the beating node has been observed in our experiment (see Fig.) giving convincing evidence of the non-equilibrium electron distribution in energy.

The figure shows our main experimental result and the measurement layout (inset). GaAs/AlGaAs FET is irradiated by microwaves which power is modulated at a frequency fmod. The ac  photocurrent Iphoto of frequency fmod between the gate and the channel, comprising two layers L1 and L2, is converted into the ac voltage and detected by the Lock-in amplifier.



JETP Letters 111, issue 10 (2020)



Over the past decade, the unique properties of HgTe/CdHgTe quantum well heterostructures and their potential for practical applications in terahertz electronics and optoelectronics have been discovered and intensively studied. One of the problems impeding the advancement into the terahertz range is the carrier lifetime decrease due to recombination via impurity-defect centers, i.e. by the Shockley – Reed – Hall mechanism. It is generally accepted that the most common point defect in CdHgTe ternary alloys is a double acceptor formed by a mercury vacancy. It is natural to expect the presence of such a vacancy in HgTe/CdHgTe quantum well heterostructures. To date, only a few works investigated “below bandgap” features in the photoconductivity and photoluminescence spectra. Moreover, the relationship between the observed features and the mercury vacancy states was based on calculations only.

In this Letter, we experimentally demonstrated that the interplay “below bandgap” features in the photoconductivity spectra of HgTe/CdHgTe QW heterostructures results from the ionization of a double acceptor rather than the ionization of the states of two different single-charged acceptors. To do so, the Fermi level was driven though the bandgap by dosed blue light illumination exploiting the effect of persistent photoconductivity.

Photoconductivity spectra in the HgTe/CdHgTe heterostructure obtained under dark conditions (lower curve) and after short illuminations with blue light. Bands a and b are the observed “below bandgap” features. Transition schemes with different Fermi levels positions are shown near the spectra. The absence of the band b in the lower spectrum (when the Fermi level is in the valence band) is just the evidence that the observed features are associated with the ionization of a double acceptor.

                      Nikolaev I.D. et al.

JETP Letters 111, issue 10 (2020)




As distinct from the quantized vortices in mass superfluids, which have quantized circulation of superfluid velocity, the spin vortices in antiferromagnets have quantized circulation of spin current. That is why in the rotating container with superfluid liquid the lattice of quantized vortices represents the ground or equilibrium state of the liquid. On the other hand, in the rotating antiferromagnets the spin vortices are not formed, because the orbital rotation does not act on the spin currents.

Here we discuss the spin vortices in the spin triplet p-wave superfluids. We show that under certain conditions the lattice of spin vortices can be formed in the rotating vessel. The first condition is the applied sufficiently large magnetic field.

The second condition is that the formation of the mass vortices must be suppressed. This condition is not the problem for some phases of superfluid 3He (the superfluid 3He-B and the polar phase). In both phases there is a large barrier for the creation of mass vortices. In experiments, the mass vortices are created under rotation if either the large critical velocity is exceeded, or if the liquid is cooled down from the normal state to the superfluid state under rotation.

If the mass vortices are not formed, the superfluid in the rotating state vessel is in the Landau vortex-free state. In this state one has the counterflow of the normal and superfluid components of the liquid: the normal component experiences the solid body rotation, while the superfluid component is at rest. In the presence of magnetic field, the spin vortices feel the effect of rotation from the rotating counterflow and form the spin vortex lattice with low density.


 G.E. Volovik                                           

JETP  Letters 111, issue 10  (2020)       



Creating a fully functional multi-qubit quantum computer using superconducting, qubits is a difficult problem due to the relatively short lifetime of superconducting qubits  several hundred microseconds. Such a computer requires efficient multi-qubit quantum memory with significantly longer lifetime. The quantum memory can be created with high Q microwave resonators which enable increasing the lifetime of qubits to tens of milliseconds. Previous studies [S.A. Moiseev, K.I. Gerasimov, R.R. Latypov, N.S. Perminov, K.V. Petrovnin, and O.N. Sherstyukov. Scientific Reports, 8, 3982 (2018)] have shown that the system of coupled resonators with a periodic spectral structure of resonance lines is capable of playing the role of a highly efficient quantum memory and interface. Due to the spectral optimization, such multiresonator systems can efficiency store short pulses of arbitrary temporal modes in a wide spectral range.

In this letter, we study the multiresonator quantum memory connected to an external resonator via a controlled switchable coupling. The memory block includes 3 resonators connected with a common resonator, whose coupling  k(t) with an external resonator can be controlled in time (see Fig. 1). Using algebraic methods, we  found a single set of optimal  spectroscopic parameters of the resonators and its coupling constants which show the possibility of highly efficient controlled reversible transfer of information into the memory block and its multi-cycle storage after decoupling with external resonator (k(t)=0). The presence of switchable coupling allows use of the multiresonator system both for the longer quantum storage and quantum processing of the stored quantum state on the memory resonators.


Fig.1. A quantum memory with three resonators x1, 2, 3 (t) of initial frequencies (D, 0,- D) connected to resonators y1 and y2 having frequencies (0,0), coupling through the switch k (t). For switched off coupling k(t)≠0, the loading/unloading the field from the mode y2(t) to the memory block is implemented. When the coupling k(t)=0 is turned off, the regime of cyclic energy exchange between the resonator modes y1(t) and x1,2,3(t) performs reversible processing of the stored state.


S.A. Moiseev and N.S. Perminov

JETP Letters 111, issue 9 (2020).

In modern biology and medicine, increasing attention is paid to the development of  optical visualization methods for   processes occurring at the cellular level. For this purpose, specially synthesized particles with intense luminescent properties are introduced into cells and biotissues. At the same time, one of the main problems that inhibit the development of entire areas of molecular biology and biomedicine is the separation of the useful signal against the background of so-called autofluorescence (the fluorescence of natural fluorophores of biological tissue), whose spectrum overlaps with the photoluminescence spectrum of the nanoparticles themselves. One of the most promising ways to solve this problem is time-resolved spectroscopy. Since the fluorescence lifetime of natural fluorophores is usually units of nanoseconds, for successful visualization it is necessary to use nanoparticles with the lifetime of radiative states lying in the micro- and millisecond range. In this context, ions of rare earth element are very promising, since they have relatively long-lived excited states


The authors of this paper study new solid solutions based on the low-temperature modification of the NaGdF4 matrix doped with europium ions. The combination of small sizes of the crystalline particles and the presence of alloying impurities provides high efficiency and stability of luminescence of such materials.

The paper presents the results of the Judd - Ofelt theory application for determining the lifetime of excited states of NaGdF4:Eu solid solutions  from their integral luminescence spectra. A good agreement between the experimentally measured and theoretically calculated lifetime values of the excited states of these complexes in suspensions showed the adequacy of the Judd - Ofelt model for describing photophysical processes in samples. The application of the Judd - Ofelt theory enables  to estimate the lifetime of radiative states in solid solutions of rare earth elements without resorting to direct measurement of the luminescence lifetime; therefore, such approach  can be used by researchers in the absence of appropriate experimental equipment. The obtained results indicate the prospects of using solid solutions of NaGdF4:Eu for optical imaging in biotissues by time-resolved spectroscopy.


S.А. Burikov et.al.

JETP Letters 111, issue 9 (2020).



In the two-dimensional turbulence there is a tendency to form larger and larger eddies, that leads to formation of the so-called inverse cascade. In the homogeneous case, a chaotic flow with stationary statistics is realized. However, inhomogeneity (say, presence of walls) could lead to appearing coherent structures with well-defined mean flow. Here we demonstrated possibility of arising the coherent vortex around a rotating disc immersed into a two-dimensional turbulent flow. We found the radial profile of the mean azimuthal velocity in such vortex.

As it was shown in our previous works, a coherent vortex without a solid disc inside is characterized by the profile with constant velocity. The mean velocity amplitude is determined by the energy production rate per unit mass and the bottom friction coefficient. The immersed uniformly rotating disc, whose axis coincides with the center of the vortex, imposes boundary conditions for the flow. We showed that the presence of the disc does not destroy the vortex, and the mean velocity amplitude tends to its unperturbed value far from the disc. We found how the disc changes the flow in its vicinity in case the velocity of the disc rotation is not equal to the asymptotic value of the mean velocity.




A.B.Buzovkin, I.V.Kolokolov, V.V. Lebedev, S. S.Vergeles

JETP Letters 111, issue 8 (2020)

Due to the unique properties, carbon nanotubes (CNT) are currently of great interest for different applications. One of the promising areas is their use in electronics. CNTs have a wide variety of electronic properties from metallic to semiconducting, with a band gap up to 2 eV. Electronic properties of the nanotubes are entirely determined by their geometric structure. One of the most important problems of practical implementation of CNT is the complexity of the synthesis of CNT of a predefined geometry and, therefore, with desired properties.

Nanotubes with predefined width were experimentally obtained in 2013 from bilayer graphene in AA-package  [1]. Bilayer graphene nanoribbons were produced using transmission electron microscope. Interaction of electrons with the nanoribbon induces closure of the edges and thinning, leading to the formation of a single-wall nanotube with a diameter less than one nanometer.

This work is devoted to modelling of the new flattened carbon nanotubes (FCNT), which can be prepared from twisted bilayer graphene with the Moiré angle Θ=27.8°. Bilayer nanoribbons are cut out and their chemical active edges are folded, forming structures similar to the known compressed carbon nanotubes. We describe in detail the FCNT geometry. Ab-initio calculations show energy stability and Young modulus ~0.7 TPa of the new nanotubes. Electronic band structure analysis shows metallic type of conductivity for all new nanotubes except one semiconducting with the width of 14Å and energy gap Eg=0.2 eV (Fig.1a). Band gaps of other FCNT open under compression/stretching deformations.

We believe that such structures can be useful for nanoelectronics as transition bridges between two disordered graphene monolayers (Fig.1a) or as conductive channels between two bilayer graphene arrays (Fig.1b).



Figure 1. a) – FCNT connecting two disordered graphene monolayers, b) – conductive FCNT channel connecting two arrays of bilayer graphene with Θ=27.8°

[1]     G. Algara-Siller, A. Santana, R. Onions, M. Suyetin, J. Biskupek, E. Bichoutskaia, and U. Kaiser, Carbon 65, 80 (2013)


 Demin V.A., Artyukh A.A., Soroko V., Chernozatonskii L.A. 

JETP Letters 111, issue 7 (2020)



Turbulence in classical liquids is often encountered in real life and is important for numerous technical and engineering applications. A characteristic feature of turbulence is a complicated motion of liquid in the form of eddies carrying rotational motion at different length scales. Quantum fluids, like superfluid helium, ultracold atomic gases forming Bose-Einstein condensates and interior of neutron stars, can be involved in non-trivial rotating motion only when topological linear objects, quantized vortices, are formed. How is turbulence then structured in such quantum systems? It is believed currently, based on experimental, theoretical and numerical work that at length scales significantly exceeding the average vortex separation, turbulence in quantum systems can mimic that in classical fluids. But at scales smaller than the intervortex distance, turbulence looks completely differently: instead of turbulence of eddies one expects turbulence of oscillations of individual vortices, Kelvin waves.

There is no experimental data available on such turbulence so far and various approaches to its theoretical description resulted in a rather heated debate. With recent progress in experimental techniques, in particular in fabricating nanomechanical oscillators which can be used to agitate waves on individual vortices, one can hope for direct observation of the Kelvin-wave turbulence. In this letter, we provide expressions relating the amplitude of the waves with the energy flux needed to support such turbulence – one of the first relations required to interpret future experiments.

Example configurations of vortex lines, agitated to generate Kelvin waves. (a) A single vortex, attached to an oscillating device. (b) An array of vortices, stretched between parallel plates and agitated by shear or torsional oscillations of the plates.



Eltsov V.B., L'vov V.S.

JETP Letters 111, issue 7 (2020)

The effective detection of electromagnetic radiation in THz - near IR frequency band is the problem of interest due wide modern possibilities of application of such radiation: broadband communication systems, detectors for tracing concentrations of drugs and explosives, non-invasive diagnostics, near-field spectroscopy, surface studies using electronic paramagnetic resonance, etc.

In this letter, we propose a general physical approach to increase the sensitivity and selectivity of a number of THz and near-IR detectors. The essence of this approach is in the addition of a dielectric structure (resonator) under the conducting layer (“dielectric” plasma, metal, superconductor) that is opaque for an incident wave. This allows one to increase significantly both the field strength behind the mentioned layer and absorption in the conductor. The set of dielectric resonators separated by conductive layers forms the photonic crystal with the absorption band. The properties of such detector are governed by parameters of the dielectric and conducting layers.

The photonic crystal as a set of dielectric and conducting layers forming the band of THz radiation absorption in a given spectral range. Plots of absorption versus radiation frequency are given for different number of the layers in the structure.


A.E. Schegolev, A.M. Popov, A.V. Bogatskaya, P.M. Nikiforova, M.V. Tereshonok, N.V. Klenov

JETP Letters 111, issue 7 (2020)


       There are several scenarios of emergent gravity. Gravity may emerge in the vicinity of the topologically stable Weyl point; the analogue of curved spacetime emerges in hydrodynamics with the so-called acoustic metric for the propagating sound waves; etc. There are two very different scenarios, which however have unusual common property: the tetrad fields in these theories have dimension of inverse length. As a result, all the physical quantities which obey diffeomorphism invariance are dimensionless.

This was first noticed by Diakonov and Vladimirov in the scenario, where tetrad fields emerge as bilinear combinations of the fermionic fields. In another scenario, tetrads with dimension of inverse length emerge in the model of the superplastic vacuum. The reason is that the superplastic vacuum can be arbitrarily deformed, and the equilibrium size of the elementary cell is absent. There is no preferred microscopic length scale (such as Planck scale), and the distances (say, between the points A and C in Figure) are measured in terms of the integer positions of the nodes in the crystal.

In both systems, such physical quantities as Newton constant, scalar curvature, cosmological constant, particle masses, etc., are dimensionless.  Some of these physical quantities become integer-valued quantum numbers, which characterize the topology of quantum vacuum. Examples are the parameters describing the 3+1 dimensional quantum Hall effect in topological insulators and in the Nieh-Yan anomaly. 


   G.E. Volovik                                        

JETP  Letters 111, issue 7 (2020)       

Remarkable features of iron pnictide LiFeAs with critical temperature 17 K, such as superconductivity in stoichiometric state, absence of magnetism, and nontrivial band structure [1], still challenge experimenters. Unfortunately, the available experimental studies are not so numerous due to LiFeAs instability in the presence of water vapors or oxygen. In order to reveal the structure of the superconducting order parameter, here we used multiple Andreev reflection (MAR) spectroscopy. The superconductor-normal metal-superconductor (SnS) junctions with ballistic high-transparent barrier were produced by a break-junction technique [2,3]. This technique provides local probing bulk order parameter (unaffected by surface), and enables to resolve its fine structure (anisotropy).

            In Li1-d FeAs single crystals with Tc = 15.6-17 K  [4], we observe three superconducting gaps: an isotropic small gap, and anisotropic middle and large gaps. Following the ARPES data interpretation [1], the observed gaps are attributed to the outer Fermi surface sheet near the G point, at the electron barrels near the M point, and at the inner G-barrel, respectively. The directly measured temperature dependence of the gaps and their anisotropy, zero-bias conductance and the Andreev excess current may be interpreted in the framework of the three-gap model and demonstrate self-consistency of our data. We also discuss the relation between superconducting and normal-state features, in particular, a flat band presence in the vicinity of the Fermi level.



Fig. 1. Directly measured temperature dependence of the three superconducting gaps in LiFeAs. Following the ARPES data [1], DS develops at the outer G-barrel, DL – at electron M-point barrels, and DG at the inner G-barrel of the Fermi surface below Tc. “In” and “out” indexes mark the minimum and maximum values of Cooper pair binding energy in the kxky-plane of the momentum space (gap anisotropy). Dash-dot lines show single-gap BCS-like curves. The inset shows the temperature dependence of the anisotropy of the middle DL and the large DG gaps taken as 100%∙(1-Diin/Diout).



1.S.V. Borisenko, et al., Symmetry 4, 251 (2012).

2. S.A. Kuzmichev, T.E. Kuzmicheva, Low Temp. Phys. 42, 1008 (2016).

3. T.E. Kuzmicheva, et al., Phys. Rev. B 97, 235106 (2018).

4. I. Morozov, et al., Cryst. Growth&Design 10, 4429 (2010).


T. E. Kuzmicheva, S.A. Kuzmichev, I.V. Morozov, S. Wurmehl, B. Büchner

JETP Letters 111, issue 6 (2020)


Light bullets are bunches of the light energy localized in all directions that can propagate in both homogeneous and inhomogeneous media [1]. The formation of such objects requires at least the presence of nonlinearity, dispersion, and diffraction. In connection with  possible applications of light bullets in optical communication systems, the question of their stability is very important. To date, light bullets have been studied theoretically and experimentally in media with nonlinearities of various physical nature [2 - 4]. In addition to quasi-monochromatic light bullets [1, 3], the few-cycle light bunches were considered [2, 4].

The theory of “breathing” parametrical light bullets propagating in media with quadratic nonlinearity was developed recently for both anomalous [5] and normal [6] group-velocity dispersions (GVD). One should emphasize that the latter case can be realized only in an inhomogeneous medium, for instance, in a waveguide. Interplay between nonlinearity, dispersion, diffraction and waveguide geometry defines stability areas of such spatiotemporal solitons.

Various nonlinear-dispersive effects accompany the process of second-harmonic generation. Their character depends, in particular, on the magnitude and sign of GVD coefficients. Actually, the most interesting case is when one of pulse carrier frequencies locates near zero GVD.

In this paper we investigate the pulse-beam propagation in a medium with quadratic nonlinearity provided zero GVD coefficient of the second harmonic. Our study shows that such conditions don’t prevent the
formation of a two-frequency parametric light bullet. In this case, the pulse at the fundamental frequency, generating the second-harmonic signal, experiences dispersion and diffraction broadening. Тhese processes are stopped by nonlinearity and as the result, a localization of energy is formed at the fundamental frequency. In turn, this localization captures and localizes the second-harmonic signal generated by it. Due to the absence of GVD, the second harmonic pulse experiences twice as much nonlinear selfcompression in the propagation direction as the pulse at the main carrier frequency. The transverse dimensions of both components of the light bullet are the same.


[1] Ya.V. Kartashov, G.E. Astrakharchik, B.A. Malomed, and L. Torner, Nature Review / Physics 1, 185 (2019).
       [2] H. Leblond and D. Mihalache, Phys. Rep. 523, 61 (2013).
       [3] V.P. Kandidov, V.O. Kompanets, and S.V. Chekalin, JETP Letters 108, 287 (2018).
       [4] S.V. Chekalin, V.O. Kompanets, A.E. Dormidonov, and V.P. Kandidov, Physics - Uspekhi 62, 282 (2019).
       [5] S.V. Sazonov, M.S. Mamaikin, M.V. Komissarova, and I.G. Zakharova, Phys. Rev. E 96, 022208 (2017).
       [6] S.V. Sazonov, A.A. Kalinovich, M.V. Komissarova, and I.G. Zakharova, Phys. Rev. A 100, 033835 (2019).

S.V. Sazonov and M.V. Komissarova

JETP Letters 111, issue  6 (2020).

The phenomenon of topological superconductivity and Majorana bound states (MBSs) have attracted much attention of researchers mainly due to the prospects of implementing quantum computing that is stable against decoherence processes. From the standpoint of available technologies one of the most promising systems for detecting the MBSs is semiconductoring wire with strong spin-orbit coupling in contact with a superconductor (hereinafter, superconducting wires). Then, under the influence of an external magnetic field the Majorana modes with zero energy should emerge at the opposite ends of such a hybrid nanostructure [1, 2].

As a result, in the experiment, the MBS should manifest itself as a conductance peak at zero bias voltage. In the 2010s considerable efforts were directed toward the MBS detection in these systems utilizing local tunneling spectroscopy [3,4]. However, it was shown that the MBS may not be the only reason for observing the mentioned resonances [5]. Thus, today the urgent task is to search for alternative ways to probe the MBS, in particular, using the nonlocal nature of this excitation. In this study we propose a method for detecting the MBS nonlocality in a situation where the superconducting wire connects two arms of an interference device. With an asymmetric connection of such a device to the contacts, the asymmetric Fano resonances occur in the conductance. It was found that the width of these resonances is proportional to the overlap of the Majorana wave functions localized at opposite ends of the superconducting wire. Thus, if a true MBS is realized, then these Fano resonances collapse. In the framework of the spinless model it is shown that the discovered effect is associated with an increase in the degree of degeneracy of the structure zero-energy state leading to the appearance of a bound state in continuum.


[1] R. M. Lutchyn, J. D. Sau, and S. Das Sarma, Phys. Rev. Lett. 105, 077001 (2010).

[2] Y. Oreg, G. Refael, and F. von Oppen, Phys. Rev. Lett. 105, 177002 (2010).

[3] V. Mourik, K. Zuo, S. M. Frolov, et al., Science 336, 1003 (2012).

[4] H. Zhang, C.-X. Liu, S. Gazibegovic, et al., Nature 556, 74 (2018).

[5] C.-X. Liu, J. D. Sau, T. D. Stanescu, and S. Das Sarma, Phys. Rev. B 96, 075161 (2017).

S.V.Aksenov and M.Yu.Kagan
JETP Letters 111, issue 5 (2020)



During the last decade, much attention was focused on high energy collisions of particles near black holes. This is due to the effect discovered by Banados, Silk ad West (the BSW effect, after names of its authors) who observed that under certain conditions the energy $E_{c.m.}$ in the center of mass of colliding particles can grow unbounded [1]. This happens if one of two particles is fine-tuned (it is called critical). There are two main scenarios in which such collisions occur. In the first one described in the original paper [1], particles collide near a black hole  horizon of a rotating black hole, the critical particle has a special relation between the energy and angular momentum. There is also direct analogue of the BSW effect if a black hole is non-rotating but electrically charged. Then, a special relation should exist between the energy and electric charge of the critical particle [2]. At first, the BSW effect was found for extremal black holes, later it was shown for nonextremal ones [3].

It was believed that if a black hole is neither rotating nor charged, the BSW effect is impossible. In particular, it was shown that for the Schwarzschild black hole $E_{c.m.}$ $\leq 2\sqrt{5}m$ [4]. Meanwhile, this is true if a particle is free or moves under the action of the electrostatic force caused by interaction with a black hole. However, it is demonstrated in the present work, that a situation changes radically if some force is exerted on a particle in the background of a static neutral black hole. The analogue of the BSW effect exists eve for a simplest case of radial motion. What is especially interesting, this is valid even for the Schwarzschild black hole. I doing so, we do not specify the nature of a force. In a particular case of the Reissner-Nordstrom metric and Columb interaction, the previous results are recovered. But, the results are much more general.

There is also one more interesting point. Traditionally, it was believed that additional interaction of a particle with surroundings act against the BSW effect [5, 6], and one was led to prove that the BSW effect retains its validity even in spite of the presence of the force [7, 8]. However, in the case under discussion, such a presence is not an obstacle but the main ingredient of the effect.

If a black hole is surrounded by external electromagnetic fields, we can suppose that the described mechanism promotes high energy collisions near black holes. The Schwarzschild metric and radial motion give us the simplest exactly solvable example but it is quite probable that qualitatively the similar results hold in a more realistic situation as well.

