Editor's Choice Anomalous scaling of the energy of ion beams in the current sheet Ion fluxes with group velocities up to 2000 km/s were detected in the plasma sheet boundary layer on high-apogee spacecrafts [1]. These fluxes are formed in the current sheet of the small-scale ion beams – beamlets [2], which are accelerated by the electric field at various distances along the magneto-tail of separated resonant N zones and, then, move along the magnetic field lines towards the auroral region. Experimental test [3] of the theoretically predicted scaling WN ~ NA (where WN is the energy of the Nth resonance and A ~ 1.33) [4] shows that the real scaling of resonance energies varies in a wide range A ∈ [0.61, 1.75]. Model calculations [3] with the addition of an electric field Ez perpendicular to the current sheet are in good agreement with the experimental data. This paper reports an experimental study of the energy scaling of beamlets (seven resonance zones N=1-7 with resonances R=1-7 were identified) using the data from SC-1 and SC-4 CLUSTER satellites for the event of 05.02.2003. Analysis of the ion beam signatures in the auroral magnetosphere in the range 1-20 kev showed that the energy of beamlets scales differently (0.04 and 0.40 for zones with resonances R=1-4, and 0.83 and 1.14 for zones with R=5-7, according to satellites SC-1 and SC-4, respectively). For zones with R=5-7, the energy scaling of the beamlets can be explained in accord  with the results of the work [3]. The observed parameters A in zones N=1-4 may be related to the fact that the normal component of the magnetic field Bz, which controls the increment of the ion beams energy in the current sheet, has spatial decay lower in the region of these resonant zones than in the region containing zones N=5-7. Therefore, the current sheet is inhomogeneous and is characterized by various conditions of the formation of its parts. [1] K. Takahashi, and E.W. Hones, J. Geophys. Res. 93, 8558 (1988). [2] L.M. Zelenyi, E.E. Grigorenko, and A.O. Fedorov, JETP Lett. 80, 663 (2004). [3] R.A. Kovrazhkin, M.S. Dolgonosov, and J.-A. Sauvaud, JETP Lett. 95, 234 (2012). [4] L.M. Zelenyi, M.S. Dolgonosov, E.E. Grigorenko, and J.-A. Sauvaud, JETP Lett. 85, 187 (2007).     R. A. Kovrazhkin, A.L. Glazunov, and G.A. Vladimirova JETP Letters 111, issue 4 (2020)         Four-fold anisotropy of the parallel upper critical magnetic field in a layered d-wave superconductor at T=0 Since the discovery of unconventional d-wave superconductivity in high-temperature superconductors, physical consequences of d-wave electron pairing have been intensively investigated. One of such physical properties is a four-fold symmetry of the parallel upper critical magnetic field in this quasi-two-dimensional (Q2D) superconductors. From the beginning, it was recognized that the four-fold anisotropy of the parallel upper critical magnetic field disappears in the Ginzburg-Landau (GL) region and has to be calculated as a non-local correction to the GL results. Another approach was calculation of the parallel upper critical magnetic field at low temperatures and even at T=0 using approximate method, which was elaborated for unconventional superconductors with closed electron orbits in an external magnetic field. Note that Q2D conductors in a parallel magnetic field are characterized by open electron orbits, which makes the calculations to be inappropriate. The goal of our article is to suggest an appropriate method to calculate the parallel upper critical magnetic field in a Q2D d-wave superconductor. For this purpose, we explicitly take into account almost cylindrical shape of its Fermi surface (FS) and the existence of open electron orbits in a parallel magnetic field. We use the Green's functions formalism to obtain the Gorkov's gap equation in the field. As an important example, we numerically solve this integral equation to obtain the four-fold anisotropy of the parallel upper critical magnetic field in a d(x^2-y^2}-wave Q2D superconductor with isotropic in-plane FS. In particular, we demonstrate that the so-called supercondcting nuclei at T=0 oscillate in space in contrast to the previous results. We also suggest the gap equation which take both the orbital and paramagnetic spin-splitting mechanisms against superconductivity. A.G.Lebed and Sepper O. JETP Letters 111, issue 4 (2020) On Planckian limit for inelastic relaxation in metals In recent years, a number of interesting papers appeared [1,2], where from the analysis of experiments on rather wide range of compounds, it was shown that in the $T$ - linear region of resistivity growth, the scattering rate of electrons (inverse relaxation time) with rather high accuracy is described as  $\Gamma=\frac{1}{\tau}=\alpha \frac{k_BT}{\hbar}$, where  $\alpha\sim 1$ and is weakly dependent on the choice of the material. In connection with these results the notion of the universal (independent