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"Tubular" lanthanum hydride as a new class of high-temperature superconducting material

    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)


"Tubular" lanthanum hydride as a new class of high-temperature superconducting material

    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)


High-temperature superconductivity of graphite particles embedded in polystyrene

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)



Folding in two-dimensional hydrodynamic turbulence

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).

Terahertz spectroscopy of two-dimensional semimetal in three-layer InAs/GaSb/InAs quantum well

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)     


Light absorption properties related to long-living ensemble spin excitations in an unpolarized quantum Hall system

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)

Search for high-energy neutrinos from GW170817 with the Baikal-GVDneutrino telescope


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  180, issue 12 (2018)





Spin diffusion in liquid $^3$He confined in planar aerogel
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)

Chiral torsional effect
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)


Hidden Fermi surface in $K_xFe_{2-y}Se_2 : LDA+DMFT $ study

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)





Search for neutrinos with a mass (0.01-1.0) MeV in beta decays of nuclei $^{144}Ce - ^{144}Pr$

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)


Non-stationary spin-polarized currents tuning in correlated quantum dot

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)     


Sphaleron rate in lattice gluodynamics

 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)



Zitterbewegung of Spin Split Electrons

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)


Terahertz cyclotron photoconductivity in strongly unbalanced 2D electron-hole system

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)

Negative differential resistance and other features of spin-dependent electron transport in double-barrier hybrid superconductor-ferromagnetic metal-normal metal structures

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)                              

Zener Tunneling between Landau Levels in two-dimensional system with one-dimensional periodic modulation

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)

Investigation of novel two-dimensional CoC phase

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

On the thermal stability of pentagraphene

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)

Magnetic skyrmions in films with modulated thickness

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  106, issue 6 (2017)

Long-lived quantum vortex knots

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).

The spin kinetics of liquid 3He in contact with the microsized DyF3 powder at ferromagnetic ordering of Dy^{3+}

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.

.. lakshin, .I. Kondratyeva, V.V. Kuzmin, .R. Safiullin, .. Stanislavovas, .V. Savinkov, .V. Klochkov,  .S. Tagirov

JETP Letters 107 issue 2, 2018

Microparticles at the surface of liquid helium. Quantum version of Archimedes' principle

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

Superconductor-insulator transition in disordered NbTiN films

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)


Detection of spin excitation transfer in a 2D electron system by photoluminescence of multi-particle exciton complexes

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 .S.,
                                                             Larionov A.V., Timofeev V. B., Kukushkin I.V. 

                                                                                      JETP Letters 106, issue 10 (2017)

Helical edge transport in the presence of a magnetic impurity

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)

Breather chimeras in the system of phase oscillators

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)

Faraday Waves and Vortices on the Surface of Superfluid He-II.

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)


Superradiance Properties of a Suspension of Composite

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)

Energy Spectrum of the Spin States in $Sr_2FeSi_2O_7$ and Origin of the Magneto- Electric Coupling

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)

Electron-topological transition in copper-oxide high-TC superconductors before superconducting transition

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 r, which is characterized by a small number of hole carriers. The appearance of the temperature singularities of rC and the sign of rC  variation (dr) 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, FN 39, 134 (2013) (in Russian).

8. V.A. Frolov, VAN, 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)

Toward a self-consistent theory of Fermi systems with flat bands

 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).  

New allotropes of carbon based in the C60 and C20 fullerenes with outstanding mechanical properties

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)


Stochastic clustering of materials by plasma - surface interaction

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)

Fluctuational shift of nematic - isotropic phase transition temperature

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)

Paradox of photons disconnected trajectories being located by means of "weak measurements" in the nested Max-Zehnder interferometer

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)

Dark matter from dark energy in q-theory

   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)