[1] M. Bañados, J. Silk and S.M. West, Kerr black holes as particle accelerators to arbitrarily high energy, Phys. Rev. Lett. 103 (2009) 111102 [arXiv:0909.0169].
[2] O. Zaslavskii, Acceleration of particles by nonrotating charged black holes. Pis’ma ZhETF 92, 635 (2010) (JETP Letters 92, 571 (2010)), [arXiv:1007.4598].
[3] A.A. Grib and Yu.V. Pavlov, On particles collisions in the vicinity of rotating black holes, Pis’ma v ZhETF 92, 147 (2010) [JETP Letters 92, 125 (2010)].
[4] A. N. Baushev, Dark matter annihilation in the gravitational field of a black hole, Int. J. Mod. Phys. D 18, 1195 (2009), [arXiv:0805.0124].
[5] E. Berti, V. Cardoso, L. Gualtieri, F. Pretorius, U. Sperhake, Comment on "Kerr black holes as particle accelerators to arbitrarily high energy", Phys. Rev.Lett. 103, 239001 (2009), [arXiv:0911.2243].
[6] T. Jacobson, T.P. Sotiriou, Spinning black holes as particle accelerators, Phys. Rev. Lett. 104, 021101 (2010) [arXiv:0911.3363].
[7] I.V. Tanatarov and O. B. Zaslavskii, Bañados-Silk-West e¤ect with nongeodesic particles: Extremal horizons, Phys. Rev. D 88, 064036 (2013) [arXiv:1307.0034].
[8] I.V. Tanatarov, O.B. Zaslavskii, Bañados-Silk-West e¤ect with nongeodesic particles: Nonextremal horizons, Phys. Rev. D 90, 067502 (2014), [arXiv:1407.7463].

JETP Letters 111, issue 5 (2020)

Ion fluxes with group velocities up to 2000 km/s were detected in the plasma sheet boundary layer on high-apogee spacecrafts [1]. These fluxes are formed in the current sheet of the small-scale ion beams – beamlets [2], which are accelerated by the electric field at various distances along the magneto-tail of separated resonant N zones and, then, move along the magnetic field lines towards the auroral region. Experimental test [3] of the theoretically predicted scaling WN ~ NA (where WN is the energy of the Nth resonance and A ~ 1.33) [4] shows that the real scaling of resonance energies varies in a wide range A ∈ [0.61, 1.75]. Model calculations [3] with the addition of an electric field Ez perpendicular to the current sheet are in good agreement with the experimental data.

This paper reports an experimental study of the energy scaling of beamlets (seven resonance zones N=1-7 with resonances R=1-7 were identified) using the data from SC-1 and SC-4 CLUSTER satellites for the event of 05.02.2003. Analysis of the ion beam signatures in the auroral magnetosphere in the range 1-20 kev showed that the energy of beamlets scales differently (0.04 and 0.40 for zones with resonances R=1-4, and 0.83 and 1.14 for zones with R=5-7, according to satellites SC-1 and SC-4, respectively). For zones with R=5-7, the energy scaling of the beamlets can be explained in accord  with the results of the work [3]. The observed parameters A in zones N=1-4 may be related to the fact that the normal component of the magnetic field Bz, which controls the increment of the ion beams energy in the current sheet, has spatial decay lower in the region of these resonant zones than in the region containing zones N=5-7. Therefore, the current sheet is inhomogeneous and is characterized by various conditions of the formation of its parts.

[1] K. Takahashi, and E.W. Hones, J. Geophys. Res. 93, 8558 (1988).

[2] L.M. Zelenyi, E.E. Grigorenko, and A.O. Fedorov, JETP Lett. 80, 663 (2004).

[3] R.A. Kovrazhkin, M.S. Dolgonosov, and J.-A. Sauvaud, JETP Lett. 95, 234 (2012).

[4] L.M. Zelenyi, M.S. Dolgonosov, E.E. Grigorenko, and J.-A. Sauvaud, JETP Lett. 85, 187 (2007).



R. A. Kovrazhkin, A.L. Glazunov, and G.A. Vladimirova
JETP Letters 111, issue 4 (2020)





Since the discovery of unconventional d-wave superconductivity in high-temperature superconductors, physical consequences of d-wave electron pairing have been intensively investigated. One of such physical properties is a four-fold symmetry of the parallel upper critical magnetic field in this quasi-two-dimensional (Q2D) superconductors. From the beginning, it was recognized that the four-fold anisotropy of the parallel upper critical magnetic field disappears in the Ginzburg-Landau (GL) region and has to be calculated as a non-local correction to the GL results. Another approach was calculation of the parallel upper critical magnetic field at low temperatures and even at T=0 using approximate method, which was elaborated for unconventional superconductors with closed electron orbits in an external magnetic field. Note that Q2D conductors in a parallel magnetic field are characterized by open electron orbits, which makes the calculations to be inappropriate. The goal of our article is to suggest an appropriate method to calculate the parallel upper critical magnetic field in a Q2D d-wave superconductor. For this purpose, we explicitly take into account almost cylindrical shape of its Fermi surface (FS) and the existence of open electron orbits in a parallel magnetic field. We use the Green's functions formalism to obtain the Gorkov's gap equation in the field. As an important example, we numerically solve this integral equation to obtain the four-fold anisotropy of the parallel upper critical magnetic field in a d(x^2-y^2}-wave Q2D superconductor with isotropic in-plane FS. In particular, we demonstrate that the so-called supercondcting nuclei at T=0 oscillate in space in contrast to the previous results. We also suggest the gap equation which take both the orbital and paramagnetic spin-splitting mechanisms against superconductivity.

A.G.Lebed and Sepper O.
JETP Letters 111, issue 4 (2020)

In recent years, a number of interesting papers appeared [1,2], where from the analysis of experiments on rather wide range of compounds, it was shown that in the $T$ - linear region of resistivity growth, the scattering rate of electrons (inverse relaxation time) with rather high accuracy is described as  $\Gamma=\frac{1}{\tau}=\alpha \frac{k_BT}{\hbar}$, where  $\alpha\sim 1$ and is weakly dependent on the choice of the material. In connection with these results the notion of the universal (independent of interaction strength) "Planckian'' upper limit of inelastic scattering rate in metals was introduced as $\frac{1}{\tau_P}=\Gamma_P=\frac{k_BT}{\hbar}$ [3]. To explain this "universality'' a number of relatively complicated theoretical models were proposed [4, 5], including some rather exotic, based on the analogies taken from the black hole physics, cosmology and superstring theory (e.g. see Refs. [6-9]). It is shown here that the  "Planckian'' limit for the temperature dependent relaxation rate actually follows from a certain procedure used in Refs. [1, 2] to derive $\frac{1}{\tau}$ from experimental data on resistivity, using the effective electron mass, determined from low - temperature experiments. Thus, the  "experimentally'' observed universal "Planckian'' relaxation rate in metals, independent of interaction strength, is nothing more than a kind of  delusion.

[1] J.A.N. Bruin, H. Sakai, R.S. Perry, A.P. MacKenzie. Science 339, 804 (2013)
      [2] A. Legros, S. Benhabib, W. Tabis, F. Laliberte, M. Dion, M. Lizaire, B. Vignole, D. Vignolles, H, Raffy, Z.Z. Li, P. Auban-Senzier, N. Doiron-Leyraud, P. Fournier, D. Colson, L.Taillefer, C.Proust. Nature Physics 15, 142 (2019)
      [3] J. Zaanen. Nature 430, 512 (2004)
      [4] V.R. Shaginyan, M.Ya. Amusia, A.Z. Msezane, V.A. Stephanovich, G.S. Japaridze, S.A. Artamonov. JETP Letters 110, 290 (2019)
      [5] A.A. Patel, S. Sachdev. Phys. Rev. Lett. 123, 066601 (2019)
      [6] J. Zaanen. Nature 448, 1000 (2007)
      [7] S.A. Hartnoll. Nature Physics 11, 54 (2015)
      [8] C.P. Herzog, P. Kovtun, S. Sachdev, D.T. Son. Phys. Rev. D 75, 085020 (2007)
      [9] S.A. Hartnoll, P.K. Kovtun, M. Muller, S, Sachdev. Phys, Rev. B 76, 144502 (2007)

M.V. Sadovskii

JETP Letters 111, issue 3 (2020)


Discovery of high critical temperatures of superconductivity in sulfur [1, 2], lanthanum, and yttrium hydrides [3-5] led to the active search for stable structures of hydrides of other elements, including iron. Iron hydrides are characterized by a critical temperature of ~50 K and can conditionally be classified as high-temperature superconductors. On the other hand, hydrogen is considered as one of the possible light elements of the Earth’s and planets core, which causes interest in phase relationships for the Fe-H system over a wide range of pressures and temperatures.

In this work, within the density functional theory, the thermodynamic stability of iron hydrides Fe4H, Fe2H, FeH, Fe3H5, FeH2, FeH3, FeH4, Fe3H13, FeH5 and FeH6 at temperatures up to 5000 K in the pressure range of 100-400 GPa was estimated and the corresponding phase PT-diagrams were calculated. We performed a topological analysis of all stable iron hydrides. The regularity of the formation of dumbbell-shaped hydrogen molecules with increasing hydrogen concentration in iron hydrides was established.

 [1] A. Drozdov, M. Eremets, I. Troyan, V. Ksenofontov, S. Shylin, Nature 525, 73 (2015)

 [2] D. Duan, Y. Liu, F. Tian, D. Li, X. Huang, Z. Zhao, H. Yu, B. Liu, W. Tian, T. Cui, Scientific Reports 4, 6968 (2014).

 [3] A. Drozdov, P. Kong, V. Minkov, S. Besedin, M. Kuzovnikov, S. Mozaffari, L. Balicas, F. Balakirev, D. Graf, V. Prakapenka, Nature 569, 528 (2019).

 [4] H. Liu, I. I. Naumov, R. Hoffmann, N. Ashcroft, R. J. Hemley, Proceedings of The National Academy of Sciences 114, 6990 (2017).

 [5] M. Somayazulu, M. Ahart, A. K. Mishra, Z. M. Geballe, M. Baldini, Y. Meng, V. V. Struzhkin, R. J. Hemley, Physical Review Letters 122, 027001 (2019).

D.N. Sagatova et al.

JETP Letters 111, issue 3 (2020)


The search of a quark-gluon plasma (QGP), where hadrons dissolve and quarks are supposed to be free and deconfined, is difficult due to the short QGP lifetime. Various signals were proposed for detection of the QGP phase, and the ''horn'', which appears in the ratio of positive charged kaon to pion, was supposed be one of them [1]. Nowdays the picture of this peak becomes more clear on the experimental side: the peak appears in the ratio of positive charged kaons and pions at the collision energy $\sqrt{s_{NN}}\sim$ 7-10 GeV for the large-size systems in  Au+Au and Pb+Pb collisions. With decreasing system size, the sharp peak becomes lower and for Be+Be,  p+p collisions the ratio demonstrates smooth behaviour [2].
On the theoretical side, the quick increase in the $K^+/\pi^+$ ratio and its decreasing and flattering with further energy increasing is interpreted as a sequence of the chiral symmetry breaking and subsequent deconfinement effect.

In our works [3, 4], including the present one, we discussed the chiral phase transition, deconfinement transition and in-medium behaviour of the pseudo-scalar mesons in the framework of the SU(3) Polyakov loop extended NJL model. Using the model it was shown how $K/\pi$ ratio changes as function of $T/\mu_B$, when T and $\mu_B$ are chosen on the phase diagram along the chiral phase transition curve and discussed in this way how the chiral phase transition can affect to the $K/\pi$ behaviour.   Several modifications of the model was considered, including the model with vector interaction, where the situation with the absence of the first order transition region can appear when the vector coupling constant is high enough. We can conclude that the peak appears in the range of low temperatures and high baryon chemical potential (which corresponds to low collision energy).  The appearance of the peak is weakly sensitive to the type of phase transition in the high density region, as the replacement of the the first order transition to the soft crossover only leads  to a changing in the peak hight. The peak structure is more sensitive to the slope of the phase transition curve at low T and the properties of the matter. For example, the hight of the peak is sensitive to the chemical potential of the strange quark. For the case with the zero strange chemical potential ($\mu_S(\mu_K) = 0$), the $K^+/\pi^+$ ratio shows smooth behaviour, and when the strangeness neutrality is introduced, the $K^+/\pi^+$ ratio does not show a clear peak structure.
1. S. V. Afanasiev et al. (NA49 Collabration), Phys. Rev. C 66, 054902 (2002); C. Alt,et al (NA49 Collaboration) Phys.Rev. C 77, 024903 (2008).
2. A. Aduszkiewicz (NA61/SHINE Collaboration) Nucl. Phys. A 967, 35 (2017).
3. A. V. Friesen, Yu. L. Kalinovsky, V. D. Toneev Phys. Rev. C 99, 045201 (2019).
4. A. V. Friesen, Yu. L. Kalinovsky, V. D. Toneev, PEPAN Letters, 16, 681 (2019).
A. V. Friesen, Yu. L. Kalinovsky, V. D. Toneev
JETP Letters 111, issue 3 (2020)


Monolayer films of transition metal dichalcogenides (TMD) (in particular, MoS$_2$, MoSe$_2$, WS$_2$, and WSe$_2$) can be considered an ideal system for studying a high-temperature electron-hole liquid (EHL). The quasi-two-dimensional nature of electrons and holes defines a stronger interaction compared to bulk semiconductors. Screening of the Coulomb interaction in monolayer heterostructures is significantly weakened, because it is determined by permittivity of the environment (e.g., vacuum and substrate), which are much smaller than that of TMD films. The multivalley structure of the charge carriers energy spectrum in TMD many times reduces the kinetic energy. This leads to  increase in the equilibrium density and binding energy of EHL. 

The optical properties of the monomolecular TMD layers are generally determined by excitons and trions. The binding energy of the exciton $E_x$ in the TMD is hundreds of meV. For example, in the monolayers MoS$_2$ $E_x=420$ meV [1].

The binding energy of EHL on one electron-hole pair is $\left|E_\text{EHL}\right|\sim E_x$, and the critical temperature for the gas--liquid phase transition is $T_c\sim0.1\left|E_\text {EHL}\right|$ [2--4]. So, we can expect that EHL will be observed in TMD monolayers even at room temperature. A high-temperature strongly bound EHL with $T_c\simeq500$ K was already observed in the MoS$_2$ monolayers [5].

In this paper, we are theoretically investigating the possibility of the formation of EHL in monolayers of multi-valley semiconductors. We consider a thin film of a model multi-valley semiconductor on an insulator substrate in vacuum. The semiconductor has a large identical number of equivalent electron $\nu_e$ and hole $\nu_h$ valleys $\nu_e=\nu_h=\nu\gg1$. A large number of valleys can be achieved due to the presence of several monomolecular layers in the film. We found analytically the binding energy of EHL and its equilibrium density and compared the results of calculations with experimental values.

[1] Y. Yu, Y. Yu, Y. Cai, W. Li, A. Gurarslan, H. Peelaers, D.E. Aspnes, C.G. Van de Walle, N.\,V. Nguyen, Y.-W. Zhang, and L. Cao, Sci. Rep.5, 16996 (2015).

[2] E.A. Andryushin, V.S. Babichenko, L.V. Keldysh, T.A. Onishchenko, and A.P. Silin, JETP Lett. 24, 185 (1976).

[3] E.A. Andryushin, L.V. Keldysh, and A.P. Silin, JETP 46, 616 (1977).

[4] Electron-Hole Droplets in Semiconductors ed. C.D. Jeffries and L.V. Keldysh (Amsterdam: North-Hollalnd, 1983).

[5] Y. Yu, A.W. Bataller, R. Younts, Y. Yu, G. Li, A.A. Puretzky, D.B. Geohegan, K. Gundogdu, and L.Cao,  ACS Nano 13, 10351 (2019).

P.L. Pekh, P.V. Ratnikov, and A.P. Silin

JETP Letters111, issue 2 (2020)



Ten years after recognition of the Nobel Prize, the chirped pulse amplification technique, was first implemented [1] and the unique regime of long-range femtosecond pulse propagation was discovered [2]. This propagation regime without beam divergence, or filamentation, was studied  with  Ti:Sapphire laser systems centered at ~800 nm with pulse peak power of 1010–1013 W [3]. Ultrashort pulse filamentation is accompanied by supercontinuum conical emission [4]. The atmospheric transparency window [5] in the visible range ensures lossless propagation of supercontinuum blue wing in the course of backward propagation after reflection from the cloud [6]. However, the fingerprints of atmospheric molecular pollutants are in the mid- and far-infrared range [5]. Besides, the critical power for self-focusing is proportional to the squared wavelength and achieves several hundreds of gigawatts for mid-infrared pulse propagating in air. This requires the pulse energy of at least several tens of milliJoules (pulse duration of about 100 fs) to form a filament on an atmospheric path. In order to target the application of femtosecond lidar in the mid-infrared part of the spectrum, we suggested the generalized approach for identification of the optimum laser wavelength for supercontinuum remote sensing applications [7,8]. We also developed the gas cell [9] for pressures 10–3–120 bar and temperatures up to 150°C to reach the filamentation with sub-milliJoule pulses. Our long cell of 75-cm length provides the filamentation in high-pressure gas in the quasi-collimated geometry close to atmospheric path experiments. The gas dispersion in the cell can be continuously tuned from normal to anomalous in the vicinity of water absorption band at 1.35 mm. The reservoir with water is installed into the gas cell and is additionally heated. In our experiments the cell was filled with nitrogen (30 bar) and water vapor (200 Pa). The laser pulses of ~100-mJ energy and 1.3-mm central wavelength propagate in the cell. The nonlinearly enhanced linear absorption was revealed in the long-wavelength part of the supercontinuum spectrum; this observation confirmed the theoretical prediction [7] of launching the pulse on the red (long-wavelength) side of the absorption line to ensure the maximum transmission through gases.


[1] D. Strickland and G. Mourou, Opt. Commun. 55, 447 (1985).

[2] A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, Opt. Lett. 20, 73 (1995).

[3] S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, Can. J. Phys. 83, 863 (2005).

[4] O. G. Kosareva, V. P. Kandidov, A. Brodeur, C. Y.Chien, and S. L. Chin, Optics letters 22, 1332 (1997).

[5] L. Rothman et al., J. Quantum Spectrosc. Radiat. Transfer 130, 4 (2013), HITRAN2012 special issue.

[6] J. Kasparian et al., Science 301, 61 (2003).

[7] N. A. Panov, D. E. Shipilo, V. A. Andreeva, O. G. Kosareva, A. M. Saletsky, H. Xu, and P. Polynkin Phys. Rev. A 94, 041801 (2016).

[8] N. A. Panov, D. E. Shipilo, A. M. Saletsky, W. Liu, P. G. Polynkin, and O. G. Kosareva Phys. Rev. A 100, 023832 (2019).

[9] V. O. Kompanets, D. E. Shipilo, I. A. Nikolaeva, N. A. Panov, O. G. Kosareva, S. V. Chekalin “Nonlinear enhancement of resonant absorption under filamentation of mid-infrared laser pulse in high-pressure gas” JETP Lett. accepted for publication, December 2019.

V. O. Kompanets, D. E. Shipilo, I. A. Nikolaeva, N. A. Panov, O. G. Kosareva, S. V. Chekalin

JETP Letters 111, issue 1 (2020)



  Quasiparticles with the Dirac spectrum arise in a number of materials. Well-known examples are graphene, topological insulators, Dirac semimetals. More recently, it has been found that there are also materials in which the vertices of the Dirac cone are not at one or more points of the Brillouin zone, but form a line [1]. A feature of nodal-line Dirac semimetals is the much higher density of Dirac states than in materials with Dirac points, which allows us to hope for a more vivid manifestation of the properties due to Dirac fermions.
  ARPES study supported by first-principle calculations show that InBi is a Dirac semimetal in which the vertices of the Dirac cone form the lines in the momentum space along the directions MA and XR of the Brillouin zone, i.e. in the directions along the c axis [2]. Earlier studies of magnetoresistance in InBi indicate the presence of an extremely large positive transverse quadratic magnetoresistance, which exceeds 2 orders of magnitude and does not saturate in high magnetic fields [3]. The absence of saturation and its anomalously high value are associated with the equality of the concentrations of electrons and holes whose mobility at helium temperatures exceeds 104 cm2/V·s [3].   
  In this work, we present the results of high precision measurements of the transverse magnetoresistance in InBi. These enable us to distinguish features which were not observed previously. In particular, we found that the dependence of the resistance R on  magnetic field B does not follow the simple quadratic law  R(B) = R0 + bB2. Namely, at B < 0.1 T, it is characterized by high curvature,  at B > 1 T it approaches a quadratic law with a curvature several times smaller, and in the intermediate region it is described by the sum of linear and quadratic contributions. The observed deviation from the quadratic dependence corresponds to a linear contribution, which is expected for nodal-line Dirac semimetals [4]. We also proposed a simple formula

                                                           R(B) = R0+R1(1+η2B2)1/2+bB2,            
describing all the detected features of the magnetoresistance of the nodal-line Dirac semimetal InBi within the experimental accuracy of a few percent.


[1] A. A. Burkov, M. D. Hook, and L. Balents, Phys. Rev. B 84, 235126 (2011).
       [2] S.A. Ekahana, Sh.-Ch. Wu, J. Jiang, K. Okawa, D. Prabhakaran, Ch.-C. Hwang, S.-K. Mo, T. Sasagawa, C. Felser, B. Yan, Zh. Liu and Yu. Chen, New J. Phys. 19, 065007 (2017).
       [3] K. Okawa, M. Kanou, H. Namiki, and T. Sasagawa Phys. Rev. Materials 2, 124201 (2018).
       [4] H. Yang and F. Wang, arXiv:1908.01625.


S.V. Zaitsev-Zotov and I.A. Cohn
JETP Letters 111, issue 1 (2020)

Superfluid 3He is a well-known condensed matter whose properties are described by quantum field theory. Upon transition to superfluid states, gauge and spin and orbital rotational symmetries are violated simultaneously, demonstrating the properties of antiferromagnetic superfluid liquid crystals. In these systems, spin superfluidity was discovered - quantum transfer of spins controlled by the gradient of the magnetization precession phase. Spin supercurrents provide coherence during the magnetization precession: the precession becomes coherent even in a strongly inhomogeneous magnetic field. This leads to a long-lived signal of free induction, which was observed experimentally, see Review [1]. An even more complex interaction between the spin and orbital degrees of freedom leads to the formation of an extremely long live signal, which was explained in terms of the Coleman Q-ball model [2].

For a long time, magnetic resonance in solid-state magnets was considered in the limit of small perturbations, which corresponds to a low concentration of no equilibrium magnons. However, at high concentrations, magnons can experience Bose condensation, as in superfluid 3He. Moreover, in the case of a repulsive interaction, magnons can form a superfluid state and exhibit spin superfluidity properties in a solid magnets [3]. In particular, manifestations of a superfluid spin state in yttrium iron garnet (YIG) at room temperature have recently been discovered [4].

This article presents the results of observations of a very long-lived induction decay signal obtained in a YIG at room temperature. Its properties are partially similar to the Q-ball observed in superfluid 3He. Nevertheless, there are some fundamental differences with the Q-ball, which require the correct theoretical explanation. The formation of this long-lived signal can be a manifestation of quantum field theory at room temperature.

 [1]. Yu. M. Bunkov, G. E. Volovik  “Spin superfluidity and magnon BEC”

Chapter IV of the book "Novel Superfluids", eds. K. H. Bennemann and J. B. Ketterson, Oxford University press, (2013) .

[2].  S. Autti, Yu. M. Bunkov, V. B. Eltsov,   et al. “Self-trapping of magnon Bose-Einstein condensates in the ground and excited levels: from harmonic  to a box confinement” 

Phys. Rev. Lett. 108, 145303 (2012).