of interaction strength) "Planckian'' upper limit of inelastic scattering rate in metals was introduced as $\frac{1}{\tau_P}=\Gamma_P=\frac{k_BT}{\hbar}$ [3]. To explain this "universality'' a number of relatively complicated theoretical models were proposed [4, 5], including some rather exotic, based on the analogies taken from the black hole physics, cosmology and superstring theory (e.g. see Refs. [6-9]). It is shown here that the  "Planckian'' limit for the temperature dependent relaxation rate actually follows from a certain procedure used in Refs. [1, 2] to derive $\frac{1}{\tau}$ from experimental data on resistivity, using the effective electron mass, determined from low - temperature experiments. Thus, the  "experimentally'' observed universal "Planckian'' relaxation rate in metals, independent of interaction strength, is nothing more than a kind of  delusion. [1] J.A.N. Bruin, H. Sakai, R.S. Perry, A.P. MacKenzie. Science 339, 804 (2013)       [2] A. Legros, S. Benhabib, W. Tabis, F. Laliberte, M. Dion, M. Lizaire, B. Vignole, D. Vignolles, H, Raffy, Z.Z. Li, P. Auban-Senzier, N. Doiron-Leyraud, P. Fournier, D. Colson, L.Taillefer, C.Proust. Nature Physics 15, 142 (2019)       [3] J. Zaanen. Nature 430, 512 (2004)       [4] V.R. Shaginyan, M.Ya. Amusia, A.Z. Msezane, V.A. Stephanovich, G.S. Japaridze, S.A. Artamonov. JETP Letters 110, 290 (2019)       [5] A.A. Patel, S. Sachdev. Phys. Rev. Lett. 123, 066601 (2019)       [6] J. Zaanen. Nature 448, 1000 (2007)       [7] S.A. Hartnoll. Nature Physics 11, 54 (2015)       [8] C.P. Herzog, P. Kovtun, S. Sachdev, D.T. Son. Phys. Rev. D 75, 085020 (2007)       [9] S.A. Hartnoll, P.K. Kovtun, M. Muller, S, Sachdev. Phys, Rev. B 76, 144502 (2007) M.V. Sadovskii JETP Letters 111, issue 3 (2020)   Phase diagrams of iron hydrides at pressures of 100-400 GPa and temperatures 0-5000 K Discovery of high critical temperatures of superconductivity in sulfur [1, 2], lanthanum, and yttrium hydrides [3-5] led to the active search for stable structures of hydrides of other elements, including iron. Iron hydrides are characterized by a critical temperature of ~50 K and can conditionally be classified as high-temperature superconductors. On the other hand, hydrogen is considered as one of the possible light elements of the Earth’s and planets core, which causes interest in phase relationships for the Fe-H system over a wide range of pressures and temperatures. In this work, within the density functional theory, the thermodynamic stability of iron hydrides Fe4H, Fe2H, FeH, Fe3H5, FeH2, FeH3, FeH4, Fe3H13, FeH5 and FeH6 at temperatures up to 5000 K in the pressure range of 100-400 GPa was estimated and the corresponding phase PT-diagrams were calculated. We performed a topological analysis of all stable iron hydrides. The regularity of the formation of dumbbell-shaped hydrogen molecules with increasing hydrogen concentration in iron hydrides was established.  [1] A. Drozdov, M. Eremets, I. Troyan, V. Ksenofontov, S. Shylin, Nature 525, 73 (2015)  [2] D. Duan, Y. Liu, F. Tian, D. Li, X. Huang, Z. Zhao, H. Yu, B. Liu, W. Tian, T. Cui, Scientific Reports 4, 6968 (2014).  [3] A. Drozdov, P. Kong, V. Minkov, S. Besedin, M. Kuzovnikov, S. Mozaffari, L. Balicas, F. Balakirev, D. Graf, V. Prakapenka, Nature 569, 528 (2019).  [4] H. Liu, I. I. Naumov, R. Hoffmann, N. Ashcroft, R. J. Hemley, Proceedings of The National Academy of Sciences 114, 6990 (2017).  [5] M. Somayazulu, M. Ahart, A. K. Mishra, Z. M. Geballe, M. Baldini, Y. Meng, V. V. Struzhkin, R. J. Hemley, Physical Review Letters 122, 027001 (2019). D.N. Sagatova et al. JETP Letters 111, issue 3 (2020)   The role of the chiral phase transition in modelling the kaon to pion ratio The search of a quark-gluon plasma (QGP), where hadrons dissolve and quarks are supposed to be free and deconfined, is difficult due to the short QGP lifetime. Various signals were proposed for detection of the QGP phase, and the ''horn'', which appears in the ratio of positive charged kaon to pion, was supposed be one of them [1]. Nowdays the picture of this peak becomes more clear on the experimental side: the peak appears in the ratio of positive charged kaons and pions at the collision energy $\sqrt{s_{NN}}\sim$ 7-10 GeV for the large-size systems in  Au+Au and Pb+Pb collisions. With decreasing system size, the sharp peak becomes lower and for Be+Be,  p+p collisions the ratio demonstrates smooth behaviour [2]. On the theoretical side, the quick increase in the $K^+/\pi^+$ ratio and its decreasing and flattering with further energy increasing is interpreted as a sequence of the chiral symmetry breaking and subsequent deconfinement effect. In our works [3, 4], including the present one, we discussed the chiral phase transition, deconfinement transition and in-medium behaviour of the pseudo-scalar mesons in the framework of the SU(3) Polyakov loop extended NJL model. Using the model it was shown how $K/\pi$ ratio changes as function of $T/\mu_B$, when T and $\mu_B$ are chosen on the phase diagram along the chiral phase transition curve and discussed in this way how the chiral phase transition can affect to the $K/\pi$ behaviour.   