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

 

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

JETP Letters 112, issue 3 (2020)

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

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

 

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

 

 

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

 

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

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

 

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

 

 

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

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

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

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

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

 

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

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

 

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

 

 

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

JETP Letters 112, issue 1 (2020)

 

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

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

 

 

V.I. Kukushkin et al.

JETP Letters 112, issue 1 (2020).

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

 



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

JETP Letters111, issue 11 (2020)
 

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

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

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

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

V.V. Val’kov

JETP Letters 111, issue11 (2020)

 

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

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

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

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

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

 

S.N.Molotkov
JETP Letters 111, issue 11 (2020)

 

 

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

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

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

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

 

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


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

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

JETP Letters 111, issue 12 (2020)

 

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

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

 

S.I.Dorozhkin

JETP Letters 111, issue 10 (2020)

 

 

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

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

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

                      Nikolaev I.D. et al.

JETP Letters 111, issue 10 (2020)

 


 

 

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

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

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

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

 

 G.E. Volovik                                           

JETP  Letters 111, issue 10  (2020)