[3]. Yu. M. Bunkov,  E. M. Alakshin,2 R. R. Gazizulin, et al., “High-Tc Spin Superfluidity in Antiferromagnets” Phys. Rev. Lett. 108, 177002 (2012).

[4]. Yu. M. Bunkov, A.Farhutdinov A. N. Kuzmichev, et al., “The magnonic superfluid droplet at room temperature”  https://arxiv.org/pdf/1911.03708.pdf



Yu.M.Bunkov, P.M.Vetoshko, A.N.Kuzmichev, G.V.Mamin. S.B.Orlinsky, T.R.Safin, V.I.Belotelov, M.S.Tagirov.  

JETP Letters 111, issue 1 (2020)



In recent years, a rapidly developing field of science and technology - spintronics - has attracted much attention. New principles for the operation of devices have been proposed, in which the electronic spin is used along with its charge to transmit and process information. The main tasks of semiconductor spintronics are the investigations of the carrier spins injection, orientation, accumulation and detection processes and the study of the possibilities of controlling them by optical and electrical methods. Diluted magnetic semiconductors and nanostructures based on II – VI materials with manganese ions are considered as model objects for possible applications in spintronics. In such structures, magnetic Mn2+ ions isoelectronically replace metal ions in cationic sublattices.

The low-temperature spectra of magneto-optical photoluminescence provide quantitative information on the temperature and magnetization of the Mn ions subsystem. Indeed, the exciton luminescence line shift in external magnetic fields is directly proportional to the magnetization, which makes it possible to experimentally implement the internal thermometer of the magnetic ions spin temperature, since temperature increase leads to a decrease in the Zeeman shift of the emission band. Measurements of the low-temperature exciton luminescence spectra with time resolution in external magnetic fields also allow one to study the dynamics of changes in the spin subsystem magnetization and temperature of diluted magnetic semiconductor structures when non-equilibrium magnetization is created in them, for example, using high-power pulsed optical pumping [1].

To determine the real interaction time of carriers with magnetic ions, it is very important to study diluted magnetic semiconductor superlattices with type II band alignment. In such structures based on (Zn,Mn)Se/(Be,Mn)Te the type II band alignment makes it possible to experimentally change the interaction time of photoexcited carriers with magnetic ions. At high levels of optical excitation inside ZnSe/BeTe superlattices, due to the high concentration of spatially separated charges of electrons and holes, strong electric fields arise, which in turn lead to strong band bending [2]. Strong band bending leads to the formation of metastable above-barrier hole states [3], which increases the hole lifetimes in the ZnSe layer.

In the present paper the magnetization kinetics in diluted magnetic semiconductor type II superlattices Zn0.99Mn0.01Se/Be0.93Mn0.07Te in external magnetic fields was studied using an optical technique with a high temporal resolution ~ 2 ps. For the first time, direct measurements of the picosecond kinetics of the process of energy and spin transfer from photoexcited carriers due to the exchange interaction with the localized spins of Mn2+ ions were performed and the energy and spin transfer time τ ≈ 17 ± 2 ps was determined.

[1] M.K. Kneip, D.R. Yakovlev, M. Bayer, A.A. Maksimov, I.I. Tartakovskii, D. Keller, W. Ossau, L.W. Molenkamp, and A. Waag, Phys. Rev. B 73, 035306 (2006).

[2] S.V. Zaitsev, V.D. Kulakovskii, A.A. Maksimov, D.A. Pronin, I.I. Tartakovskii, N.A. Gippius, M.Th. Litz, F. Fisher, A. Waag, D. R. Yakovlev, W. Ossau, and G. Landwehr, JETP Lett. 66, No. 5376-381 (1997).

[3] A.A. Maksimov, S.V. Zaitsev, E.V. Filatov, A.V. Larionov, I.I. Tartakovskii, D.R. Yakovlev, and A. Waag, JETP Lett. 88, No. 8, 511–514 (2008).

A.A. Maksimov, E.V. Filatov, I.I. Tartakovskii, D.R. Yakovlev, A. Waag

JETP Letters 110, issue 12 (2019)


Observation of the polar Kerr effect in $\mathrm{Sr_2RuO_4}$ [1], a layered material considered to realize the chiral $p_x+ip_y$ superconducting state, has lead to extensive theoretical investigations of the anomalous Hall response $\sigma_{xy}(\omega)$ in $p_x+ip_y$ superconductors. These studies consider either multi-band superconductor models or effects of potential disorder caused by weak impurities.

This work generalizes existing theories of disorder-induced Hall response [2-5] to the case of strong impurities. We consider a low concentration of strong short-range potential impurities characterized by a scattering phase $\delta$. We show that such impurities in the $p$-wave superconductor lead to sub-gap bound states at energy $\Delta\cos\delta$ similar to Yu-Shiba-Rusinov states hosted by magnetic impurities in $s$-wave superconductors. These states form an impurity band which also governs the Hall response. We calculate $\sigma_{xy}(\omega)$ as function of temperature and frequency. It exhibits rich behaviour and sharp threshold features at frequencies $\omega=\Delta\pm\Delta\cos\delta$ which we identify with particular transition processes between the condensate, the impurity band and the continuous spectrum of the $p_x+ip_y$ superconductor.

[1] J. Xia, Y. Maeno, P. T. Beyersdorf, M. M. Fejer, and A. Kapitulnik, Phys. Rev. Lett. 97, 167002 (2006).

       [2] J.Goryo, Phys. Rev. B 78, 060501(R) (2008).

       [3] R. M. Lutchyn, P. Nagornykh, V. M.Yakovenko, Phys. Rev. B 80, 104508 (2009).

       [4] S. Li, A. V. Andreev, and B. Z.Spivak, Phys. Rev.B 92, 100506 (2015).

       [5] E. J. König, A. Levchenko, Phys. Rev. Lett.118, 027001 (2017).

Ioselevich P.A., Ostrovsky P.M.

JETP Letters 110, issue 12 (2019)


Most materials found in nature exhibit negligible nonlinear optical behaviors. To observe them, it is necessary to increase the interaction length  (for example, using optical fibers) and/or to amplify the pump intensity with high-powered pulse lasers. It means that the third-order nonlinear optical processes, for example, stimulated Raman scattering (SRS), optical Kerr effect, to name a few, do not appear within highly confined media or from single molecules exposed to continuous-wave low-powered laser light. Nonlinear enhancement of light becomes possible due to giant local electric fields and/or changes in higher-order nonlinear susceptibility. The nonlinear optical effects were found to occur in plasmonic and/or epsilon-near-zero (ENZ) materials [1-4]. In paper [5], the authors, for the first time, have succeeded to synthesize a metal-dielectric nanocomposite exhibiting the 2-ENZ behavior in the visible and near-infrared region. In such a medium, multiple plasmon resonances at different wavelengths are available.

In this paper, we study SRS effects using a percolated 50 nm titanium oxynitride (TiON) thin film that exhibits the 2-ENZ behavior in the visible and near-infrared region. This film was fabricated using dc reactive magnetron sputtering in an argon-nitrogen environment at elevated temperature and post-oxidation in air. In order to enhance the SRS effect we have patterned the TiON thin film by making square-shaped planar nanoantennas with focused ion beam milling. Using tip-enhanced Raman scattering, we have proved that this nanocomposite film can be represented as the mixture of metallic TiN and dielectric TiO2 nanoparticles. The underlying mechanism to observe the SRS is linked to the enhanced effective third-order susceptibility due to plasmon resonances at the ENZ wavelengths. Earlier, we have experimentally demonstrated a far-field Raman color superlensing effect by showing a sub-wavelength resolution of l/6NA (l  is the excitation wavelength, NA - numerical aperture) at different SRS overtones using multi-walled carbon nanotubes of 40 nm in diameter directly dispersed on the TiON thin film [6]. This allows one to use this material for developing a multi-resonant meta-lens pushing a spatial resolution beyond the diffraction limit without post-recovery. The meta-lens serves as a SERS substrate that not only enhances a scattered light but provides the sub-wavelength resolution. The metal-dielectric 2-ENZ nanocomposite film can be used as a broadband perfect absorber for thermophotovoltaic cells.     

[1] Reshef O., De Leon I., Alam M. Z., Boyd R. W. Nat. Rev. Mater. 4, 535 (2019).

[2] Caspani, Kaipurath R. P. M., Clerici M.,et al.,  PRL 116, 233901 (2016)

[3] Kharintsev S.S., Kharitonov A.V., Saikin S.K., Alekseev A.M., Kazarian S. G.  Nano Lett. 17, 5533 (2017).

[4] Kharintsev S.S., Kharitonov A.V., Alekseev A.M., Kazarian S. G. Nanoscale 11, 7710 (2019).

[5] Braic L., Vasilantonakis N., Mihai A.,et al., ACS Appl. Mater. Interfaces 9, 29857 (2017).

[6] Kharintsev S.S.  Opt. Lett. 44 (24), 5909-5912 (2019).


Tyugaev M.D., Kharitinov A.V., Gazizov A.R., Fishman A.I., Salakhov M.Kh., Dedkova A.A., Alekseev A.M., Shelaev A.V., Kharintsev S.S.

JETP Letters 110, issue 12 (2019)


In 1982 Nieh and Yan introduced the quantum gravitational anomaly caused by the gravitational torsion field [1, 2]. Since that time the torsional anomaly has been debated, because the coefficient in the Nieh-Yan anomaly term contains the ultraviolet energy cut-off, which is not well defined.

In this paper we discuss the temperature correction to the Nieh-Yan anomaly. As distinct from the zero temperature term, the $T^2$ temperature correction  does not depend on the ultraviolet cut-off and thus can be universal. Such $T^2$ Nieh-Yan term may exist not only in the relativistic quantum field theories, but also in condensed matter with Weyl fermions. In the topological  Weyl semimetals and in the chiral $p+ip$ superfluids and superconductors, this term is fully determined by the quasirelativistic physics in the vicinity of the Weyl nodes.

[1] H. T. Nieh and M. L. Yan, J. Math. Phys. 23, 373  (1982).

[2] H. T. Nieh and M. L. Yan, Ann. Phys.138, 237 (1982).

Nissinen J., Volovik G.E.

JETP Letters 110, issue 12 (2019)

Nematic aerogels consist of nearly parallel strands. In liquid 3He in such aerogels, the strands lead to anisotropy of 3He quasiparticles scattering that makes favorable new superfluid phases: polar, polar-distorted A (PdA) and polar-distorted B  [1]. A distinctive feature of this work is that experiments were performed with 3He in two samples of nematic aerogel one of which was squeezed by 30% in the direction transverse to the strands. The squeezing leads to anisotropy in a plane perpendicular to the strands that can affect superfluid phases. It was found that the superfluid transition of 3He in both samples occurred into the non-chiral polar phase, where no qualitative difference between properties of nuclear magnetic resonance in 3He in these samples was found. The difference, however, has appeared on further cooling, after a transition to the chiral PdA phase. The results agree with theoretical expectations and provide an additional proof of existence of the polar phase of 3He in nematic aerogels. The obtained quantitative characteristics of the observed phases also agree with recent theoretical paper [2] where it was stated that Anderson theorem for s-wave superconductors is applicable to superfluid 3He in ideal nematic aerogel.


[1] V.V. Dmitriev, A.A. Senin, A.A. Soldatov, and A.N. Yudin, Phys. Rev. Lett. 115, 165304 (2015).

[2] I.A. Fomin, JETP 127, 933 (2018).

V.V. Dmitriev, M.S. Kutuzov, A.A. Soldatov, A.N. Yudin

JETP Letters 110, issue 11 (2019)


After the discovery of graphene with its unique mechanical and electronic characteristics, a  number of other quasi-two-dimensional carbon structures were theoretically predicted, including octagraphene [1], pentagraphene [2], ψ-graphene [3], Stone-Wales (SW) graphene [4], as well as their various hydrogenated versions (graphane [5], pentagraphane [6], ψ-graphane [7] etc.). In this paper, SW graphane - a new allotropic modification of graphane is proposed. This quasi-two-dimensional structure is formed upon complete two-side hydrogenation of SW graphene. SW graphene is more thermodynamically stable than most other allotropic modification of carbon. This justifies possibility of the SW graphane formation.

Unlike graphane, SW graphane is an anisotropic and soft material. Depending on the direction, its Young's modulus is 194 - 221 N/m, whereas in isotropic graphane it  is 249 N/m. The density of phonon states in SW graphane differs from that in graphane. There are no sharp peaks in the density of phonon states of SW graphane, which are typical for graphane. The densities of electronic states in SW graphane and pristine graphane slightly differ from each other. As well, as for graphane, the main channel of thermal decomposition of SW graphane is the separation of atomic hydrogen. The desorption energies of hydrogen atoms for graphane and SW graphane are also very close.

1. X.-L. Sheng, H.-J. Cui, et al., J. Appl. Phys. 112, 074315 (2012).

2. S. Zhang, J. Zhou, et al., Proc. Natl. Acad. Sci. U.S.A. 112, 2372 (2015).

3. X. Li, Q. Wang, P. Jena, The J. of Phys. Chem. Lett. 8, 3234 (2017).

4. H. Yin, X. Shi, et al., Phys. Rev. B 99, 041405 (2019).

5. J. O. Sofo, A. S. Chaudhari, and G. D. Barber, Phys.Rev. B 75, 153401 (2007).

6. H. Einollahzadeh, et al., Sci. Technol. Adv. Mater. 17, 610 (2017).

7. X. Huang, M. Ma, L. Cheng, and L. Liu Physica E 115, 113701(2020).


Podlivaev A.I.

 JETP Letters 110, issue 10 (2019)



At present the interest to Coulomb impurity centers in semiconductors, particularly in silicon and germanium, is revived due to their natural zero-dimensional origin . The specific properties of such centers and advancement in modern technology allow one to create, a qubit with optically controlled coherent states [1], or a source of the THz coherent radiation which utilizes the conventional laser scheme or stimulated Raman scattering [2]. Such applications require accurate knowledge of optical excitation and relaxation processes within an impurity center.

In weakly and moderately doped semiconductors, the lifetime of excited states for a shallow impurity center is controlled by phonon-assisted relaxation. Recently [3], the relaxation times for arsenic donor states in bulk germanium have been calculated; these values are encouraging and suggest that the population inversion and THz lasing can be realized under optical pumping.

The present work is devoted to studying the low-temperature relaxation of the excited states of As donors in Ge crystal using a pump-probe technique. We show that the lifetime of lower odd parity 2p states are close to one ns. At the same time, experimental study of the inverse relaxation rate for the first excited state 1s(T2) yields value not longer than 160 ps. The data obtained are compared with the results of theoretical calculations [3] and confirm the possibility to reach THz amplification on the 2p – 1s(T2) transitions of optically excited As donors in Ge.


  1. K.J. Morse, R. J. S. Abraham, A.D. Abreu et al., Sci. Adv. 3, e1700930, (2017).
  2. S. G. Pavlov, R. Kh. Zhukavin, V. N. Shastin et al., Phys. Stat. Sol. (b) 250, 9 (2013).
  3. V.V. Tsyplenkov, V.N. Shastin, Semiconductors, 52, 1573 (2018).



Zhukavin R. Kh., Kovalevskii K.A., Choporova Yu. Yu. et al. (Collaboration)

JETP Letters 110, issue 10 (2019)


Electron spin resonance (ESR) is one of the most fruitful approaches for the exploration of spin physics in a great deal of different materials including two-dimensional electron systems (2DES) confined in semiconductor heterostructures [1]. The conventional technique for the observation of spin resonance in a 2DES relies on the high sensitivity of a 2D electron channel resistance to the absorption of microwave radiation in the regime of integer quantum Hall effect. In the presented manuscript we propose the complementary experimental approach for the ESR detection as a sharp peak in the microwave induced photovoltage measured between the ohmic contacts to the 2DES. In the presented manuscript we have demonstrated that the suggested experimental approach works well in different semiconductor heterostructures and in various contact geometries.

Detection of ESR in such a way requires no current flow through the sample, thereby protecting 2DES from potential overheating, and from resulting negative impact on  subtle physical phenomena like high-order fractional quantum Hall effect [3]. Furthermore, the flow of nonequilibrium charge carriers that is responsible for the generated voltage is at least partly spin polarized, as spin dephasing time in the quantum Hall regime [4] exceeds the transport scattering time.

[1] M. Dobers, K. v. Klitzing, and G. Weimann, Phys. Rev. B 38, 5453 (1988).

[2] D. Stein, K.v. Klitzing and G. Weimann, Phys. Rev. Lett. 51, 130 (1983).

[3] R. Willett, J. P. Eisenstein, H. L. Stoermer, D. C. Tsui, A. C. Gossard, and J. H. English Phys. Rev. Lett. 59, 1776 (1987)

[4] A. V. Shchepetilnikov, Y. A. Nefyodov, and I. V. Kukushkin, JETP Lett. 97, 574 (2013).




  Periodic driving transforms the stationary energy spectrum into the Floquet modes spectrum (quasienergies). This can be associated with the so-called synthetic dimension introduced by the Floquet modes [1, 2]. Perturbation frequency in this case becomes an additional degree of freedom, which opens new ways of manipulating the quantum systems spectrum. In this context, periodic driving can introduce phenomena, which are typical for higher dimensional systems, in lower dimensional samples.

  In a finite system, periodic driving can effectively change its topology (connectivity of tunneling paths). In present letter, we study interference features in the high-frequency conductance of a two-state model system within the Keldysh formalism for non-equilibrium Green functions in tight-binding basis. We provide a clear and illustrative correspondence between high-frequency response and stationary transmittance of spatially symmetric configurations of the model system considered. In particular, we show that the synthetic frequency dimension provides the possibility for effective degeneracy of eigenstates in a simply connected linear quantum conductor, which is impossible in statics. It turns to be the dynamical counterpart of the situation considered in [3] for stationary tunneling. In dynamical transport, this phenomenon manifests itself by the destructive quantum interference and resonance coalescence, described by an exceptional point of a generalized transmission coefficient. As a result, for instance, one can observe a dip in the real part of the conductance at resonant frequency.

[1] E. Lustig, S.Weimann, Y. Plotnik et al. Nature 567, 356 (2019).

[2] L.Yuan, Q. Lin, M. Xiao et al. Optica 5 (11), 1396 (2018).

[3] A. A. Gorbatsevich, G.Ya. Krasnikov, and N. M. Shubin. Scientific Reports 8, 15780 (2018).

Gorbatsevich A.A., Shubin N.M.

JETP Letters 110, issue 9  (2019)


 Specific features of the band structure of transition metal dichalcogenides (TMDCs) monolayers — the presence of two valleys, strong spin – orbit interaction — have recently become the subject of a large number of theoretical and experimental studies. Relatively few papers are available on the spatially inhomogeneous problems with  TMDCs – quantum dots and quantum wires (QW).  

 In the present work we consider a QW made of TMDCs monolayer in the form of straight strip. Our analysis is based on the Dirac-type Hamiltonian with the finite gap and with accounting for the spin splitting both conduction and valence bands [1, 2, 3]. We use the boundary condition for the electron wave function proposed in [4] which is a special case of the more general consideration given in [5]. Our main findings are:

 1.  There exists a certain critical value of the strip width L= Lcr that separates two types of the electron spectrum: for L> Lcr there are energy levels (subbands in which energy depends on the momentum along the wire) lying within the band gap of an infinite sample, while at L < Lcr such states are absent.  Note, that in conventional QW for particles with parabolic dispersion law there are no states in the forbidden gap for any value of width.

 2.  The optical absorption of the QWs in question differs essentially from the one in conventional QWs. First of all, for the interband transitions there is no strict selection rule  Dn=0  where  n  is the number of the transversal subbands  in the valence band and the conduction band (cf. with conventional QWs where only interband  transitions at  Dn=0  are allowed). However in our case the transitions with  Dn=0  are still much more intensive than others. Second, depending on the mutual parity of the numbers of size quantization subbands in the valence and conduction bands, optical transitions are characterized by significantly different threshold behavior of the absorption intensity. Namely, for the transitions even – even or odd – odd types the threshold dependence of the absorption is I µ  (w-w0)-1/2  while for even – odd and odd – even cases we obtain  I µ  (w-w0)1/2.


[1]  D.Xiao et al., Phys.Rev.Lett., 108, 196802 (2012).

[2]  A.Kormanyos et al., 2D Materials, 2, 022001 (2015).

[3]  V.V.Enaldiev, Phys.Rev.B, 96, 235429 (2017).

[4]  M.V.Berry and R.J.Mondragon, Proc.R.Soc.Lond., A412, 53 (1987).

[5]  V. A. Volkov and T. N. Pinsker, Sov. Phys. Solid State 23, 1022 (1981).


R.Z.Vitlina, L.I.Magarill, A.V.Chaplik

JETP Letters 110, issue 8  (2019)


The discovery of superconductivity in iron-based pnictides and chalcogenides with a relatively high transition temperature has attracted considerable interest due to the unusual correlations between magnetism and superconductivity in these compounds [1-3]. Several theoretical models of superconductivity based on pair interactions associated with magnetic fluctuations have been proposed [3-7]. Much attention is paid to studying the interaction of superconductivity, nematicity of the electronic structure, and quantum paramagnetism in FeSe and FeSe1-xSx compounds [8,9]. The coexistence of ferromagnetism and superconductivity in FeSe crystals doped with Bi2Se3 was reported recently [10]. 

In the present work, the method of Mössbauer spectroscopy on 57Fe nuclei was used to study magnetic correlations and possible structural and electronic transformations that are expected in the temperature range of nematic and superconducting transitions in single crystals of iron selenide doped with sulfur Fe (Se0.91 ± 0.01S0.09 ± 0.01)1-δ. It was found that at room temperature, FeSe0.91S0.09 samples have a tetragonal β-FeSe structure of the PbO type (space group P4/mmm), which transforms into the orthorhombic phase when the crystal is cooled down to Ts ≈ 80 K. The temperature of the superconducting transition is Тс = 10.1 К.

The temperature dependence of the hyperfine interaction parameters obtained from the Mössbauer spectra revealed a number of anomalies in the temperature range of the superconducting Tc, structural Ts, and nematic T* phase transitions. It was established that iron atoms are in a nonmagnetic state even in the region of helium temperatures, which is explained by the low-spin state of Fe2+ ions (3d6, S = 0). It is shown that this state practically does not change at temperatures of transition to the superconducting state. This means that the low-spin state of iron ions is more likely a structural factor, and is not directly related to superconductivity. Thus, there is no effect of the suppression of magnetism by superconductivity.

The electrical resistance and Mössbauer spectroscopy data show that in the Fe(Se0.91S0.09)1-δ crystal, the temperature of the nematic transition T* is about 200 K and is much higher than the temperature of the structural transition (Ts ≈ 80 K). The Debye temperature, obtained from Mössbauer data for the iron sublattice, is ΘM = 478 K, which turned out to be much higher than in the undoped FeSe1-δ compound (ΘM = 285 K).


[1] Y. Kamihara, T. Watanabe, M. Hirano, and H. Hosono, J. Am. Chem. Soc. 130, (2008) 3296.

[2] X. H. Chen, T. Wu, G. Wu, R. H. Liu, H. Chen, and D. F. Fang, Nature 453, (2008) 761.

[3] M.V Sadovskii. Physics-Uspekhi 59(10), (2016) 947.

[4] Y. Mizuguchi, Y. Hara, K. Deguchi, et al., Supercond. Sci. Technol. 23, (2010) 054013.

[5] J. Paglione and R. L. Greene, Nat. Phys. 6 (2010) 645.

[6] V.A. Gasparov, JETP 111(2), (2010) 313.

[7] A.A. Kordyuk, Low Temp. Phys. 38, (2012) 888.

[8] K.K. Huynh, Y. Tanabe, T. Urata, et al., Phys. Rev. B 90, (2014) 144516.

[9] Q. Wang, Y. Shen, B. Pan, et al., Nature Materials 15 (2016) 159.

[10] Y. Liu, X.Y. Pu, K. Zhao, X.S. Yang, Y. Zhao, Solid State Comm. 281, (2018) 27.


K.V. Frolov, I.S. Lyubutin, D.A. Chareev and M. Abdel-Hafiez

JETP Letters 110, issue 8 (2019)


  The original TKNN invariant [1] responsible for the Hall conductivity has been derived for the uniform magnetic field (constant both as a function of time and space coordinates). The expression for the Hall  conductivity discussed in the present paper  is an extension of the TKNN invariant to the case of varying (in space) magnetic fields. Therefore, its consideration is important and should be interesting for the wide audience. The non - renormalization of the Hall conductivity (given by the original TKNN invariant) by interactions has been discussed earlier [2-6]. But this consideration was limited by the case of constant magnetic fields. Now we present the proof that the QHE conductivity (given by our extension of the TKNN invariant) is robust to the introduction of interactions in the case of varying magnetic field. This result has never been obtained in the past, to the best of our knowledge.
  In addition, the mathematical form of the topological invariant in phase space discussed here is somehow similar to the one of the topological invariant in momentum space composed of the two - point Green function. The latter topological invariant and its variations are used widely (see G.E. Volovik "Universe in a Helium droplet"). Now the Green function is substituted by its Wigner transformation depending on both space coordinates and momentum. The ordinary products are therefore changed to the Moyal (star) product, thus leading to the beautiful mathematical structure.  The resulting expression may be used in the presence of interaction for the calculation of Hall conductivity. One simply has to insert to it the interacting (Wigner transformed) two - point Green function. The Green functions with larger number of legs do not contribute to the Hall conductivity (this also has been proved in the presented paper).
  We would also like to emphasize, that our proof is valid to all orders in the perturbation theory.
[1] D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Phys. Rev. Lett. 49, 405(1982).
[2] Ryogo Kubo, Hiroshi Hasegawa, Natsuki Hashitsume, Journal of the Physical Society of Japan 14(1) (1959) 56-74 DOI: 10.1143/JPSJ.14.56
[3] Q. Niu, D. J. Thouless, and Y. Wu, Phys. Rev. B 31, 3372 (1985).
[4] B. L. Altshuler, D. Khmel'nitzkii, A. I. Larkin and P. A. Lee, Phys.Rev.B 22, 5142 (1980).
[5] B.L. Altshuler and A.G. Aronov, Electron-electron inter-action in disordered systems (A.L.Efros, M. Pollak, Ams-terdam, 1985).
[6] S. Coleman and B. Hill, Phys. Lett. B159 (1985) 184 T. Lee, Phys. Lett. B171 (1986) 247

C.X.Zhang, M.A.Zubkov
JETP Letters 110, issue 7 (2019)

Landau quantization in a two-subband Fermi electronic system placed in an external perpendicular magnetic field B leads not only to the well-known Shubnikov – de Haas (SdH) oscillations, but also to another type of quantum resistance oscillations — the magneto-intersubband oscillations (MISO) [1, 2]. MISO are not suppressed by the temperature broadening of the Fermi distribution function and therefore allow one to study quantum transport under conditions when SdH oscillations cannot be used for these purposes [3, 4]. The present work is devoted to the study of MISO in a one-dimensional (1D) lateral superlattice (LSL), where 1D periodic potential is applied to a two-subband electronic system.

The 1D LSL was created on the basis of a selectively doped GaAs/AlAs heterostructure [5, 6]. The measurements were carried out using Hall bars fabricated by means of optical lithography and wet etching. The 1D LSL of period a = 300 nm was created as an array of metal strips on a planar surface of Hall bars using electron beam lithography and the method of exploding an Au/Ti bilayer metallic film. The potential modulation in the studied LSL arises without applying voltage to the metal strips. One of the reasons for this modulation is elastic mechanical stresses between metal strips and a heterostructure [7].

The measurements were carried out at the temperature T = 4.2 K in magnetic fields B < 2 T. It has been shown that commensurability oscillations (CO) of resistance co-exist with MISO in the studied LSL. It has been found that 1D periodic potential in a two-subband electron system leads not only to COs but also to MISO amplitude modulation, which is caused by periodic modulation of Landau level width in a 1D LSL in external inverse magnetic field. It has been shown that increased intersubband scattering time in a two-subband system under 1D periodic potential modulation is one of the reasons of MISO amplitude damping in a 1D LSL.

[1] V. M. Polyanovskii, Sov. Phys. Semicond. 22, 1408 (1988).

[2] D. R. Leadley, R. Fletcher, R. J. Nicholas, F. Tao, C. T. Foxon, and J. J. Harris,

Phys. Rev. B 46, 12439 (1992).

[3] A. A. Bykov, A. V. Goran, and S. A. Vitkalov, Phys. Rev. B 81, 155322 (2010).

[4] O. E. Raichev, Phys. Rev. B 81, 195301 (2010).

[5] K.-J. Friedland, R. Hey, H. Kostial, R. Klann, and K. Ploog, Phys. Rev. Lett. 77, 4616 (1996).

[6] D. V. Dmitriev, I. S. Strygin, A. A. Bykov, S. Dietrich, and S. A. Vitkalov, JETP Lett. 95, 420 (2012).

[7] Ivan A. Larkin, John H. Davies, Andrew R. Long, and Ramon Cuscó, Phys. Rev. B 56, 15242 (1997).


A.A. Bykov, I.S. Strygin, A.V. Goran, D.V. Nomokonov,

I.V. Marchishin, A.K. Bakarov, E.E. Rodyakina, A.V. Latyshev

JETP Letters 110, issue 5 (2019).



It has been shown in [1] that any photoluminescent body in thermal equilibrium obeys the following relation:

$ P(\lambda_1, T) F(\lambda_1, \lambda_2, t) = P(\lambda_2, T) F(\lambda_2, \lambda_1, t) $ (1)

where P(λT) is the Planck function, which describes the spectral density of thermal radiation at wavelength λ and temperature T, and F(λ1λ2t) is the time-resolved excitation-emission matrix, which describes the probability density of emitting a photon with wavelength λ2 at time t as a result of absorption of a photon with wavelength λ1 at time t = 0. For fixed λ1, the function F(λ1λ2t) is the photoluminescence spectrum PL(λλ0t) at time t after a short-pulse excitation at wavelength λ0: PL(λλ0t) = F(λ0λt). For fixed λ2, the function F(λ1λ2t) is the photoluminescence excitation spectrum PLE(λλ0t) detected at wavelength λ0 at time t after a short-pulse excitation at wavelength λ: PLE(λλ0t) = F(λλ0t). Equation (1) rearranged to

$ \frac{ PL(\lambda;\lambda_0, t) }{ PLE(\lambda;\lambda_0, t) } = \frac{ P(\lambda, T) }{ P(\lambda_0, T) } $ (2)

is a new universal photoluminescence law stating that for any luminophore in thermal equilibrium, the ratio of the corresponding time-resolved photoluminescence and photoluminescence-excitation spectra, PL(λλ0t) and PLE(λλ0t), is equal to the ratio of black-body radiation spectra at wavelengths λ and λ0.

For fixed λ1 and λ2, the function F(λ1λ2t) is the kinetics of decay of photoluminescence excited instantaneously at λ1 and detected at λ2. Since the right-hand side of equation (2) does not depend on time, the left-hand side is also time-independent. This means that the photoluminescence decay kinetics is invariant under interchange of the excitation and detection wavelengths up to a time-independent factor.

The aim of the present study is to test the relation (2) experimentally by measuring the photoluminescence decay kinetics with interchanging the excitation and detection wavelengths. This implies that when the forward process is a Stokes photoluminescence, then the reverse process is an anti-Stokes photoluminescence. Colloidal solutions of InP/ZnS quantum-dot nanoclusters, which do not obey the Vavilov law about the independence of the photoluminescent properties of a luminophore of  the excitation wavelength, have been used in the study to test the invariance of the decay kinetics under interchange of the excitation and emission wavelengths.

[1]. S. A. Tovstun, V. F. Razumov, et all. // J. Lumin. 190, 436 (2017).


Razumov V.F., Tovstun S.A., Kuzmin V.A.

JETP letters 110, Issue 5 (2019)




Studies of oscillatory magnetotransport effects are one of the most reliable methods for investigating energy spectrum of 2D carrier systems. A magnetic field normal to the plane of a 2D gas leads to orbital quantization of the spectrum and, as a consequence, to the appearance of oscillations of the magnetoresistance (ρxx) at low temperatures (Shubnikov de Haas oscillations). These oscillations are periodic in the inverse magnetic field and their frequency f is determined by the carrier concentration.

  In systems in which two (or several) branches of the spectrum E1,2 (k) are filled, the oscillations are observed with frequencies f1 and f2, determined by the carrier concentration in its branch. The sum of these oscillations manifests itself as a beating of oscillations of ρxx,, causing nodes and antinodes at certain magnetic fields.

In the presence of transitions between the branches, new oscillations arise with a difference frequency, f1 - f2. They are called magneto-intersubband oscillations (MISO) [1,2]. The simplest qualitative examination shows that the positions of the antinodes in magnetic field must coincide with the ρxx maxima of MISO. Such mutual positions of the antinodes and the MISOs were investigated for the structures based on wide-gap semiconductors with double quantum wells, for wide quantum wells where two branches of the spectrum are formed due to the Coulomb repulsion of electrons, and for structures with two filled subbands of the size quantization.

Along with the cases described above, the two branches of the spectrum for a single quantum well can arise due to the strong spin-orbit (SO) interaction. The large SO splitting can occur for the quantum wells of narrow-gap (InAs, InSb) and gapless (HgTe, HgSe) semiconductors, as well as for many new topological insulators. Such MISO oscillations were considered only theoretically [3, 4], but were never observed experimentally.

This work reports an experimental study of rxx  in  the gated structures with HgTe quantum wells of 8-20 nm widths with an inverted spectrum. It was found that, unlike all other cases and theoretical predictions, the mutual position of the antinodes and MISO is quite opposite. Namely, the positions of the antinodes in a magnetic field coincide with the ρxx minima of MISO. A possible reason for such unusual behavior is discussed.

1. В.М. Поляновский, ФТП, 22, 2230. (1988)

2. D.R Leadly, R. Fletcher and R. J. Nicholas, Phys. Rev.B, 46, 12439- (1992)

3. M. Langenbuch, M. Suhrke and U. Ro^¨ssler, Phys. Rev. B  69, 125303 (2004)

4. S. G. Novokshonov, Low Temperature Physics 39, 378 (2013)

G.M. Minkov, O.E. Rut, A.A. Shestobitov, S.A.Dvoretski, N.N. Mikhailov

JETP Letters 110, issue 4 (2019)




Precisely mapping the phase diagram of strongly-interacting matter is a challenging problem. Lattice simulations of QCD, the field theory of strong interactions, are reliable at zero density, but become less precise when the density is finite and at the moment are not capable to map the whole phase diagram of strong interactions.
The most dramatic phenomenon that happens when strongly interacting matter is heated to extreme temperatures is restoration of chiral symmetry, a key symmetry of QCD that largely determines properties of hadrons and interactions among them. Chiral symmetry restoration is a sharp crossover at zero density that happens at temperature $T_{0}\simeq 157\,{\rm Mev}$ accurately known  from lattice simulations \cite{Bazavov:2018mes}.  Various model estimates predict that at larger baryon densities the crossover becomes sharper and eventually merges into a line of first-order phase transitions at a critical endpoint whose precise location on the $T-\mu $ plane is not entirely known. Model estimates vary by a factor of a few  \cite{Stephanov:2004wx} depending on the model assumptions.
The order parameter of the chiral symmetry breaking is the quark condensate $ \bar{\psi }\psi$, which has a non-zero expectation value in the vacuum. The pseudo-Goldstone modes that arise from the chiral phase of the condensate: $\bar{\psi }\psi \sim \Sigma\,{\rm e}\,^{\gamma ^5 T^{a}\pi _{a}} $ are identified with pions, kaons and the $\eta $-meson, which are substantially lighter than other hadrons. Chiral symmetry restoration is typically associated with melting of the quark condensate, but can also proceed via disordering of the condensate's phase. Strong pion fluctuations, such that $\left\langle \mathop{\mathrm{tr}}\,{\rm e}\,^{iT^{a}\pi _{a}}\right\rangle=0$, will restore chiral symmetry even if condensate's modulus is non-zero.
This paper studied this slightly unconventional scenario of chiral symmetry restoration. Following \cite{Zarembo:2001wr} the shape of the pseudocritical line on the $T-\mu $ plane can then be predicted from the low-energy effective field theory. An interesting consequence of this scenario is an absence of the critical endpoint. The symmetry restoration always proceeds through a crossover which moreover becomes weaker with growing baryon density.
1. A. Bazavov et al., 1812.08235.
2. M. A. Stephanov, Prog. Theor. Phys. Suppl. 153, 139 (2004).
3. K. Zarembo, JETP Lett. 75, 59 (2002).

K. Zarembo

JETP Letters 110, issue 3 (2019).


Recently, a number of quasi-two-dimensional (Q2D) high-temperature and intermediate-temperature superconductors have been discovered. The anisotropic upper magnetic critical fields in some of them can be described by the Lawrence-Doniach model, which is relevant to Q2D superconductors with high anisotropic properties. On the other hand, there are many Q2D superconductors with intermediate anisotropy of the upper critical magnetic fields, which are usually described by the so-called effective masses (EM) model, partially based on the anisotropic Ginzburg-Landau equations. The most popular such Q2D compounds are MgB2 and Fe-based superconductors [1]. It is possible to define anisotropic ratio in Q2D superconductors, g, as the ratio of the parallel and perpendicular upper critical magnetic fields, which is always bigger than 1, g > 1. In accordance with EM model, the ratio g doesn’t have to depend on temperature. Meanwhile recent experiments show strong temperature dependence of anisotropy g, which in the case of superconductor MgB2 increases with decreasing temperature.

   The previous explanations of this phenomenon were based on some approximate many-band calculations of the upper critical magnetic fields and were prescribed to many-band effects. In this Letter, we investigate anisotropy ratio, g, more carefully by using derivation and investigation of an integral equation for the so-called superconducting nucleus, using the Gor’kov equations for non-uniform superconductivity (see, for example, the corresponding derivations for a 3D isotropic case in Ref.[2]) . For the first time, we show that the superconducting nucleus is not of the Gaussian shape for the parallel upper critical magnetic field and even changes its sign with space coordinate. This circumstance breaks down the EM model and predicts a factor of 1.3 increase of the upper critical magnetic fields ratio, g, with decreasing temperature. We prescribe the experimentally observed increase of the parameter g in the superconductor MgB2 [1] to the breakdown of the EM model suggested in the Letter. This issue is an important one since Q2D high-temperature and intermediate-temperature superconductors are good candidates for some scientific and industrial applications in high magnetic fields.

[1] See, for example, review V.G. Kogan and R. Prozorov, Rep. Prog. Phys. 75, 114502 (2012).

[2] L.P. Gor’kov, Sov. Phys. JETP, 37(10), 42 (1960).

                                                                                                                                                       Lebed A.G.

                                                                                                                      JETP Letters 110, issue 3 (2019).


The formation of metallic hydrogen, predicted in [1], was observed experimentally in [2]. It is also assumed that this state of solid hydrogen is a superconductor at room temperature. However, the possibility of practical application of the metallic hydrogen is significantly limited by the pressure of formation of this state. The properties of stability and metastability of metallic hydrogen depend on the structure, which determines the relevance of the theoretical study of this issue. As it was shown in [3 - 6], atomic metallic hydrogen at zero temperature exists in a metastable state up to normal pressure.
In the present work, the quantum molecular dynamics method within the framework of the density functional theory is applied for the calculation of the equation of state, the pair correlation function, and the static electrical conductivity of solid hydrogen in the region of the possible formation of the conducting phase. A hysteresis of the dependence of pressure on density is observed under compression and following expansion in the pressure range from 350 GPa to 625 GPa, corresponding to the region of existence of metastable states of molecular and non-molecular solid hydrogen. Thus, the magnitude of the metastability region is 275 GPa. An estimate of the equilibrium pressure of the transition to the non-molecular state 487.5 GPa was obtained.
During compression, the transition of molecular hydrogen with the C2/c symmetry to a conducting non-molecular state with the C2221 symmetry through an intermediate conducting molecular phase with Cmca-4 symmetry was detected. Under expansion, the transition of the non-molecular structure of C2221 to the molecular Cmca-4 occurs through an intermediate non-molecular state with the P21/c symmetry group. The possibility of the existence of conductive non-molecular crystalline hydrogen with P21/c symmetry under expansion up to a pressure of 350 GPa is shown.

[1] E. Wigner, H. B. Huntington, J. Chem. Phys. 3, 764 (1935).
[2] R. Dias, I. F. Silvera, Science 355, 715 (2017).
[3] Yu. Kagan and E. G. Brovman, Sov. Phys. Usp. 14, 809 (1971).
[4] E. G. Brovman, Yu. Kagan, and A. Kholas, Sov. Phys. JETP 34, 1300 (1972).
[5] E. G. Brovman, Yu. Kagan, and A. Kholas, Sov. Phys. JETP 35, 783 (1972).
[6] Yu. Kagan, V. V. Pushkarev, and A. Kholas, Sov. Phys. JETP 46, 511 (1977).

I.M. Saitov
JETP Letters 110, №3 (2019)

There are a number of physical systems in which, under certain conditions, spatially ordered electronic superstructures are formed. Charge and spin density waves (CDW and SDW), Wigner crystals and vortex lattices in type-II superconductors in a magnetic field are examples of such systems. The interaction of the superstructure with local lattice imperfections (various point defects, impurities, etc.) leads to its  pinning. In the simplest case, such a pinning (let's call it local) is divided into collective (weak) and individual (strong).
In the present work, it is experimentally shown that, in the Peierls conductor {\it o}-TaS$_3$, a new type of CDW pinning appears as a result of samples quenching. It is characterized by a number of fundamental differences from pinning by local pinning centres, namely:
  1.   Pinning by quenching defects is not described by the $\sqrt {E_T} \propto \Delta T_P$ law typical for both weak and strong local pinning centres. Нere $E_T$ is  the threshold field for onset of CDW sliding and $\Delta T_P$ is pinning-induced change of the Peierls transition temperature. 
  2.  In the case of pinning by quenching defects, only a slight smoothing of the Peierls transition occurs even for a large  $\Delta T_P$, whereas in the case of local pinning  with similar changes in $\Delta T_P$, the Peierls transition is almost completely suppressed due to the loss of three-dimensional ordering.
  3.  Pinning provided by quenching defects is unstable and can be eliminated  by thermocycling in the temperature range  $T <T_P$. As a result, it becomes spatially inhomogeneous with a lower concentration of quenching defects at the ends of the crystal.

 The presence of these features allows us to conclude that quenching defects are macroscopic (non-local) objects, for example, dislocations, which can glide along the crystal. They lead to a previously unknown type of CDW pinning with properties different from local pinning ones. The feature of Peierls conductors is strong CDW interaction with defects. As a result of this interaction, forced diffusion of quenching defects and their exit from the crystal takes place during low-temperature thermocycling.



V.E.Minakova, A.M.Nikitina, S.V.Zaitsev-Zotov

                                                                              JETP letters, v. 110, issue1 (2019)


In connection with recent report on the first detection of terahertz (THz) emission due to intra-exciton radiative transitions in semiconductors [1] and a number of theoretical works predicting the possibility to achieve intra-exciton population inversion at intense band-to-band optical excitation of a crystal (see [2] and also [3] and other references therein) it is very important to verify experimentally the possibility of implementing an exciton THz laser.

In this work, we studied the THz photoluminescence (PL) from high-purity silicon due to radiative transitions between the energy levels of free excitons under conditions of continuous-wave interband photoexcitation with a maximum density of up to 120 W/cm2. The appearance of the superlinear dependence of the intensity of the intra-exciton THz emission on the pump intensity at temperatures above 20-25 K was found. The transition from the linear to superlinear dependence of the THz PL intensity on the pump intensity occurs at a photoexcitation density of about 7 W/cm2. The observed regular patterns are explained by the appearance of the THz stimulated emission and, accordingly, population inversion in the system of excitons at their high density. The THz gain spectrum was obtained, which shows the lines at 13.7 and 15.5 meV, the gain values ​​of which are 0.5 and 1 cm-1, respectively, at 25 K and the photoexcitation density of order of 35 W/cm2. The line at 13.7 meV is due to the population inversion between highly excited exciton states and the ground state of free excitons. The gain line at 15.5 meV possibly corresponds to the population inversion between the two-exciton and bi-exciton states. The values ​​of the terahertz gain indicate that a new type of THz laser can be created on transitions between energy levels of free excitons in silicon under conditions of interband photoexcitation.


[1] A.V. Andrainov, and A.O. Zakhar’in – Intrinsic Terahertz Photoluminescence from Semiconductors – Appl. Phys. Lett., 112, 041101 (2018).

[2]  M. Kira, and S.W. Koch -  Exciton-Population Inversion and Terahertz Gain in Semiconductors Excited to Resonance - Phys. Rev. Lett., 93, 076402 (2004).

[3]  G.K. Vlasov, and S.G. Kalenkov – Sources of Coherent Far-Infrared Radiation on Hot Excitons in Crystals - Int. J. Infrared Millimeter Waves, 4, 955 (1983).

Zakhar’in A.O., Andrianov A.V. Petrov A.G.

                                                                              JETP letters, v. 109, issue12 (2019)






Non-linear Hall effect has been predicted in a wide class of time-reversal invariant materials [1], like topological crystalline insulators, two-dimensional transition metal dichalcogenides, and three-dimensional Weyl and Dirac semimetals. Recently,  the time-reversal-invariant non-linear Hall (NLH) effect  has been reported for two-dimensional layered  dichalcogenides [2, 3]. It stimulates a search for the Berry curvature dipole induced NLH effect in  three-dimensional  crystals, where  Dirac and Weyl semimetals are excellent candidates.
In the experiments [2, 3] on two-dimensional WTe$_2$,  the the second-harmonic Hall voltage depends quadratically on the longitudinal current. On the other hand, topological materials are  characterized by strong thermoelectric effects, which also appear as a second-harmonic  quadratic signal.  For this reason, it is important to experimentally distinguish between the Berry curvature dipole induced NLH effect  and a thermoelectric response while searching for the NLH effect in  nonmagnetic materials.
We experimentally investigate a non-linear Hall effect  for three-dimensional  WTe$_2$ and  Cd$_3$As$_2$ single crystals, representing  Weyl and Dirac  semimetals, respectively. We observe finite second-harmonic Hall voltage, which  depends quadratically on the longitudinal current  in zero magnetic field, as it has been predicted theoretically.  We demonstrate that second-harmonic Hall voltage shows odd-type dependence on the direction of the magnetic field, which is a strong argument in favor of current-magnetization effects. In contrast, one order of magnitude higher thermopower signal is independent of the magnetic field direction. Thus, the magnetic field dependence allows to distinguish the non-linear Hall effect from a thermoelectric response.
[1] Sodemann and Liang Fu, Phys. Rev. Lett., 115, 216806 (2015).
[2] Kaifei Kang, Tingxin Li, Egon Sohn, Jie Shan, Kin Fai Mak, arXiv:1809.08744 (2018).
[3] Qiong Ma, et al., arXiv:1809.09279 (2018).


Shvetsov O.O., Esin V.D., Timonina A.V., Kolesnikov N.N., Deviatov E.V. 

JETP Letters 109, issue 11 (2019)


Non-classical squeezed light is one of the most attractive quantum objects. Squeezed light is in the center of scientific interest nowadays due to its unique features, such as entanglement of large number of photons, twin-beam correlations and suppressed variance of one of the field quadratures. Such light is very important for many applications in quantum information, quantum tomography and measurements with noise reduction beyond the standard quantum limit.

It was shown that squeezed light can be presented as superposition of Schmidt modes, which are orthogonal and carry all its non-classical features [1]. For applications it is necessary to be able to control and manipulate the properties and mode content of squeezed light. To solve this task, the scheme based on the sum-frequency generation process seeded by squeezed light was suggested [2-4]. The proposed scheme was able to block a certain temporal mode of non-classical light by converting its photons into the sum-frequency mode with a narrow Gaussian spectral profile.

In this work we develop further the idea of the sum-frequency generation with the squeezed light at the input and give detailed theoretical description of this process in the frame of Schmidt modes. We analyze the transformation of spectral properties of squeezed light and predict new effects. We describe quantum-optical gate which provides wide opportunities for managing the spectral signal of squeezed light and allows to control the Schmidt mode weights. The complete blocking of the signal in a certain Schmidt mode is shown to redistribute the weights of other modes and therefore gives the possibility of engineering the spectral and temporal properties of outgoing signal. In the full conversion regime the quantum-optical gate is demonstrated to transfer all the features of non-classical squeezed vacuum state to the light generated in the sum frequency channel.


[1] P.R. Sharapova, O.V. Tikhonova, S. Lemieux et. al., Phys. Rev. A. 97, 053827 (2018)

[2] A. Eckstein, B. Brecht and C. Silberhorn, Optics Express. 19, 13770 (2011).

[3] B. Brecht, A. Eckstein, A. Christ et al, New J. Phys. 13, 065029 (2011).

[4] V. Ansari, J. Donohue, B. Brecht and C. Silberhorn, Optica 5, 534-550 (2018).


V.V. Sukharnikov, O.V. Tikhonova

JETP Letters 109, issue 9 (2019)





    In 2018, a number of experimental works [1-3] were published, in which it was shown that lanthanum hydrides at high pressures P = 150¸190 GPa are superconductors with very high critical temperatures Tc = 215¸260 K. The detected crystalline phase is considered to have FM-3M symmetry and LaH10 stoichiometry.  However, calculations of the phonon spectrum of this structure show that it is dynamically stable only for pressures of P>210 GPa, which is beyond the pressure range of experimental work.

    This paper presents the results of a search for new structures of lanthanum hydride, which could correspond to the experimental results [1-3] and would be dynamically stable at pressures in the range P = 150¸200 GPa. Based on quantum calculations in the framework of the density functional theory, a new structure of lanthanum hydride La2H24 was predicted for the first time. This structure is dynamically stable up to pressures of the order of 150 GPa. It is a semimetal and has a low symmetry of crystal lattice P-1. An important feature of the structure is the presence of quasi-molecular hydrogen  chains, which leads to the presence of frequencies of about 420 meV in the phonon spectrum, exceeding the maximum oscillation frequency of the metallic hydrogen FDDD phase (ω~360 meV). These properties allow us to expect to achieve a high superconducting critical temperature for lanthanum hydride La2H24.

[1] A. P. Drozdov, V. S. Minkov, S. P. Besedin, P. P. Kong, M. A. Kuzovnikov, D. A. Knyazev, M. I. Eremets – Superconductivity at 215 K in lanthanum hydride at high pressures – arXiv:1808.07039.

[2] M.Somayazulu, M.Ahart, A.Mishra, Z.M. Geballe, M.Baldini, Y.Meng, V.V. Struzhkin, and R.J.Hemley – Evidence for superconductivity above 260 K in lanthanum superhydride at megabar pressures – arXiv:1808.07695.

[3] A. P. Drozdov, P. P. Kong, V. S. Minkov, S. P. Besedin, M. A. Kuzovnikov, S. Mozaffari, L. Balicas, F. Balakirev, D. Graf, V. B. Prakapenka, E. Greenberg, D. A. Knyazev, M. Tkacz, M. I. Eremets.  Superconductivity at 250 K in lanthanum hydride under high pressures – arXiv:1812.01561.


Degtyarenko N.N., Grishakov K.S., Mazur E.A.

JETP Letters 109, issue 6 (2019)


To date, a significant number of indirect observations indicating the existence of a superconducting state up to room temperature in some small regions of highly oriented pyrolytic graphite (HOPG) samples have been reported [1]. The main problem was that the super-conducting regions included only a small amount of carbon material with an unknown structural nature and, consequently, showed poor reproducibility of the superconductivity effect for different samples of HOPG with the same macroscopic dimensions. Significant progress in controlling the effect of superconductivity was obtained by embedding multilayer multilayered graphene flakes into a polystyrene matrix, so that covalent bonds are formed between the multilayered graphene flakes and the polystyrene [2,3]. In those papers, we reported a current–voltage characteristic of Josephson type up to temperatures higher than room temperature. In the present paper, we show that for the resulting magnetic moment of the same composite a  magnetic field dependence typical of superconductors is observed in the same temperature range where previously a Josephson current-voltage characteristic was observed. In the experiment, we used a vibrating magnetometer of the PPMS-9 series (Quantum Design) in the temperature range 2-400 K and with magnetic fields of 0 – ± 10 T. 

            The reason for the emergence of superconductivity in multilayered graphene, as was first discussed in [2,3], may be the formation of covalent bonds with the polystyrene, leading to deformation of the graphene. Such deformation can produce a shift or rotation at different angles, including the magic angle [4], of one layer of graphene relative to another in multilayered graphene flakes embedded in a polystyrene matrix. As a result, within the interface regions between the graphene layers, flat energy zones arise, which can lead to room-temperature superconductivity [5].

[1] P. Esquinazi, N. García, J. Barzola-Quiquia, P. Rödiger, K. Schindler, J.-L. Yao, M. Ziese, Indications for intrinsic superconductivity in highly oriented pyrolytic graph. Phys. Rev. B 78(1–8), 134516 (2008)

[2] A.N. Ionov, Technical Physics Letters 41(7), 651 (2015)

[3] A.N. Ionov, J Low Temp Phys, 185, 515 (2016).

[4] Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, P. Jarillo-Herrero, Nature, 556, 43 (2018).

[5]  G. E. Volovik, JETP Lett. 107, 516 (2018).

A.N.Ionov, M.P.Volkov, M.N.Nikolaeva 

 JETP Letters 109, issue 3  (2019)



In the 2D developed hydrodynamic turbulence at  high Reynolds numbers the formation of the  Kraichnan direct cascade  with a constant enstrophy flux  is due to the appearance of the vorticity quasi - shocks, because of the compressibility of continuously distributed lines of the di-vorticity field ${\bf B}=\mbox{rot}\,\mathbf{\omega}$ [1]. This property follows directly from the frozenness equation for ${\bf B}$,
\begin{equation} \label{Helmholtz}
\frac{\partial {\bf B}}{\partial t} =\mbox{rot}[{\bf v}\times {\bf B}],\,\,\mbox{div}\,{\bf v}=0,
 whence one can see that ${\bf B}$ changes only  by virtue of the velocity component ${\bf v_n}$ normal to the di-vorticity vector. In the general situation, $\mbox{div}\,{\bf v_n}\neq 0$ and
this is the reason for the compressibility of continuously distributed di-vorticity lines and, accordingly, the tendency to breaking, that results in the formation of vorticity quasi-shocks.

In the case of freely decaying turbulence, this process is dominant, leading to a strong anisotropy of the turbulence spectrum due to the presence of jets generated by quasi-shocks [1, 2].  As shown by the numerical experiments, for typical initial conditions the growth of the di-vorticity is 2 – 2.5 orders of magnitude, and the transverse size of the maximal area ${\bf B}$ decreases significantly.
 The key point here for understanding is the compressibility of the di-vorticity field. As is known, breaking in the gas dynamics occurs due to the compressibility of the gas when approaching the breaking point (see, e.g.[3]). Similarly, the formation of the vorticity quasi-shocks happens.

In this paper, we investigate how the maximum value of the di-vorticity varies depending on the thickness of the maximum area in order to find out whether this process can be considered as a fold formation.  As a result of numerical simulation on the grid 16384x16384, we found that between the maximum value of $B_{\max}$ and the thickness of $\ell$, at the stage of exponential growth, there is a power law dependence: $B_{\max}\sim \ell^{-\alpha}$ , where the exponent $\alpha$ is close to $2/3$.  This result indicates that the formation of quasi-shocks can be considered as a process of folding for a divergent  free vector field - the di-vorticity field.

[1] E.A.Kuznetsov, V.Naulin, A.H.Nielsen, and J.J.Rasmussen, Phys. Fluids 19, 105110 (2007).
[2] A.N.Kudryavtsev, E.A.Kuznetsov, E.V.~Sereshchenko, JETP Letters, 96, 699-705 (2013).
[3] S.F. Shandarin, Ya.B. Zeldovich,  Rev. Mod. Phys. 61, 185 (1989).
[4] D.S. Agafontsev, E.A. Kuznetsov and A.A. Mailybaev, Phys. Fluids 30, 095104 (2018).


E.A. Kuznetsov, E.V. Sereshchenko,

JETP Letters 109, issue 4 (2019).

The quantum spin Hall insulator state (QSHI) is a two-dimensional topological phase of matter with insulating 2D bulk state and a pair of spin-polarized gapless helical edge states. These edge states may have spintronic applications, which are made possible by the all-new demonstration of QSHI state at 100 K performed on a WTe2 monolayer [1]. However, device engineering involving monolayer materials is challenging, often because of structural or chemical instabilities.

The realistic candidates for high-temperature QSHI in semiconductor heterostructures with mastered technological process are the three-layer InAs/Ga(In)Sb/InAs quantum wells (QWs) confined between wide-gap AlSb barriers [2]. Depending on their layer thicknesses, these QWs host trivial, QSHI and semimetal states. A major advantage of the three-layer QWs, compared to the widely studied HgTe QWs, is a temperature-insensitive inverted band-gap [3], which under certain condition exceeds the value of 45 meV known for WTe2 monolayers [1].

This work reports experimental study of 2D semimetal state in InAs/GaSb/InAs QWs. Already observed in inverted HgTe QWs [4,5], these topologically non-trivial states are characterized by a non-local overlap between conduction and valence bands. To probe the bulk states of the grown sample, we carried out THz photoluminescence measurements and Landau spectroscopy. By analyzing experimental results, we have demonstrated the existence of a non-radiative recombination channel due to the overlap of the conduction and valence bands.

[1] S. Wu, V. Fatemi, Q. D. Gibson et al. (Collaboration), Science 359, 76 (2018).

[2] S. S. Krishtopenko and F. Teppe, Sci. Adv. 4, eaap7529 (2018).

[3] S. S. Krishtopenko, S. Ruffenach, F. Gonzalez-Posada et al. (Collaboration), Phys. Rev. B 97, 245419 (2018).

[4] Z. D. Kvon, E. B. Olshanetsky, D. A. Kozlov et al. (Collaboration), JETP Lett. 87, 502 (2008).

[5] G. M. Gusev, E. B. Olshanetsky, Z.D. Kvon et al. (Collaboration), Phys. Rev. Lett. 104, 166401 (2010).


S.S.Krishtopenko, S. Ruffenach, F. Gonzalez-Posada et al. (Collaboration)

JETP  Letters 109, issue 2 (2019)     


In connection with recent studies of extremely long-living cyclotron spin-flip excitations [1-3] (CSFE) - actually magneto-excitons in a quantum Hall electron gas, the contribution to light absorption related to such a magneto-excitonic ensemble is discussed. The CSFE relaxation found experimentally in the unpolarized quantum Hall system created in a real GaAs/AlGaAs heterostructure reaches 100 $\mu$s [4] at finite temperature $T\!\simeq\!0.5\,$K,
that seems to be a record value for a delocalized state excited in the conduction band of mesoscopic systems. Such a slow relaxation suggests that ensemble of the weakly interacting excitations, obeying the Bose-Einstein statistics, can experience at sufficiently high concentration a transition to a coherent state - Bose-Einstein condensate,  where all momenta of CSFEs have the same value. In the work a comparative analysis of both incoherent and coherent cases is done.
Role of randomness of the electrostatic field is discussed. In the incoherent phase the distribution of CSFE momenta is determined by a smooth random potential. Due to cool-down processes, diffusion and drift, which are fast compared to the CSFE lifetime, the magnetoexciton gets ``stuck'' in the smooth random electrostatic potential with minimum total energy, i.e. with zero group velocity.
 Appearance of the coherent phase is associated with the interaction of magnetoexcitons. The intensity of optical absorption in the coherent phase under some conditions is found to be an order of magnitude higher than that in the incoherent phase. Conditions for a phase transition from the incoherent state to the coherent one are discussed. The considered problem is related to optical probing of the 2D electron system in the experimental
study of spin-cyclotron excitations in the quantum-Hall system. The obtained results are of interest for future experimental studies of CSFEs in a spin-unpolarized quantum-Hall system.

  1.  C. Kallin and B.I. Halperin, Phys. Rev. B 30, 5655 (1984).
  2.  S. Dickmann and I.V. Kukushkin, Phys. Rev. B 71, 241310(R) (2005).
  3.  S. Dickmann, Phys. Rev. Lett. 110, 166801 (2013).
  4.  L.V. Kulik , A.V. Gorbunov, A.S. Zhuravlev, V.B. Timofeev, S. Dickmann, I.V. Kukushkin, Nature Sci. Rep. 5, 10354 (2015).


S. Dickmann

JETP Letters 109, issue 1 (2019)


A gravitational wave signal, GW170817, from a binary neutron star merger has been recordedby the Advanced LIGO and Advanced Virgo observatories on August 17, 2017 [1]. The deep underwater neutrino telescope Baikal Gigaton Volume Detector (Baikal-GVD) is currently under construction in Lake Baikal [2].In this work we present results of searches for high-energy neutrinos in coincidence with GW170817 by Baikal-GVD. Two different time windowswere used for the search. First, a ±500 s time window around the merger was used to search for neutrinos associated with prompt and extended gamma-ray emission. Second, a 14-day time window following the GW detection, to cover predictions of longer-lived emission processes. Since background events from atmospheric muons and neutrinos can be significantly suppressed by requiring time and space coincidence with the GW signal, relatively weak cuts can be used for neutrino selection. For the search for neutrino events within a ±500 s window around the GW event, 731 events were selected, which comprise >5 hit light sensors at>2 hit strings. After applying cascade reconstruction procedures and dedicated quality cuts, two events were selected. Finally, requiring directional coincidence with GW170817y< 20° no neutrino candidates survived.The absence of neutrino candidates associated with GW170817 in the ±500 s window as well as in 14 day window allows to constrain the fluence of neutrinos from GW170817. Assuming an E-2 spectrum single-flavor differential limits to the spectral fluence in bins of one decade in energy have been derived. In the range from 5 TeV to 10 PeV a 90% CL upper limit is 5.2×(E/GeV)-2 GeV-1cm-2for ±500 s time window search. The corresponding upper limit to the spectral fluencefor 14 day search window is 9.0×(E/GeV)-2 GeV-1cm-2over the same energy range.



  1. B.P. Abbott, R. Abbot, T.D. Abbot et al. (LIGO and VIRGO Collaborations), Phys. Rev. Lett., 119, 161101 (2017).
  2. A.D. Avrorin, A.V. Avrorin, V.M. Aynutdinov et.al. (Baikal Collaboration)  PoS (ICRC2017),1034, (2017)


A.D. Avrorin, A.V. Avrorin, V.M. Aynutdinov et.al. (Baikal Collaboration) 

JETP Letters  108, issue 12 (2018)





Transport phenomena in anisotropic porous media are widely discussed in the literature. We investigate the Knudsen regime diffusion in alumina aerogels~---~high porosity materials composed of long cylindrical strands. The theory and experimental results for nematic aerogel with nearly parallel strands were reported earlier [1].
In the present paper we explore a different type of anisotropic aerogel-like metamaterial, which we call the planar aerogel. Like nematic aerogel, it is a macroscopically uniform system with axial symmetry which consists of strands of diameter $10\,\text{nm}$. The directions of these strands, however, are uniformly distributed in a plane perpendicular to the symmetry axis (rather than parallel to it, as in nematic aerogel). Proposed theory is based on the assumption that elastic collisions with the strands is the most important scattering mechanism. We consider two opposite limits: specular and diffuse scattering (denoted by the subscripts $S$ and $D$). Axially symmetric diffusion tensor has two distinct principal values: $D^{xx}=D^{yy}$ for diffusion in the aerogel plane and $D^{zz}$ along the symmetry axis. From the theory it follows, somewhat surprisingly, that the diffusion anisotropy in the specular scattering model is smaller than that in the diffuse model: $D^{xx}_\text{S}/D^{zz}_\text{S}=1.97$ and $D^{xx}_\text{D}/D^{zz}_\text{D}=2.50$.
In the experiments we used the spin echo technique to investigate the spin diffusion in normal liquid $^3$He confined in the planar aerogel. At very low temperatures $T\sim 1\,\text{mK}$, where the Fermi quasiparticle population is small and the Knudsen regime is achieved, our experimental results are in a good agreement with the theory for the case of the specular scattering.

[1] V.V.Dmitriev, L.A.Melnikovsky, A.A.Senin, A.A.Soldatov, and A.N.Yudin, JETP Lett. 101, 808 (2015).


Dmitriev V.V., Kutuzov M.S., Melnikovsky L.A., Slavov B.D., Soldatov A.A.,Yudin A.N. 
JETP Letters 108, issue 11(2018)

The non - dissipative transport effects have been widely discussed recent years. These effects are to be observed in the non - central heavy ion collisions [1]. They have also been considered for the  Dirac and Weyl semimetals [2] and in $^3$He-A [3].
Among the other effects their family includes  the chiral separation effect (CSE) [4], the chiral vortical effect (CVE) [5], the anomalous quantum Hall effect (AQHE) [2]. All those phenomena have the same origin - the chiral anomaly.
In the present paper we  propose the new non - dissipative transport effect - the chiral torsional effect (CTE). Namely, we will discuss the emergence of  axial  current of thermal quasiparticles in the presence of torsion. It will be shown that this effect is intimately related to the chiral vortical effect [5], i.e. the latter may be considered as the particular case of the CTE. It is well  - known that in conventional general relativity  torsion vanishes identically, it appears only in its various extensions. However, the background (non - dynamical) gravity with torsion emerges in certain condensed matter systems.  For example, elastic deformations in graphene and in Weyl semimetals induce the effective torsion experienced by  the quasiparticles [6]. In $^3$He-A torsion appears dynamically when motion of the superfluid component is non - homogeneous.
[1] W. T. Deng and X. G. Huang, \Vorticity in Heavy-Ion Collisions," Phys. Rev. C 93, no. 6,
064907 (2016) [arXiv:1603.06117 [nucl-th]].
[2] A. A. Zyuzin and A. A. Burkov, \Topological response in Weyl semimetals and the chiral
anomaly," Phys. Rev. B 86 (2012) 115133 [arXiv:1206.1868 [cond-mat.mes-hall]].
[3] G.E. Volovik, The Universe in a Helium Droplet, Clarendon Press, Oxford (2003).
[4] \Anomalous Axion Interactions and Topological Currents in Dense Matter",Max A. Metlitski
and Ariel R. Zhitnitsky,Phys. Rev. D 72 (2005), 045011
[5] A. Vilenkin, Phys. Rev. D 22, 3080 (1980)
[6] G.E.Volovik, M.A.Zubkov, Annals of Physics 340/1 (2014), pp. 352-368, arXiv:1305.4665 [cond-mat.mes-hall].
Z.V.Khaidukov, M.A.Zubkov
JETP Letters 108, issue 10(2018)


Investigation of the superconductivity in novel iron-based superconductors is one of the main trends in modern condensed matter physics [1]. Some of iron chalcogenide superconductors [2] have qualitatively different electronic properties from other iron-based superconductors (e.g. iron pnictides) [3]. Among them, the KxFe2−ySe2 compound and the FeSe monolayer on the SrTiO3 substrate take quite a special place. Early days angular resolved photoemission spectroscopy (ARPES) experiments practically could not resolve hole-like  Fermi surface sheets near the Γ-point of the Brillouin zone in contrast to the iron pnictides and some iron chalcogenides (e.g. bulk FeSe).

       Recently in the work [4]  ARPES observation of a “hidden” hole-like band approaching the Fermi level near the Γ-point for the K0.622Fe1.7Se2 system and thus proposing a hole-like Fermi surface near the Γ-point was reported.

       Inspired by the work [4] we show by LDA+DMFT [6] study that for K0.62Fe1.7Se2 system near the Γ-point there are two hole-like bands crossing the Fermi level and forming the Fermi surface near the Γ-point. Its appearance can justify  spin-fluctuation mechanism of superconductivity in this class of systems [6] with a rather high critical temperature Tc∼30K. Good qualitative and even quantitative agreement of the calculated and ARPES Fermi surfaces is obtained.

1M.V. Sadovskii. Usp. Fiz. Nauk 178, 1243 (2008).

2M.V. Sadovskii. Usp. Fiz. Nauk 186, 1035 (2016).

3M.V. Sadovskii, E.Z. Kuchinskii, I.A. Nekrasov, JMMM 324 3481, (2012).

4M. Sunagawa et al., J. Phys. Soc. Jpn. 85, 073704 (2016).

5K. Held et al. Int. J. Mod. Phys. B 15, 2611 (2001).

6P.J. Hirshfeld, M.M. Korshunov, I.I. Mazin. Rep. Prog. Phys. 74, 124508 (2011).

I.A.Nekrasov, N.S.Pavlov

     JETP Letters  108 , issue 9 (2018)





The discovery of solar and atmospheric neutrino oscillations means that at least two of the three mass neutrino states are non-zero. Certain values ​​of the oscillation parameters together with restrictions on the sum of the light neutrino masses obtained from the Planck space telescope data limit the heaviest mass state (ν1, ν2, ν3) of three known types of neutrinos (νe, νμ, ντ) to 70 meV.

The measured decay width of the Z-boson indicates that the heavier neutrino mass states, if they exist, must be related to the sterile neutrino. The simplest mechanism of mass formation is ensured by the existence of right-handed, sterile neutrino interactions. Such neutrinos can be mixed with three active types of neutrinos. The mixing effect leads to neutrino oscillations, it can manifest itself in the processes of production of active neutrinos and lead to the decay of sterile neutrinos into particles of the Standard Model (SM).

Sterile neutrinos, in one form or another, appear in many extensions of the SM, they are well-motivated candidates for the role of dark matter particles. Although the search for sterile neutrinos has been conducted for many years, convincing results of their existence have not yet been obtained [1].

This paper is devoted to the search for the manifestations of massive neutrinos in the measured electron spectra arising from the decay of nuclei 144Ce – 144Pr. The source of electronic antineutrinos 144Ce – 144Pr is one of the most suitable for studying neutrino oscillations into a sterile state with a mass of about 1 eV. We decided to test the possibility of radiation in these beta transitions of heavy sterile neutrinos with a mass of from 1 keV to 3 MeV. The range of possible studied neutrino masses is determined by the resolution of the spectrometer used [2] and the boundary energy of beta decay of the 144Pr nucleus.

A spectrometer consisting of a Si(Li) full-absorption detector and a transition Si-detector was used for precision measurements of the electron spectrum arising from the beta decays of 144Ce – 144Pr nuclei. The beta spectrum measured during 364 h is analyzed to find the contribution from heavy neutrinos with masses from 10 keV to 1 MeV. For neutrinos with a mass in the range (150–350) keV, new upper limits on the mixing parameter at the level |UeH|2 ≤ 2×10–3 - 5×10−3 for 90% confidence level have been obtained.

The achieved sensitivity to |UeH|2 can be increased several times after precision measurement of the response function when using a 4π-geometry spectrometer, in which the response function for monochromatic electrons practically coincides with the Gaussian function [3].

[1]. K.N. Abazajian, M.A. Acero, S.K. Agarwalla et al. (Collaboration), Light Sterile Neutrinos: A White Paper, arXiv:1204.5379v1 (2012).

[2]. I. E. Alexeev, S.V. Bakhlanov, N.V. Bazlov, E. A. Chmel, A. V. Derbin, I. S. Drachnev, I.M. Kotina, V.N. Muratova, N.V. Pilipenko, D.A. Semyonov, E.V. Unzhakov, V.K. Yeremin, Nuclear Inst. And Methods in Physics Research A 890, 647 (2018).

[3]. A.V. Derbin, A. I. Egorov, I.A. Mitropolskii, V. N. Muratova, S.V. Bakhlanov, and L.M. Tukhkonen, JETP Lett. 65, 605 (1997).


A.V. Derbin, I.S. Drachnev, I.S. Lomskaya, V.N. Muratova. N.V. Pilipenko,

D.A. Semenov, L.M. Tykhkonen, E.V. Unzhakov, A.Kh. Khusainov

 JETP Letters 108, issue 8 (2018)


The possibility to create, manipulate and detect spin-polarized currents is at the very heart of semiconductor spintronics [1]. Stationary spin polarized currents were successfully generated in various semiconductor heterostructures and low-dimensional mesoscopic samples [2]. However, controllable manipulation of charge and spin states, applicable for ultra small size electronic devices design requires analysis of non-stationary effects and transient properties [3-5]. Consequently, the problem of non-stationary evolution of initially prepared spin and charge state in correlated nanostructures (quantum dots, impurity atoms, etc.) is really vital.

In the present paper we analyze non-stationary spin-polarized currents flowing through the correlated single-level quantum dot localized between non-magnetic leads in the presence of applied bias voltage and external magnetic field. We reveal, that spin polarization and direction of the non-stationary currents can be simultaneously inverted by sudden changing of applied bias voltage. We also analyze time evolution of the spin polarization degree and demonstrate the possibility of its sign changing following the applied bias polarity. This effect opens the possibility for the spin-polarization train pulses generation with the opposite degree of polarization. Application of external magnetic field allows to consider correlated single-level quantum dot as an effective non-stationary spin filter.

[1] I. Zutic, J. Fabian, S. Das Sarma, Rev. Mod. Phys., 76, 323 (2004)

[2] M.E. Torio, K. Hallberg, S. Flach, A.E. Miroshnichenko, M. Titov, Eur. Phys. J. B37, 399 (2004)

[3] N.S. Maslova, I. V. Rozhansky, V.N. Mantsevich, P.I. Arseyev, N.S. Averkiev, E. Lahderanta, Phys. Rev. B 97, 195445 (2018)

[4] V.N. Mantsevich, N.S. Maslova, P.I. Arseyev, Physica E, 93,224 (2017)

[5] N.S. Maslova, P.I. Arseyev, V.N. Mantsevich, Solid State Comm. 248, 21 (2016)


Mantsevich V.N., Maslova N.S., Arseyev P.I.

JETP  Letters 108, №7 (2017)     


 It is well known that Yang-Mills theory possesses a nontrivial topological structure: it has an in nite series of energetically degenerate but topologically distinct classical vacua. At nite temperature thermal uctuations of elds can lead to (sphaleron) transitions between various vacuums. Due to the chiral anomaly the rate of these transitions describes the evolution of the chiral charge in Quantum Chromodynamics or baryon charge in electroweak theory.
 For the rst time the sphaleron rate
$\Gamma$ was measured by means of lattice simulations in gluodynamics with gauge group SU(3). Calculations are carried out on the basis of Kubo formula, which relates the sphaleron rate and correlator of the topological charge density. Topological charge density correlator was measured by Gradient Flow method. The inversion of the Kubo formula was carried out by Backus-Gilbert method. The nal result is $\Gamma/T^4=0.062(18)$ at the temperature $T/T_c=1.24$, what is in agreement with the results of real time calculations at weak coupling [1].

[1] G. D. Moore and M. Tassler, JHEP 1102, 105 (2011) doi:10.1007/JHEP02(2011)105 [arXiv:1011.1167 [hep-ph]].



JETP Letters 108, issue 6 (2018)



At the birth of quantum mechanics, E. Schrödinger realized that a free relativistic electron, described by the Dirac Hamiltonian, exhibits oscillations in space resulting from the interference of the positive and the negative-energy solutions of the Dirac equation [1]. Recently, it was suggested that Zitterbewegung is not limited to free electrons but is a common feature of systems with a gapped or level-split spectrum exhibiting a formal similarity to the Dirac Hamiltonian [2]. Here, we study the motion of electrons in a semiconductor system with spin-orbit coupling and the Zeeman gap opened by an external magnetic field. It is shown that, in addition to the well-known Brownian motion, electrons experience an inherent trembling motion of quantum-mechanical nature. The effect originates from the fact that the electron velocity is not a conserved quantity and contains an oscillating contribution. The Zitterbewegung occurs for all the electrons, also for electrons in thermal equilibrium. Experimental study of the electron Zitterbewegung in such conditions requires the use of noise spectroscopy. We show that the Zitterbewegung of individual electrons can be phase-synchronized by initializing the electrons in the same spin state. In this case, the coherent precession of the individual electron spins drives their back-and-forth motion in real space giving rise to a macroscopic high-frequency electric current. Such a coherent Zitterbewegung is maintained as long as the coherent spin precession of the electrons is not destroyed by the processes of spin dephasing. We develop a theory of the coherent Zitterwebegung for the cases of ballistic and diffusive electron transport, predict its enhancement at the plasmon resonance conditions, and discuss its relation to the spin-galvanic effect [3,4].

[1] E. Schrödinger, Über die kräftefreie Bewegung in der relativistischen Quantenmechanik, Sitz. Press. Akad. Wiss.Phys.-Math. 24, 418 (1930).

[2] W. Zawadzki and T. M. Rusin, Zitterbewegung (trembling motion) of electrons in semiconductors: a review, J. Phys.: Condens. Matter 23, 143201 (2011).

[3] E.L. Ivchenko, Yu.B. Lyanda-Geller, and G.E. Pikus, Current of thermalized spin-oriented photocarriers, Sov. Phys. JETP 71, 550 (1990).

[4] S.D. Ganichev, E.L. Ivchenko, V.V. Bel’kov, S.A. Tarasenko, M. Sollinger, D. Weiss, W. Wegscheider, and W. Prettl, Spin-galvanic effect, Nature 417, 153 (2002).


S. A. Tarasenko, A. V. Poshakinskiy, E. L. Ivchenko, I. Stepanov,

M. Ersfeld, M. Lepsa, and B. Beschoten

JETP Letters 108, issue 5 (2018)


Cyclotron resonance photoconductivity (CRP) is one of the power tools for study of the interaction of two-dimensional particles with electromagnetic radiation especially after the discovery of microwave induced magnetoresistance oscillations [1] that have created a lot of questions in the area, where, after the issue of the well-known review [2], it seemed that everything was clear. In this work, we report on the observation of CRP of two-dimensional (2D) electrons under very unusual conditions – in 2D semimetal in that their number (109 – 1010) cm-2 is much (from one to three orders) less than number of holes. So for the first time the cyclotron resonance have been observed from the electrons moving through the hole liquid, which strongly screens an impurity scattering potential and an electron-electron interaction. At first glance, it is impossible to observe CRP in this situation because of a very small absorption rate; however it has been detected in our experiments. Moreover, at 432 µm wavelength no decreasing of the CRP amplitude was observed when electron density decreased from 1010 cm2 to 109 cm2 . The experiments demonstrate that interaction of 2D electrons in semiconductor structures with the high frequency electromagnetic field is not so simple problem. It is likely there is a strong field enhancement in 2D system due to many particle effects in the spirit of a recent theory work [3]. Anyway, the further study of this phenomenon is of undoubted interest.

[1] I. A. Dmitriev, A. D. Mirlin, D. G. Polyakov, and M. A. Zudov, Rev. Mod. Phys. 84, 1709 (2012).

[2] T. Ando, A. B. Fowler, and F. Stern, Rev. Mod. Phys. 54, 673 (1982).

[3] A. D. Chepelianskii, D. L. Shepelyansky, Phys. Rev. B 97, 125415 (2018).

Z.D. Kvon

JETP Letters 108, issue 4 (2018)

Investigation of hybrid structures containing superconductors and magnetic materials attracts great interest due to different interesting phenomena such as spin-triplet superconducting pairing, anomalous superconducting and magnetic proximity effects and other ones that were reviewed in several articles [1-5]. In this work, the spin-dependent electron transport phenomena have been studied theoretically for double-barrier structures S-IF1-F-IF2-N, where S is a superconductor, F is a ferromagnetic metal, N is a normal metal, IF is a spin-active barrier. It was predicted that under certain conditions the negative differential resistance may be realized in the structures S-IF1-F-IF2-N, if the polarization at least one of the barriers is not small: │Rb↑ - Rb↓│ is of the order of ( Rb↑ + Rb↓ ), where Rb↑ , Rb↓ are the contributions to the (normal state) resistance of the barrier related with spin-up and spin-down electrons, respectively. It was shown that the negative differential resistance is realized if the superconducting proximity effect is strong, the thickness of the F layer is short enough, the exchange field in this layer is not small with respect to the superconducting energy gap Δ, and the spin-orbit relaxation time due to impurity scattering in the F layer is significantly greater than ħ/Δ. Another investigated features of the differential resistance of the S-IF1-F-IF2-N structures are its voltage asymmetric dependences and its strong dependence on the mutual orientations of the exchange fields in the barriers and in the F layer, that is the reason of the giant magnetoresistance effect.

  1. F.S. Bergeret, A.F. Volkov, and K.B. Efetov, Rev. Mod. Phys. 77, 1321 (2005).
  2. A.I. Buzdin, Rev. Mod. Phys. 77, 935 (2005).
  3. A.A. Golubov, M.Yu. Kupriyanov, and E. Il'ichov, Rev. Mod. Phys. 76, 411 (2004).
  4. Matthias Eschrig, Rep. Progr. Phys. 78 , 104501 (2015).
  5. Sebastian Bergeret, Mikhail Silaev, Pauli Virtanen, and Tero T. Heikkilӓ, cond-mat/1706.08245.   


                                                                                                                                                      Zaitsev A.V.

JETP Letters 108, issue 3 (2018)                              

Nonlinear magneto-transport in two-dimensional (2D) electron systems reveals fascinating novel physical phenomena such as quantal Joule heating [1], zero differential resistance [2] or conductance [3] states, and Zener tunneling between Landau levels [4]. The later effect is related to a backscattering of 2D electrons colliding with a short range, sharp impurity potential.  The effect is considered to be absent for a smooth, long range disorder. Surprisingly, this paper shows that a long-range, smooth periodic modulation of the electrostatic potential affects significantly the electron backscattering leading to an unexpected interference of the Zener and commensurability oscillations of the magnetoresistance [5].

The electrostatic modulation is obtained via a fabrication of a periodic array of nano-scaled metallic strips with a period a = 200nm located on top of the studied samples. The interference leads to a dramatic modification of the commensurability oscillations of the magnetoresistance reminiscent of a beating pattern. Due to the long range periodic electrostatic modulation the proposed model relates the observed interference to a modification of the electron spectrum, in particular, the electron lifetime. The model is in a good agreement with the experiment, indicating the relevance of the proposed explanation. The obtained results indicate that the quantization of the electron spectrum is of a paramount importance for nonlinear electron transport in low dimensional systems.

1. Jing Qiao Zhang, Sergey Vitkalov and A. A. Bykov, Phys. Rev. B 80, 045310  (2009).

2. A. A. Bykov, J.-Q. Zhang, S. A. Vitkalov, A. K. Kalagin, and A. K. Bakarov, Phys. Rev. Lett. 99, 116801 (2007).

3. A. A. Bykov, Sean Byrnes, Scott Dietrich, and Sergey Vitkalov, Phys. Rev. B 87, 081409(R) (2013).

4. C. L. Yang, J. Zhang, R. R. Du, J. A. Simmons, J. L. Reno, Phys. Rev. Lett. 89, 076801 (2002).

5. D. Weiss, K. von Klitzing, K. Ploog, and G. Weimann, Europhys. Lett. 8, 179 (1989).


A. A. Bykov, I. S. Strygin, E. E. Rodyakina, S. A. Vitkalov

JETP Letters 108, issue 2 (2018)

Recent progress on novel two-dimensional metal-based compounds [1,2] have encouraged us to pay attention to this underinvestigated and highly promising class of materials. Here we would like to present the prediction of a new CoC phase which is very intriguing by uncommon symmetry as well as electronic and mechanical properties.

In particular, both the ab initio bending analysis and phonon calculations have shown that 2D CoC demonstrates stability of orthorhombic lattice structure in contrast to probably more expected hexagonal or square types. Moreover, from electronic structure analysis, it was obtained that the cobalt net and carbons dimers are connected through a combination of covalent, ionic and metallic bonding. The estimated mechanical elastic modulus for 2D CoC are comparable to those for h-BN and only 30% lower than for the “world-record” graphene, whereas Poisson’s ratios and flexural rigidity are higher (or equal) than for the well-known 2D structures.

The predicted metallic states of 2D CoC and promising mechanical properties might be of practical importance for future CoC-based heterostructure synthesis, whereas thorough description of potentially interesting magnetic and optical properties have to motivate further studies.

[1]  Kano, E.; Kvashnin, D. G.; Sakai, S.; Chernozatonskii, L. A.; Sorokin, P. B.; Hashimoto, A.; Takeguchi, M. One-Atom-Thick 2D Copper Oxide Clusters on Graphene. Nanoscale 2017, 9 (11), 3980–3985.

[2]   Zhao, J.; Deng, Q.; Bachmatiuk, A.; Sandeep, G.; Popov, A.; Eckert, J.; Rümmeli, M. H. Free-Standing Single-Atom-Thick Iron Membranes Suspended in Graphene Pores. Science 2014, 343 (6176), 1228–1232.


Larionov K.V., Popov Z.I.,

Vysotin M.A., Kvashnin D.G., Sorokin P.B.

JETP Letters, 108, issue 1, 2018

Successful exfoliation of one-atom-thick graphene layer from the graphite crystal in 2004 [1] stimulated the search for new two-dimensional carbon nanostructures. In graphene each carbon atom is bonded to its three nearest neighbors, so that C-C bonds form a pattern of hexagons, while pentagons are considered as topological defects. Recently, a new carbon allotrope, pentagraphene, composed entirely of pentagons, has been proposed [2]. Later, however, it was argued that pentagraphene cannot be made experimentally because, first, it is thermodynamically unstable and rapidly restructures toward graphene [3] and, second, intrinsic mechanical stress created by two mutually orthogonal sublattices of carbon dimers results in the growth of strongly curved rather than planar pentagraphene layers [4].

We draw attention to another weak point of pentagrafene, its thermal stability. Tight-binding molecular dynamics simulation showed that after the formation of a single defect of the Stone-Wales type, the disordered region does not remain localized, but rapidly spreads over the entire sample. The lifetime of the pentagrafene sample until complete disordering of its structure decreases exponentially with increasing temperature and is inversely proportional to the sample area. At room temperature, mesoscopic samples of pentagrafene may have rather high thermal stability.

1. K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, Y. Zhang, S.V. Dubonos, I.V. Grigorieva, and A.A. Firsov, Science 306, 666 (2004).

2. S. Zhang, J. Zhou, Q. Wang, X. Chen, Y. Kawazoe, and P. Jena, Proc. Nat. Acad. Sci. 112, 2372 (2015).

3. C.P. Ewels, X. Rocquefelte, H,W. Kroto, M.J. Rayson, P.R. Briddon, and M.I. Heggie, Proc Nat. Acad Sci. U S A. 112, 15609 (2015).

4. P. Avramov, V. Demin, M. Luo, C.H. Choi, P.B. Sorokin, B. Yakobson, and L. Chernozatonskii, J. Phys. Chem. Lett. 6, 4525 (2015).


Openov L.A., Podlivaev A.I.

JETP Letters 107, issue 11 (2018)

Until recently, the electromagnetic field has been considered as being quantum one with few photons and classical one with quite a few of them. Then a macroscopic quantum state of a field with many photons - a squeezed field - was discovered. In addition, the reverse case was also made possible: a one-photon wave packet may not prove to be a quantum one. An effect that is very sensitive to the state of the "one-quantum" object, allowing us to distinguish between the classical and quantum states of a one-photon field was found in the present work. The effect is due to the possibility of complete suppression of collective decay of an ensemble of identical excited atoms localized within the area far smaller than that of the characteristic wavelength [1]. The well-known Dicke model is generalized for accounting the interaction with a vacuum electromagnetic field of zero photon density up to the second - order algebraic perturbation theory [1,2]. Then the effects of quantum interference of various radiation processes are correctly described, and the dynamics of the atomic ensemble is characterized as non-Wiener dynamics [1].

In this work, the joint effect of a broadband one-photon wave packet and a vacuum electromagnetic field on the atomic ensemble is investigated. The master equations of non-Wiener dynamics are obtained in [3]. The state of one-photon field can both be prepared in two different ways and presented in different states. If such a field interacts with a localized excited atomic ensemble under suppression of collective decay, then a strong effect is observed. The case of semi-excited atomic ensemble is calculated analytically, which shows diametrically opposite difference in the type of radiation. The quantum one-photon source produces a pulse of superradiation (collective decay), whose intensity is proportional to the square of the number of atoms of the ensemble. On the other hand, in the case of a classical one-photon source an incoherent radiation is generated, similar to that of the one generated by the emission of independent atoms.

1. A.M. Basharov, Phys. Rev. A 84, 013801 (2011).

2. A.I. Maimistov, A.M. Basharov, Nonlinear optical waves, Dordrecht: Kluwer Academic, 1999.

3. A.I. Trubilko, A.M. Basharov. JETP, 2018 (in press)


A.I. Trubilko, A.M. Basharov

     JETP Letters  107 , issue 9 (2018)

Experimental observation of the magnetic topological states - magnetic skyrmions in chiral magnets [1] caused the rising interest to them. Such attention is motivated both by the hopes to use their unique properties (such as high mobility in electric current) in novel spintronic devices and by their topologically caused attributes interesting to the fundamental condensed matter physics, topological Hall effect for example [2]. In the chiral magnets the magnetic skyrmions are naturally stabilized by weak relativistic Dzyaloshinskii–Moriya interaction and thus, the skyrmions can exist only within a narrow temperature-field region which hinders their application. So the search of the possibilities of the skyrmion stabilization in the common magnetic materials at room temperature is the actual problem.

The idea of our work is spatially modulate the energy of the domain wall surrounding skyrmion core by nanostructurisation of the film and so artificially create the potential well (or the lattice of such wells) for the skyrmionic state. This well will prevent skyrmion transformation to the labyrinth domain structure. The first possible way to the goal is to spatially modulate the material parameters of the magnetic film [3]. In this presented work we experimentally studied the alternative way of the nanostructurisation, namely the spatial modulation of the thickness of the CoPt multilayered film with the perpendicular anisotropy. The structure is the regular lattice (period is 300 nm) of the stubs (diameters is 150 nm) etched on the surface of the film. The magnetic force microscopy allows to observe skyrmion formation in the system during the magnetizing in the uniform perpendicular field. The skyrmons stay stable even after reducing the field to zero. The magnetization curve of the system is studied both by Hall magnetometry and by magnetooptical methods. The experimentally observed topological magnetic configurations and hysteresis loops are verified by micromagnetic simulations.

[1] U. K. Rossler, N. Bogdanov, and C. Pleiderer, Spontaneous skyrmion ground states in magnetic metals, Nature (London) 442, 797 (2006).

[2] N. Nagaosa and Y. Tokura, Topological properties and dynamics of magnetic skyrmions, Nat. Nanotech. 8, 899 (2013).

[3] M.V. Sapozhnikov, S.N. Vdovichev, O.L. Ermolaeva, N.S. Gusev, A.A. Fraerman, S.A. Gusev, Yu.V. Petrov, Artificial dense lattice of magnetic bubbles, Appl. Phys. Lett. 109, 042406 (2016).


M. V. Sapozhnikov, O. L. Ermolaeva, E.V. Skorohodov, M.N. Drozdov

JETP Letters  107, issue 6 (2017)

In the bulk of a superfluid, besides well-known and experimentally observed quantum vortex rings, theoretically there can exist (developing in time) also solitary topologically non-trivial excitations as vortex knots [1-3]. The simplest of them are torus knots ${\cal T}_{p,q}$, where  $p$ and $q$ are co-prime integers, while parameters of torus are the toroidal (large) radius $R_0$ and the poloidal (small) radius $r_0$, both sizes being large in comparison with a width of quantum vortex core $\xi$. It was believed on the basis of previously obtained numerical results that such knots are unstable and they reconnect during just a few typical times, traveling a distance of several $R_0$ (the lifetime is somewhat longer for smaller ratios $B_0=r_0/R_0$). The mentioned results were obtained for not too large ratios $R_0/\xi\lesssim 20$, and with a very coarse step (about 0.1) on parameter $B_0$.
 In this work it was numerically found that actually the situation is much more complicated and interesting. The dynamics of trefoil knot ${\cal T}_{2,3}$ was accurately simulated within a regularized Biot-Savart law using a small step on $B_0$. At fixed values of parameter $\Lambda=\log(R_0/\xi)$, the dependence of knot lifetime on parameter $B_0$ turned out to be drastically non-monotonic on sufficiently small $B_0\lesssim 0.2$. Moreover, at $\Lambda\gtrsim 3$ quasi-stability bands appear, where vortex knot remains nearly unchanged for many dozens and even hundreds of typical times. Qualitatively similar results take place also for  ${\cal T}_{3,2}$ knot. These observations essentially enrich our knowledge about dynamics of vortex filaments.

 [1] D. Proment, M. Onorato, and C. F. Barenghi,  Vortex knots in a Bose-Einstein condensate, Phys. Rev. E 85, 036306 (2012).
 [2] D. Proment, M. Onorato, and C. F. Barenghi, Torus quantum vortex knots in the Gross-Pitaevskii model for Bose-Einstein condensates, J. Phys.: Conf. Ser. 544, 012022, (2014).
 [3] D. Kleckner, L. H. Kauffman, and W. T. M. Irvine, How superfluid vortex knots untie, Nature  Physics  12, 650 (2016).

                                                                            V. P. Ruban 

JETP Letters  107, issue 5 (2018).

For the first time the magnetic phase transition in DyF3 at low temperatures was observed by 3He NMR. The spin kinetics of liquid 3He in contact with a mixture of microsized powders LaF3 (99.67%) and DyF3 (0.33%) at temperatures 1.5-3 K was studied by pulse NMR technique. The DyF3 is a dipole dielectric ferromagnet with a phase transition temperature Tc = 2.55 K, while as the diamagnetic fluoride LaF3 used as a diluent for optimal conditions for observation of 3He NMR. The phase transition in DyF3 is accompanied by a significant changes in the magnetic fluctuation spectrum of the dysprosium ions. The spin kinetics of 3He in contact with the substrate is sensitive to this fluctuations. An significant change in the rates of the longitudinal and transverse nuclear magnetization of 3He in the region of magnetic ordering of solid matrix was observed. A technique is proposed for studying the static and fluctuating magnetic fields of a solid matrix at the low temperatures using liquid 3He as a probe.

Е.М. Аlakshin, Е.I. Kondratyeva, V.V. Kuzmin, К.R. Safiullin, А.А. Stanislavovas, А.V. Savinkov, А.V. Klochkov,  М.S. Tagirov

JETP Letters 107 issue 2, 2018

Microspheres at the surface of liquid are widely used now for visualization of wave and vortex motion [1, 2]. The experiments of this kind had been performed recently to study of turbulence at the surface of liquid helium [3]. That’s why it is of interest to consider the corrections to a classic Archimedes' principle, because while the size of a particle floating at the surface decreases, the forces of surface tension and molecular interaction start to play a significant role. 

We study the deviations from Archimedes' principle for spherical particles made of molecule hydrogen near the surface of liquid He4. Classic Archimedes' principle takes place if particle radius $R_0$ is greater than capillary length of helium $L_{k} \approx $ 500 µm and the height $h_+$  of the part of the particle above He is proportional to  $R_0$ . Over the range of $30 <R_0 <500$ µm Archimedes' force is suppressed by the force of surface tension and  $h_{+}  \sim R^{3}_{0} / L^{2}_{k}$.  When $R_0<30$µm, the particle is situated under the surface of liquid helium. In this case Archimedes' force competes with Casimir force which repels the particle from the surface to the depth of liquid. The distance from the particle to the surface $h_{-} \sim R^{5/3}_c / R^{2/3}_0$ if  $R_0>R_c...R_c$  can be expressed as  $R_c \approx (\frac {\hbar c}{\rho g}) \approx $ 1µm, $\hbar $ is Planck's constant, c is speed of light, $\rho $ is helium density. For the very small particles ( $R_0<R_c)$  $h_{-}$does not depend on their size: $h_{-}$=$R_c$.

1. S. V. Filatov,  S. A. Aliev, A. A. Levchenko, and D. A. Khramov, JETP Letters, , 104(10), 702 (2016).

2.  S. V. Filatov,  D. A. Khramov,   A. A. Levchenko, JETP Letters, 106(5), 330 (2017).

3. A. A. Levchenko, L. P. Mezhov-Deglin, A. A. Pel’menev, JETP Letters, 106(4), 252 (2017).

4. E. V. Lebedeva, A. M. Dyugaev , and P. D. Grigoriev, JETP, 110(4), 693 (2010).

5. A. M. Dyugaev,  P. D. Grigoriev, and E. V. Lebedeva, JETP Letters, 89(3), 145 (2009).


A.M. Dyugaev,  E.V. Lebedeva,

JETP Letters, 106 issue 12, 2017

One of the frontiers of quantum condensed matter physics seeks to analyze and classify scenarios of the superconductor-insulator quantum phase transition (SIT). Fermionic scenario [1] rules that disorder, when strong enough, breaks down Cooper pairs thus transforming a superconductor into a metal. The further cranking up disorder strength localizes quasiparticles turning the metal into an insulator. According to Bosonic scenario [2,3] disorder localizes Cooper pairs which survive on the insulating side of the SIT and provide an insulating gap. In the Fermionic scenario, the disorder-driven SIT is a two-stage transition through the intermediate state that exhibits finite resistance R and is ordinarily referred to as quantum metal. In Bosonic scenario, the SIT this intermediate state shrinks into a single point in which the resistance assumes the universal quantum resistance per square Rc = 6.45 kΩ/□ [3]. The disorder-driven SIT was reported in films of InOx [4, 5], Be [6], TiN [7]. However, the resistance Rc that separates superconducting and insulating states in these films is not universal. The access and detailed study of the phases in the critical vicinity of the SIT in different materials remains one of the major challenges.

            Here we observe the direct disorder-driven superconductor-insulator transition in NbTiN films with Rc = 2.7 kΩ/□ at room temperature. We show that the increasing the film's resistance suppresses the superconducting critical temperature Tc in accord with the Fermion model. We find that incrementally increasing R suppresses the Berezinskii-Kosterlitz-Thouless temperature down to zero, while the critical temperature Tc remains finite, which complies with the Bosonic model. Upon further increase of R, the ground state of system becomes insulating. Finally, we demonstrate that the temperature dependence of the resistance of insulating films follows the Arrhenius law.

[1] A. M. Finkel'stein, Superconducting transition temperature in amorphous films, JETP Lett. 45, 46 (1987).

[2] A. Gold, Dielectric properties of disordered Bose condensate, Phys. Rev. A 33, 652 (1986).

[3] M.P. A. Fisher, G. Grinstein, S. Grivin, Presence of quantum diffusion in two dimensions: Universal resistance at the superconductor-insulator transition, Phys. Rev. Lett. 64, 587 (1990).

[4] A. F. Hebard, M. A. Paalanen, Magnetic-field-tuned superconductor-insulator transition in two-dimensional films, Phys. Rev. Lett. 65, 927 (1990).

[5] D. Shahar, Z. Ovadyahu, Superconductivity near the mobility edge, Phys. Rev. B 46, 10917 (1992).

[6] E. Bielejec, J. Ruan, W. Wu, Anisotropic magnetoconductance in quench-condensed ultrathin beryllium films, Phys. Rev. B 63, 1005021 (2001).

[7] T. I. Baturina et al., Localized superconductivity in the quantum-critical region of the disorder-driven superconductor-insulator transition in TiN thin films, Phys. Rev. Lett. 99, 257003 (2007).


M. V. Burdastyh, S. V. Postolova, T. I. Baturina, T. Proslier, V. M. Vinokur,

A.Yu. Mironov

JETP Letters 106 (11) (2017)


We demonstrate that non-equilibrium spin excitations drift to macroscopically large distances in
a 2D electron gas (symmetrically doped GaAs/AlGaAs quantum well) in a quantizing magnetic
field at filling factor $\nu $ = 2. The effect is induced by low-temperature photoexcitation of a dense
ensemble of long-lived ($\sim 1 $ ms) spin excitations − cyclotron spin-flip magnetoexcitons. The spin
excitation is a bound state of an electron at the first Landau level and a Fermi-hole at the zeroth
Landau level with a total spin S = 1 [1-3]. Direct photoexcitation and radiative annihilation of
such excitations are forbidden (“dark” excitons), yet, their binding energy and spin structure are
reliably established by inelastic light scattering spectra [4, 5]. Recently, we were able to measure
the dark exciton density and relaxation rate by newly developed technique – photo-induced
resonant light reflection [6]. At the temperatures below 1 K, we discovered the condensate-like
behavior of the dense exciton ensemble [7]. Furthermore, these spin excitations modify
photoluminescence spectrum by binding to a photo-excited valence hole: an allowed radiative
recombination channel of three-particle complexes gets active [8]. Our paper presents
observation of spin exciton drift to the distance up to 200 μm. This unique phenomenon was
experimentally studied utilizing spatial separation of pump (photoexcitation) and probe
(photoluminescence detection) laser spots. Enhancement of the multi-particle complexes in
photoluminescence spectrum was observed far away from the pump area. Both pump intensity
and temperature dependencies correlate well with the phase diagram of dark exciton
condensation [7]. Time dependence of the spin drift rate in a 2D electron gas is the subject of our
near-future research.

1. Yu.A. Bychkov, S.V. Iordanskii, and G.M. Eliashberg, Two-dimensional electrons in a strong
magnetic field, JETP Letters 33, 143 (1981).
2. I.V. Lerner and Yu.E. Lozovik, Two-dimensional electron-hole system in a strong magnetic field as an
almost ideal exciton gas, Sov. Phys. JETP 53, 763 (1981).
3. C. Kallin and B.I. Halperin, Excitations from a filled Landau level in the two-dimensional electron gas,
Phys. Rev. B 30, 5655 (1984).
4. L.V. Kulik, I.V. Kukushkin, S. Dickmann, V.E. Kirpichev, A.B. Van'kov, A.L. Parakhonsky, J.H.
Smet, K. von Klitzing, and W. Wegscheider, Cyclotron spin-flip mode as the lowest-energy excitation of
unpolarized integer quantum Hall states, Phys. Rev. B 72, 073304 (2005).
5. L.V. Kulik, S. Dickmann, I.K. Drozdov, A.S. Zhuravlev, V.E. Kirpichev, I.V. Kukushkin, S. Schmult,
and W. Dietsche, Antiphased cyclotron-magnetoplasma mode in a quantum Hall system, Phys. Rev. B 79,
121310 (2009).
6. L.V. Kulik, A.V. Gorbunov, A.S. Zhuravlev, V.B. Timofeev, S.M. Dickmann, and I.V. Kukushkin,
Super-long life time for 2D cyclotron spin-flip excitons, Sci. Rep. 5, 10354 (2015).
7. L.V. Kulik, A.S. Zhuravlev, S. Dickmann, A.V. Gorbunov, V.B. Timofeev, I.V. Kukushkin, and S.
Schmult, Magnetofermionic condensate in two dimensions, Nature Commun. 7, 13499 (2016).
8. A.S. Zhuravlev, V.A. Kuznetsov, L.V. Kulik, V.E. Bisti, V.E. Kirpichev, and I.V. Kukushkin,
Artificially Constructed Plasmarons and Plasmon-Exciton Molecules in 2D Metals, Phys. Rev. Lett. 117,
196802 (2016).

                                                    Gorbunov A.V., Kulik L.V., Kuznetsov V.A., Zhuravlev А.S.,
                                                             Larionov A.V., Timofeev V. B., Kukushkin I.V. 

                                                                                      JETP Letters 106, issue 10 (2017)


Two-dimensional topological insulators are have attracted much recent interest since they feature helical edge states inside their band gap [1,2]. In the absence of time-reversal symmetry breaking, spin-momentum locking prohibits elastic backscattering of these helical states, i.e., the helical edge is a realization of an ideal transport channel with conductance equal to e2/h. However, this theoretical prediction was not confirmed by experiments on HgTe/CdTe [3-6] and InAs/GaSb [7,8] quantum wells. The time-symmetric interaction of the helical states with a "quantum magnetic impurity'' (an impurity which has its own quantum dynamics) is a leading candidate for explaining these experiments. In spite of recent theoretical studies of this problem [9-14], several key questions has not been addressed in details.

 We study theoretically the modification of the ideal current-voltage characteristics of the helical edge in a two-dimensional topological insulator by weak scattering off a single magnetic impurity. As a physical realization of such a system we have in mind the (001) CdTe/HgTe/CdTe quantum well (QW) with a Mn impurity that possesses spin S=5/2. Contrary to previous works, we allow for a general structure of the matrix describing exchange interaction between the edge states and the magnetic impurity. For S=1/2 we find an analytical expression for the backscattering current at arbitrary voltage. For larger spin, S>1/2, we derive analytical expressions for the backscattering current at low and high voltages. We demonstrate that the differential conductance may exhibit a non-monotonous dependence on the voltage with several extrema.

[1] X.-L. Qi, S.-C. Zhang, Topological insulators and superconductors, Rev. Mod. Phys. 83, 1057 (2011).

[2] M. Z. Hasan, C. L. Kane, Colloquium: Topological insulators, Rev. Mod. Phys. 82, 3045 (2010).

[3] M. Konig, S. Wiedmann, C. Brune, A. Roth, H. Buhmann, L. W. Molenkamp, X.-L. Qi, S.-C. Zhang,    Quantum spin Hall insulator state in HgTe quantum wells, Science 318, 766 (2007)

[4] K. C. Nowack, E. M. Spanton, M. Baenninger, M. Konig, J. R. Kirtley, B. Kalisky, C. Ames, P. Leubner, C. Brune, H. Buhmann, L. W. Molenkamp, D. Goldhaber-Gordon, K. A. Moler, Imaging currents in HgTe  quantum wells in the quantum spin Hall regime, Nat. Mater. 12, 787 (2013).

[5] G. Grabecki, J. Wrobel, M. Czapkiewicz, L. Cywinski, S. Gieratowska, E. Guziewicz, M. Zholudev, V. Gavrilenko, N. N. Mikhailov, S. A. Dvoretski, F. Teppe, W. Knap, T. Dietl, Nonlocal resistance and its fluctuations in microstructures of band-inverted HgTe/(Hg,Cd)Te quantum wells, Phys. Rev. B 88, 165309 (2013).

[6] G. M. Gusev, Z. D. Kvon, E. B. Olshanetsky, A. D. Levin, Y. Krupko, J. C. Portal, N. N. Mikhailov, S. A. Dvoretsky, Temperature dependence of the resistance of a two-dimensional topological insulator in a HgTe quantum well, Phys. Rev. B 89, 125305 (2014).

[7] E. M. Spanton, K. C. Nowack, L. Du, G. Sullivan, R.-R. Du, K. A. Moler, Images of edge current in InAs/GaSb quantum wells, Phys. Rev. Lett. 113, 026804 (2014).

[8] L. Du, I. Knez, G. Sullivan, R.-R. Du, Observation of quantum spin Hall states in InAs/GaSb bilayers under broken time-reversal symmetry, Phys. Rev. Lett. 114, 096802 (2015).

[9] J. Maciejko, Ch. Liu, Y. Oreg, X.-L. Qi, C. Wu, S.-C. Zhang, Kondo effect in the helical edge liquid of the quantum spin Hall state, Phys. Rev. Lett. 102, 256803 (2009).

[10] Y. Tanaka, A. Furusaki, K. A. Matveev, Conductance of a helical edge liquid coupled to a magnetic impurity, Phys. Rev. Lett. 106, 236402 (2011).

[11] J. I. Vayrynen, M. Goldstein, L. I. Glazman, Helical edge resistance introduced by charge puddles, Phys. Rev. Lett. 110, 216402 (2013).

[12] J. I. Vayrynen, M. Goldstein, Y. Gefen, L. I. Glazman, Resistance of helical edges formed in a semiconductor heterostructure, Phys. Rev. B 90, 115309 (2014).

[13] V. Cheianov, L. I. Glazman, Mesoscopic fluctuations of conductance of a helical edge contaminated by magnetic impurities, Phys. Rev. Lett. 110, 206803 (2013).

[14] L. Kimme, B. Rosenow, A. Brataas, Backscattering in helical edge states from a magnetic impurity and Rashba disorder, Phys. Rev. B 93, 081301 (2016).


      Kurilovich P.D. , Kurilovich V.D., Burmistrov I.S. , Goldstein M.                                                                               

JETP Letters 106 (9) (2017)

Chimera is, according to Greek mythology, a monstrous creature combining the parts of different animals (a lion with a head of a goat and a tail of a snake). Physicists recently adopted this name for complex states in nonlinear dynamical systems, where instead of an expected symmetric synchronous state one observes coexistence of synchronous and asynchronous elements [1]. Since the discovery of chimeras by Kuramoto and Battogtokh in 2002 [2], these states have been reported in numerous theoretical studies and experiments.
In this paper, we study formation of chimeras in a one-dimensional medium of identical oscillators with nonlinear coupling. This coupling crucially depends on the local order parameter measuring the level of synchrony: the coupling promotes synchrony for asynchronous states and breaks synchrony if it is strong [3]. As a result, spatially homogenous state in this medium is that of partial synchrony. To study the evolution of this state we formulate the problem in terms of the local complex order parameter, which describes local level of synchrony, and formulate the system of partial differential equations for this quantity [4]. This allows us to formulate the problem of inhomogeneous states as the pattern formation one. First, we construct stationary chimeras and explore their linear stability properties. Next, based on numerical modeling, we show that within a certain range of parameters, such structures can evolve into periodically varying long-lived chimera states (breather-chimeras), or, for other values of the parameters, turn into more complex regimes with irregular behavior of the local order parameter (turbulent chimeras).

[1] M. J. Panaggio, D. M. Abrams, Chimera states: coexistence of coherence and incoherence in networks of coupled oscillators, Nonlinearity 28 , R67 (2015).

[2] Y. Kuramoto, D. Battogtokh, Coexistence of Coherence and Incoherence in Nonlocally Coupled Phase Oscillators, Nonlinear Phenom. Complex Syst. 5 , 380 (2002).

[3] M. Rosenblum, A. Pikovsky, Self-Organized Quasiperiodicity in Oscillator Ensembles with Global Nonlinear Coupling, Phys. Rev. Lett. 98 , 064101 (2007).

[4] L. A. Smirnov, G. V. Osipov, A. Pikovsky, Chimera patterns in the Kuramoto-Battogtokh model, J. Phys. A: Math. Theor. 50 , 08LT01 (2017).


                                                              Bolotov M.I., Smirnov L.A., Osipov G.V., Pikovsky A.

                                                                                           JETP Letters 106, issue 6 (2017)

Well-known Faraday waves can be parametrically generated on a free surface of ordinary (classical) fluids such as water or on superfluid helium He-II surface when a sample cell is vibrated vertically. Standing-wave patterns appear on the surface, and their frequencies are one-half the driving frequency. The acceleration threshold for the parametric excitation of Faraday waves on the surface of water is near an order of magnitude higher than on the surface of He-II at the same frequencies [1]. Generation of vorticity by interacting nonlinear surface waves has been predicted theoretically in a number of papers [2, 3] and generation of vortices by noncollinear gravity waves on a water surface has been observed experimentally [4].Our study has shown that classical 2-D vortices can be generated by Faraday waves on the surface of superfluid He-II also, more over one can observe formation of the vortex lattice in addition to the wave lattice on the surface of He-II in a rectangular cell. Combined with predictions [5] that the sharpest features (about nm sizes) in the cell walls can induce nucleation of quantum vortex filaments and coils on the interface and formation a dense turbulent layer of quantum vortices near the solid walls with a nonclassical average velocity profile which continually sheds small vortex rings into the bulk of vibrating He-II, this opens up new prospects for studying the properties of a quantum liquid and turbulent phenomena on the surface and in bulk of supefluid liquids.

[1] Haruka Abe, Tetsuto Ueda, Michihiro Morikawa, Yu Saitoh, Ryuji Nomura, Yuichi Okuda, Faraday instability of superfluid surface, Phys. Rev. E 76, 046305 (2007).
[2] S.V. Filatov, V.M. Parfenyev, S.S. Vergeles, M.Yu. Brazhnikov, A.A. Levchenko, V.V. Lebedev, Nonlinear Generation of Vorticity by Surface Waves, Phys. Rev. Lett. 116, 054501 (2016).
[3] V. M. Parfenyev, S.S. Vergeles, V.V. Lebedev, Effects of thin film and Stokes drift on the generation of vorticity by surface waves, Phys. Rev. E 94, 052801 (2016).
[4] S. V. Filatov, S. A. Aliev, A. A. Levchenko, D. A. Khramov, “Generation of vortices by gravity waves on a water surface”, JETP Letters, 104(10), 702–708 (2016).
[5] G.W. Stagg, N. G. Parker, and C. F. Barenghi, Superfluid Boundary Layer. PRL 118, 135301 (2017). DOI: 10.1103/PhysRevLett.118.135301


Levchenko A.A., Mezhov-Deglin L. P., Pel’menev A.A.

JETP Letters  106, issue 4 (2017)


Nanoscale integration of organic and metallic particles is expected to open up new opportunities for the design high-performance nanoscale devices.  Optimization of heterostructures requires experimental and theoretical analysis of their specific physical properties.  Nanosystem consisting in gold
nanospheres  covered by silica shell impregnated with the organic dye molecules  comes into focus as a possible plasmonic based
nanolaser, i.e. "spaser" [1]. Depending on the distance between the emitters and metal there are possible various phenomena [2,3].
In this paper we experimentally studied the characteristics of a suspension of  spasers at the temperatures $T_N=77.4K,T_R=293K$. It was found  that the
system possesses characteristics of a laser medium. The S-shaped dependence of the radiation intensity and the compression of the lasing line with increase of the pumping power were observed. Ten-fold increase of the intensity of the radiation generated by the medium and line narrowing with  temperature change $T_R\to T_N$ was found. The experimental results were compared with a numerical simulation of a spaser model consisting of 20 two-level media and a metallic nanosphere. The temperature effects were modeled by the introduction of the Markov process.

It was found that observed effects can be explained by means of the feedback caused by the nonlinear interaction of polarizations with their total reflection in the metallic core. At low temperatures  Bloch vectors related with two-level systems form an analog of a ferromagnetic state. With increasing fluctuations, antiferromagnetic states are formed along with the desynchronization of ferromagnetic one. These properties allows us to explain the observed changes in the intensity of the and line form of laser generation with temperature.

Experimental and numerical results of the work demonstrate that the synchronization of the polarization of dye molecules caused by inverse nonlinear coupling yields an analog of plasmon-polariton superradiance.

1. D.J. Bergman  and  M.I. Stockman, Phys.Rev.Lett. 90, 027401 (2003).

2.  M. Haridas et al, J. Appl. Phys.114, 064305 (2013).

3. M. Praveena et al, Phys. Rev. B  92, 235403 (2015).

                                                               A. S. Kuchyanov, A.A. Zabolotskii, Plekhanov A.I.

                                                                                                JETP Letters 106 (2) (2017)

Recently Sr2FeSi2O7 comes into focus as a possible compound with unusual magneto-electric coupling or, in other words, as a novel potential multiferroic [1,2]. Results of terahertz spectroscopy in the paramagnetic state show that the multiplet Fe+2(S=2) of the ground state splits due to the spin-orbit coupling. However the energy intervals between the low-lying singlet state and excited states are quite small so that all spin states are populated at the temperature of about 100 K. The Fe+2 ion occupies the center of a tetragonally distorted tetrahedron. In the present communication the origin of the magneto-electric coupling is described as follows. The odd crystal field from the tetrahedral environment induces the coupling of the orbital momentum of the Fe+2( 5D) state with the external electric field. On the other hand, the orbital momentum is coupled with spin via the spin –orbit interaction. Both angular momenta are coupled with the external magnetic field, which is enhanced due to the presence of the superexchange interaction between neighboring Fe+2 ions. Combining all these couplings, the author derived the affective spin Hamiltonian for the magneto-electric coupling, which made it possible to calculate relative intensities of the electric dipole transitions between spin states and estimate the magnetization caused by the external electric field as well as the electric polarization induced by the magnetic field.



  1. Thuc T. Mai, C. Svoboda, M. T. Warren, T.-H. Jang, J. Brangham, Y. H. Jeong, S.-W. Cheong, and R. Valdes Aguilar. Phys. Rev. B,  94, 224416 (2016)
  2. Yongping Pu, Zijing Dong, Panpan Zhang, Yurong Wu, Jiaojiao Zhao, Yanjie Luo. Journal of Alloys and Compounds, 672 , 64-71 (2016)



                                                                        M.V. Eremin

                                                                              JETP Letters 105 (11) (2017)

It is well known the conductivity of high-temperature superconductors (HTSCs) with TC ~100 K (YBaCuO, BiSrCaCuO, etc.) is provided at T~300 K by hole (h) fermions [1]. It is also known the superconducting transition in such cuprates is accomplished by means of the Cooper pairing, while the fluctuating Cooper pairs with charge -2e exist even at T=TC+(~30 K) [2]. Hence it inevitably follows in the interval TC<T<300 K the hole Fermi surface (FS) of these HTSCs transforms into an electron one as a result of a topological transformation (the Lifshitz transition (LT) [3]. There is one of the central questions in the problem of the pseudogap state [1] of copper-oxide high-TC superconductors:  how and at what temperatures this transformation occurs.

To evidence the charge carrier conversion the Hall effect is used usually. As for the BiSrCaCuO and YBaCuO, their Hall coefficients (RH) have several features in the temperature range TC…300 K [4,5]. The most significant of them is observed before the TC in the region of fluctuation conductivity and can be interpreted as a manifestation of a scale hole-electron (h-e) conversion in a system of charge carriers, i.e. as the LT. However, this point of view is not universally accepted. As for the data on the transformation of the FS obtained by the ARPES (Angle Resolved Photoemission Spectroscopy) method [7], they, like [4,5], support several rearrangements of the FS, including those occurring near TC.

Meanwhile, it is the possibility to evidence the h-e conversion in a hole HTSC (the last condition is sure), which does not require either electric or magnetic fields to create the Hall potential difference. The technique developed by us [7,8] is based on the phenomenon of rearrangement of the spectrum of charge carriers in the near-surface layer of a hole HTSC being in contact with a normal metal (Me). This phenomenon is a consequence of the annihilation of "aboriginal" hole fermions in the HTSC/Me interface with electrons penetrated from Me. The essence of this technique is the registration of changes in the resistance of the HTSC/Me interface rС, which is characterized by a small number of hole carriers. The appearance of the temperature singularities of rC and the sign of rC  variation (drС) make it possible to obtain an idea of the character of the changes in the system of charge carriers of the HTSC array.

The dependences rC(T) of the Bi(Pb)SrCaCuO/Pb and YBaCuO/In interfaces have been studied and anomalies near the temperature of the pseudogap opening and before the superconducting transition have been observed. We are shown that in Bi(Pb)SrCaCuO and YBaCuO, when the temperature T=TC+(~10 K) is reached, that do not concerns to fluctuating Cooper pairs condensation. So, there is due to changing the topology of the FS. As a result, significant piece of FS becomes electronic. The most probable reason for the topological transition is the achievement of the temperature of the 2D-3D crossover (the temperature of the three-dimensionality of HTSC), which is a consequence of a modification in the electronic subsystem that leads to a change in the interaction mechanisms of the fluctuation Cooper pairs [9, 10].

1. The Physics of Superconductors, Vol.1. Conventional and High-TC Superconductors. Ed. by K.H. Bennemann and J.B. Katterson, Berlin, Springer, (2003).

2. K. Kawabata, S. Tsukui, Y. Shono, O. Michikami, H. Sasakura, K. Yoshiara, Y. Kakehi, T. Yotsuya, Phys. Rev. B58, 2458 (1998).

3. I.M. Lifshits, JETP 38, 1569 (1960) (in Russian).

4. Q. Zhang, J. Xia, M. Fang, Z. He, S. Wang, Z. Chen, Physica C 162-164, 999 (1989).

5. A.L. Solovjov, FNT 24, 215 (1998) (in Russian).

6. T. Kondo, A.D. Palczewski, Y. Hamaya, T. Takeuchi, J.S. Wen, Z.J. Xu, G. Gu, A. Kaminski, arXive: 1208.3448v1 (2012).

7. V.I. Sokolenko, V.A. Frolov, FNТ 39, 134 (2013) (in Russian).

8. V.A. Frolov, VANТ, Ser.: Vacuum, pure materials, superconductors, 1, 176 (2016) (in Russian).

9. Y.B. Xie, Phys. Rev., B46, 13997 (1992).

10. A.L. Solovjov, V.M. Dmitriev, FNT 35, 227 (2009) (in Russian).


Sokolenko V.I., Frolov V.A.

JETP Letters 105, issue 10 (2017)


Correct allowing for the interparticle interaction in many-body systems faces considerable mathematical difficulties. The most frequently used approximation in such problems is the mean field approximation (MFA) which neglects fluctuations and the particles are considered as a continuous medium of inhomogeneous density. If , moreover, the system is described by the classical distribution function ( the statistics can be a quantum one) we obtain the well known Thomas - Fermi approach .However there are situations when at least some of the degrees of freedom of the system have to be treated in accord with quantum mechanics. Such examples are electrons in quantum wells or dipolar excitons in an electrostatic trap. In such cases the density of particles appearing in MFA is to be expressed via wave functions of a particle in the effective potential. The latter, in its turn, depends on the wave functions and occupation numbers, so one has to solve a self-consistent problem. In case of a short-range interparticle pair potential (2D gas of dipolar excitons) a nonlinear wave equation arises while for the long-range ( Coulomb) pair interaction the corresponding equation becomes integro-differential (nonlocal effects).

            Two different systems are considered: bose - gas of dipolar excitons in a ring shape trap and fermi-gas of electrons in a quantum well of a MOS-structure. The trapped excitons are described by the Gross-Pitaevskyi nonlinear equation and for the very simple case of the rectangular potential of the “empty” trap the exact analytical solution is found. The most interesting result of this problem is criterion for existence of bound state in the effective potential ( in the one particle problem a 1D symmetric potential well always contains at least one bound state) . Methodologically instructive is the way of obtaining the eigenvalue of the Gross-Pitaevskyi equation: the ground state energy is found from the normalization condition.

            In case of electrons in a quantum well one deals with nonlinear integro-differential equation for which the exact solution is unknown. The direct variational method was used to find the frequency of the intersubband transition. This frequency turned out to be scaled with the electron concentration N as $N^{2/3}$.



Chaplik A.V. JETP Letters 105 (9) (2017)

 A model of fermion condensation, advanced more than 25 years ago, still remains the subject of hot debates,  due to the fact that  within its frameworks, non-Fermi-liquid (NFL) behavior, ubiquitously exhibited  by  strongly correlated Fermi systems, including electron   systems of solids, is properly elucidated.  The model  is   derived  with the aid of   the same  Landau postulate  that the ground state energy $E$ is  a functional of its quasiparticle momentum distribution $n$,  giving  rise to the conventional Landau state. However, the model discussed deals with completely different  solutions,  emergent beyond  a critical point, at which the topological stability of the Landau state breaks down, and therefore relevant solutions of the problem  are found from   the well-known   variational condition of mathematical physics  $\delta E(n)/\delta n({\bf p})=\mu$ where $\mu$ is the chemical potential. Since the left side of this condition   is nothing but the quasiparticle energy $\epsilon({\bf p})$, the variational condition    does  imply formation of the flat band or, in different words,  a fermion condensate (FC). In fact,  variational condition  furnishes an opportunity to find solely the FC quasiparticle momentum distribution $n_*({\bf p}\in \Omega)$.

    A missing point is  concerned with   the single-particle spectrum of  quasiparticles in the complementary  domain   ${\bf p}\notin\Omega$. Originally,  at variance with recent experimental data, the  model spectrum $\epsilon({\bf p}\notin\Omega )$ was assumed to be gapless. To clarify the situation with the true character of this spectrum  we employ a    microscopic  approach to theory of Bose liquid created by S.Belyaev, where the interaction between  the condensate and non-condensate particles, giving rise to the emergence of a singular part of the self-energy, is treated properly.
    Unfortunately, in systems having a FC, evaluation of any FC propagator in closed form is impossible, since in contrast to the BC, the FC occupies a finite domain of momentum space. As a result, methods appropriate to evaluation of the multi-particle BC  propagators, fail to deal with corresponding FC propagators.
    In this situation, the only practical approach to solution of the problem involves the implementation of  an iterative  procedure, appealing to the smallness of the ratio $\eta=\rho_c/\rho$ where the numerator is   the FC density  and the denominator, total density. In the article, leading,  in the limit $\eta\to 0$,  contributions  to the singular part $\Sigma_s$ of the self-energy are calculated along the  Belyaev's theory lines. By virtue of the finite range of the FC domain, the  structure  of $\Sigma_s$ turns out   to be different, compared with that in the  boson case, treated by Belyaev. As a result,  the evaluated spectrum     of single-particle excitations of Fermi  systems, hosting flat bands, acquires a gap, so that the FC itself becomes a midgap state.

 In obtaining  the gap solution  we assumed  the effective interaction between particles in the particle-particle channel to have   sign,  which  prevents Cooper pairing, implying that the  ground state constructed  is not superfluid. In this situation, the gap  in the  single-particle spectrum is a Mott-like gap.

 The  theory   constructed is applied to   the explanation of the metal-insulator transition in  low-density homogeneous  2D  electron systems, like  those, which reside in silicon field-effect  transistors. These systems are known to become insulators  at  $T\to 0$ provided electron density declines below  a critical value $n_c\simeq 0.8\times 10^{11}cm^{-2} $ [1-4], its value being substantially larger  than that dictated by a standard Wigner crystallization scenario. Importantly,  the electron effective mass $M^*(n)$,  extracted from  corresponding measurements of   the   thermopower  diverges at almost the same value $n_t=0.78\times 10^{11}cm^{-2} $ [5], in agreement with the proposed scenario for the metal-insulator  transition in MOSFETs, triggered by the onset of fermion condensation  and  subsequent   opening  the Mott-like gap in the electron single-particle spectrum.        

     This scenario is also applied to the elucidation of a challenging  phenomenon uncovered in the analysis of ARPES data on  two-dimensional anisotropic  electron systems of cuprates. It consists in  breaking down of the Fermi line   into several  disconnected segments located in the antinodal region, (the  Fermi arc structure),  and   usually attributed to superconducting fluctuations  [6]. In the context of this article, the existence or disappearance of   the Fermi line is related to the FC arrangement. In cuprates, the FC occupies four different spots, every of which  is   associated with its own saddle point. Such a    configuration of the FC spots promotes the occurrence of   a  well pronounced gap in the spectrum   of  single-particle states,  located in the antinodal region. However, for single-particle states, located in the nodal region, the situation with the gap is opposite and therefore  in this domain of momentum space,  the  spectrum $\epsilon({\bf p})$  remains  gapless, in agreement with the experiment.

[1]. V. Kravchenko et al.,  Phys. Rev. 50,8039  (1994).

[2]  S. V. Kravchenko, Phys. Rev. 51, 7038  (1995).

[3]  E. Abrahams,  S.V. Kravchenko, M. P. Sarachik, Rev. Mod. Phys. 73, 251 (2001).

[4]  A. A. Shashkin, Phys. Usp. 48, 129 (2005).

[5]  A. Mokashi et al.,  Phys. Rev. Lett. 109, 096405 (2012).        

[6] B. Keimer, S. A. Kivelson, M. R. Norman, S. Uchida, J. Zaanen, Nature 518, 179 (2015).

                                                                             Khodel V. A.,

JETP Lett. 105 (8) (2017).  

Materials harder than diamond are always attract great attention from the scientists all over the world. Many attempts were made towards the synthesis especially of carbon material harder than diamond, which is the hardest possible material nowadays. A special interest belongs to materials called as fullerites. There are several experimental and theoretical works, where the synthesis and investigation of superhard fullerite were carried out. [1]–[4] Such materials reveal outstanding mechanical properties with the bulk modulus of several times higher than that of diamond.

In this case the computational approaches and methods allow the theoretical investigations and prediction of a new materials with desired properties without using very expensive experimental equipment. Here we used the state-of-the-art theoretical methods of computational predictions to predict new carbon phases based on the fullerene molecules of different sizes (C60 and C20). Using the evolutionary algorithm, implemented in USPEX package, [5] we considered more than 3000 possible crystal structures to find the most stable ones. The important point, that predicted phases are based on the polymerized fullerites, displaying the superior mechanical properties. We defined the crystal structure of predicted 4 stable allotropes by simulating the XRD patterns. All predicted structures are highly symmetric. The mechanical properties were studied in details in terms of elastic tensor, bulk and shear moduli and velocities of acoustic waves. All predicted structures display elastic constants and bulk modulus very close to diamond, which allows to say that we indeed predict new superhard phases. The possible way of synthesis of such phases was proposed consisting in the cold compression of a mixture of graphite and C60 fullerenes. The important feature of predicted phases (besides the mechanical properties) is that they have relatively small band gap ~2.5 eV, while the cI24 phase has the direct gap of 0.53 eV.

All obtained data allows the conclusion that predicted superhard semiconducting phases based on the polymerized fullerenes reveal necessary properties for applications in the electronic as basic elements.


[1] V.D. Blank, S.G. Buga, G.A. Dubitsky, N. R Serebryanaya, M.Y. Popov, and B. Sundqvist, Carbon 36, 319 (1998).

[2] M. Popov, V. Mordkovich, S. Perfilov, A. Kirichenko, B. Kulnitskiy, I. Perezhogin, and V. Blank, Carbon 76, 250 (2014).

[3] Y.A. Kvashnina, A.G. Kvashnin, M.Y. Popov, B.A. Kulnitskiy, I.A. Perezhogin, E.V. Tyukalova, L.A. Chernozatonskii, P.B. Sorokin, and V.D. Blank, J. Phys. Chem. Lett. 6, 2147 (2015).

[4] Y.A. Kvashnina, A.G. Kvashnin, L.A. Chernozatonskii, and P.B. Sorokin, Carbon 115, 546 (2017).

[5] C.W. Glass, A.R. Oganov, and N. Hansen, Comput. Phys. Commun. 175, 713 (2006).





Kvashnina Yu.A., Kvashnin D.G., Kvashnin A.G., Sorokin P.B.

 JETP Letters  105 ( 7) (2017)


Recently  stochastic clustering  with statistical self-similarity (fractality) has been found on material surface exposed under extreme plasma thermal loads in fusion devices (see [1]). In such devices, multiple processes of erosion and redeposition of the eroded material, surface melting and motion of the surface layers lead to a stochastic surface growth on the scales from tens of nanometers to hundreds of micrometers. The moving of eroded material species during redeposition from plasma and agglomeration on the surface is governed by stochastic electric fields generated by the high-temperature plasma. The specific property of the near-wall plasma in fusion device is the non-Gaussian statistics of electric field fluctuations with long-range correlations [2]. It leads to the stochastic agglomerate growth with a self-similar structure (hierarchical granularity - fractality) of non-Gaussian statistics contrary to a trivial roughness observed in ordinary processes of stochastic agglomeration. The dominant factor in such process in fusion device is the collective effect during stochastic clustering rather than the chemical element composition and physical characteristics of the solid material. In support of this view it is reported in this Letter, that such similar stochastic fractal structure with hierarchical granularity and self-similarity is formed on various materials, such as  tungsten, carbon materials and stainless steel exposed to high-temperature plasma in fusion devices.  In the literature it is discussed hypotheses of universal scalings of stochastic objects and processes with multi-scale invariance property (statistical self-similarity), see e.g. [3]. The kinetic models propose the describing of the stochastic clustering with a self-similar structure and considering the power law solutions for the number N of agglomerating clusters with mass m (see e.g. [4]), N(m)=Cm-(3+h)/2,  where h is a self-similarity exponent of the agglomeration kinetic model, C is a constant factor.  It is surprisingly found in this Letter that such the power laws (with power exponents from -2.4 to -2.8) describing the roughness of the test specimens from fusion devices are strictly deviated from that of the reference samples formed in a trivial agglomeration process forming   Brownian-like rough surface (such as samples exposed to low-temperature glow discharge plasma  and rough steel casting with the power law exponent in  the range of -1.97 to -2.2).  Statistics of  stochastic clustering samples from fusion devices is typically non-Gaussian and has a "heavy" tails of probability distribution functions (PDF) of stochastic surface heights (of the Hurst exponent from 0.68 to 0.86). It is contrary to the Gaussian PDF of the reference samples with trivial stochastic surface.  Stochastic clustering of materials from fusion devices is characterised by multifractal statistics. Quantitative characteristics of statistical inhomogeneity of such material structure, including multifractal spectrum with broadening of  0.5 ¾ 1.2, are in the range observed for typical multifractal objects and processes in nature. This may indicate a universal mechanism of stochastic clustering of materials under the influence of high-temperature plasma.


1. V.P. Budaev et al., JETP Letters vol. 95,   2, 78 (2012).

2. V.P. Budaev, S.P. Savin, L.M.  Zelenyi,   Physics-Uspekhi 54 (9),   875   (2011)

 3. A. L. Barabasi and H. E. Stanley, Fractal Concepts in Surface Growth (Cambridge Univ. Press, Cambridge, 1995).

4. C. Connaughton, R. Rajesh, O. Zaboronski, PRL 94 (19), 194503 (2005).





V.P. Budaev, JETP Letters    vol. 105, issue 5 (2017)

Modern physics of liquid crystals is much younger than its traditional condensed matter material counterparts. Therefore the field is not yet completely elaborated and exhausted, and one may  still expect discoveries of new mesogen materials exhibiting of new types of liquid-crystalline ordering. A few years ago such a discovery of so-called bent-core or dimer mesogens which can form short pitch heli-conical nematic state (also known as twist-bend nematics, $N_{TB}$) [1, 2], attracted a lot of interest to this new state of matter with nano-scale orientational modulation. First, to understand the nature of the phase, basically different from conventional uniform nematics and from modulated in mass density smectics (see e.g., Landau theory approach, [3,4]). Second, to exploit potentially very perspective applications of the $N_{TB}$ liquid crystals. Along this way, very recently S.M.Saliti, M.G.Tamba, S.N. Sprunt, C.Welch, G.H.Mehl, A.Jakli, J.T.Gleeson [5] observed of the unprecedentedly large magnetic field induced shift $\Delta T_c(H)$ of the nematic - isotropic transition temperature. What is even more surprising $\Delta T_c(H)$ does not follow the thermodynamics text-book wisdom prediction $H^2$ scaling. Our  interpretation of such a behavior is based on singular longitudinal fluctuations of the nematic order parameter. Since these fluctuations are governed by the Goldstone director fluctuations they exist only in the nematic state. External magnetic field suppresses the singular longitudinal fluctuations of the order parameter. The reduction of the fluctuations changes the equilibrium value of the modulus of the order parameter in the nematic state, and leads  to additional (with respect to the mean field contribution) fluctuational shift of the nematic - isotropic transition temperature. The mechanism works for any nematic liquid crystals, however the magnitude of the fluctuational shift increases with decrease of the Frank elastic moduli. Since some of these moduli supposed to be anomalously small for the  bent-core or dimer mesogen formed nematic liquid crystals, just these liquid crystals  are promising candidates for the observation of the predicted fluctuational shift of the phase transition temperature.
[1] V.P.Panov, M.Nagaraj, J.K.Vij, et al., Phys. Rev. Lett., 105, 167801 (2010).
[2] M.Cestari, S.Diez-Berart, D.A.Dunmur, et al., Phys. Rev. E, 84, 031704 (2011).
[3]  E.I.Kats, V.V.Lebedev, JETP Letters,  100, 118-121 (2014).
[4] L.Longa, G.Pajak, Phys. Rev. E,  93, 040701 (2016).
[5] S.M.Saliti, M.G.Tamba, S.N. Sprunt, C.Welch, G.H.Mehl, A.Jakli, J.T.Gleeson, Phys. Rev. Lett., 116, 217801 (2016).

                                                                      E.I. Kats

JETP  Letters 105 (4)  (2017)

In a recent letter A. Danan et al. [A. Danan, D. Farfurnik, S. Bar-Ad et al., Phys. Rev. Lett. 111, 240402 (2013)] have experimentally demonstrated an intriguing behavior of photons in an interferometer. Simplified layout of the experimental setup represents a nested Mach-Zehnder interferometer (MZI) and is shown below.

The surprising result is obtained when the inner MZI is tuned to destructive interference of the light propagating toward mirror F. In that case the power spectrum shows not only peak at the frequency of mirror C but two more peaks at the frequencies of mirrors A and B, and no peaks at the frequencies of mirrors E and F. From these results authors conclude that the path of the photons is not represented by connected trajectories, because the photons are registered inside the inner MZI and not registered outside it.

These unusual results have raised an active discussion. Nevertheless, until now there was no comprehensive and clear analysis of the experiment within the framework of the classical electromagnetic waves approach.

In this letter, we calculate  the signal power spectrum at the output of the nested MZI, based on traditional concept of the classical electromagnetic waves (or quantum mechanics).  This concept imply the continuity of the wave (photon) trajectories. We give intuitive clear and  comprehensive explanation of paradoxical results. So,  there is no necessity for a new concept of disconnected trajectories.


Simplified experimental setup with two nested Mach-Zehnder interferometers. A, B, C, E, and F stands for mirrors; BS1 and BS2, and PBS1 and PBS2 stands for ordinary and polarized beam splitters respectively. The elements BS1, A, B, and BS2 form an inner MZI whereas the elements PBS1, C, E, F and PBS2 form an outer MZI. Various mirrors inside the MZI vibrate with different frequencies. The rotation of a mirror causes a vertical shift of the light beam reflected off that mirror. The shift is measured by a quad-cell photodetector QCD.  When the vibration frequency of a certain mirror appears in the power spectrum, authors conclude that photons have been near that particular mirror




                                                                 G.N.Nikolaev JETP Letters 105 (3)  (2017)

   The dynamics of the quantum vacuum is one of the major unsolved problems of relativistic quantum field theory and cosmology. The reason is that relativistic quantum field theory and general relativity describe processes well below the Planck energy scale, while the deep ultraviolet quantum vacuum at or above the Planck energy scale remains unknown. Following the condensed matter experience we develop a special macroscopic approach called q-theory, which incorporates the ultraviolet degrees of freedom of the quantum vacuum into an effective theory and allows us to study the dynamics of the quantum vacuum and its influence on the evolution of the Universe.

     The vacuum in our approach is considered as the Lorentz-invariant analog of a condensed-matter system (liquid or solid) which is stable in free space. The variable q is the Lorentz-invariant analog of the particle number density, whose conservation regulates the thermodynamics and dynamics of many-body systems. This approach is universal in the sense that the same results are obtained using different formulations of the q-field. In the paper, we choose the q-field in terms of a 4-form field strength, which has, in particular, been used by Hawking for discussion of the main cosmological constant problem -- why is the observed value of the cosmological constant many orders of magnitude smaller than follows from naive estimates of the vacuum energy as the energy of zero-point motion. In q-theory, the huge zero-point energy is naturally cancelled by the microscopic (trans-Planckian) degrees of freedom, as follows from the Gibbs-Duhem identity, which is applicable to any equilibrium ground state including the one of the physical


            In the paper, we consider a further extension of q-theory. We demonstrate that, in an expanding Universe, the variable  effectively splits into two components. The smooth part of the relaxing vacuum field is responsible for dark energy, while the rapidly oscillating component behaves as cold dark matter. In this way, q-theory provides a combined solution to the missing-mass problem and the cosmological constant problem. If this scenario is correct, the implication would be that direct searches for dark-matter particles remain unsuccessful in the foreseeable future.

F.R. Klinkhamer and G.E. Volovik,

JETP Letters  105, issue 2 (2017)

The ability to detect nonequilibrium spin accumulation (imbalance) by all electrical means is one of the key ingredients in spintronics . Transport detection typically relies on a nonlocal measurement of a contact potential difference induced by the spin imbalance by means of ferromagnetic contacts  or spin resolving detectors . A drawback of these approaches lies in a difficulty to extract the absolute value of the spin imbalance without an independent calibration. An alternative concept of a spin-to-charge conversion via nonequilibrium shot noise was introduced and  investigated in  experiment recently . Here, the basic idea is that a nonequilibrium spin imbalance generates spontaneous current fluctuations, even in the absence of a net electric current. Being a primary approach , the shot noise based detection is potentially suitable for the absolute measurement of the spin imbalance. In addition, the noise measurement can be used for a local non-invasive sensing.

In this letter, we calculate the impact of a spin relaxation on the spin imbalance generated shot noise in the absence of inelastic processes. We find that the spin relaxation increases the noise up to a factor of two, depending on the ratio of the conductor length and the spin relaxation length. The design of the system. A diffusive normal wire of the length L is attached to normal islands on both ends. Nonequilibrium energy distribution on the left hand side of the wire generates the shot noise at a zero net current. The spin imbalance on the left-hand side of the wire is due to the electric current flowing from one ferromagnetic lead (red) to another one with opposite magnetization (blue).



V.S. Khrapai and K.E. Nagaev JETP  Letters 105, №1 (2017)