Several modifications of the model was considered, including the model with vector interaction, where the situation with the absence of the first order transition region can appear when the vector coupling constant is high enough. We can conclude that the peak appears in the range of low temperatures and high baryon chemical potential (which corresponds to low collision energy).  The appearance of the peak is weakly sensitive to the type of phase transition in the high density region, as the replacement of the the first order transition to the soft crossover only leads  to a changing in the peak hight. The peak structure is more sensitive to the slope of the phase transition curve at low T and the properties of the matter. For example, the hight of the peak is sensitive to the chemical potential of the strange quark. For the case with the zero strange chemical potential ($\mu_S(\mu_K) = 0$), the $K^+/\pi^+$ ratio shows smooth behaviour, and when the strangeness neutrality is introduced, the $K^+/\pi^+$ ratio does not show a clear peak structure.   1. S. V. Afanasiev et al. (NA49 Collabration), Phys. Rev. C 66, 054902 (2002); C. Alt,et al (NA49 Collaboration) Phys.Rev. C 77, 024903 (2008). 2. A. Aduszkiewicz (NA61/SHINE Collaboration) Nucl. Phys. A 967, 35 (2017). 3. A. V. Friesen, Yu. L. Kalinovsky, V. D. Toneev Phys. Rev. C 99, 045201 (2019). 4. A. V. Friesen, Yu. L. Kalinovsky, V. D. Toneev, PEPAN Letters, 16, 681 (2019).   A. V. Friesen, Yu. L. Kalinovsky, V. D. Toneev JETP Letters 111, issue 3 (2020)       Electron-hole liquid in monolayer heterostructures based on transition metal dichalcogenides Monolayer films of transition metal dichalcogenides (TMD) (in particular, MoS$_2$, MoSe$_2$, WS$_2$, and WSe$_2$) can be considered an ideal system for studying a high-temperature electron-hole liquid (EHL). The quasi-two-dimensional nature of electrons and holes defines a stronger interaction compared to bulk semiconductors. Screening of the Coulomb interaction in monolayer heterostructures is significantly weakened, because it is determined by permittivity of the environment (e.g., vacuum and substrate), which are much smaller than that of TMD films. The multivalley structure of the charge carriers energy spectrum in TMD many times reduces the kinetic energy. This leads to  increase in the equilibrium density and binding energy of EHL.  The optical properties of the monomolecular TMD layers are generally determined by excitons and trions. The binding energy of the exciton $E_x$ in the TMD is hundreds of meV. For example, in the monolayers MoS$_2$ $E_x=420$ meV [1]. The binding energy of EHL on one electron-hole pair is $\left|E_\text{EHL}\right|\sim E_x$, and the critical temperature for the gas--liquid phase transition is $T_c\sim0.1\left|E_\text {EHL}\right|$ [2--4]. So, we can expect that EHL will be observed in TMD monolayers even at room temperature. A high-temperature strongly bound EHL with $T_c\simeq500$ K was already observed in the MoS$_2$ monolayers [5]. In this paper, we are theoretically investigating the possibility of the formation of EHL in monolayers of multi-valley semiconductors. We consider a thin film of a model multi-valley semiconductor on an insulator substrate in vacuum. The semiconductor has a large identical number of equivalent electron $\nu_e$ and hole $\nu_h$ valleys $\nu_e=\nu_h=\nu\gg1$. A large number of valleys can be achieved due to the presence of several monomolecular layers in the film. We found analytically the binding energy of EHL and its equilibrium density and compared the results of calculations with experimental values. [1] Y. Yu, Y. Yu, Y. Cai, W. Li, A. Gurarslan, H. Peelaers, D.E. Aspnes, C.G. Van de Walle, N.\,V. Nguyen, Y.-W. Zhang, and L. Cao, Sci. Rep.5, 16996 (2015). [2] E.A. Andryushin, V.S. Babichenko, L.V. Keldysh, T.A. Onishchenko, and A.P. Silin, JETP Lett. 24, 185 (1976). [3] E.A. Andryushin, L.V. Keldysh, and A.P. Silin, JETP 46, 616 (1977). [4] Electron-Hole Droplets in Semiconductors ed. C.D. Jeffries and L.V. Keldysh (Amsterdam: North-Hollalnd, 1983). [5] Y. Yu, A.W. Bataller, R. Younts, Y. Yu, G. Li, A.A. Puretzky, D.B. Geohegan, K. Gundogdu, and L.Cao,  ACS Nano 13, 10351 (2019). P.L. Pekh, P.V. Ratnikov, and A.P. Silin JETP Letters111, issue 2 (2020)     Nonlinearly enhanced linear absorption of mid-infrared pulse undergoing filamentation in high pressure gases Ten years after recognition of the Nobel Prize, the chirped pulse amplification technique, was first implemented [1] and the unique regime of long-range femtosecond pulse propagation was discovered [2]. This propagation regime without beam divergence, or filamentation, was studied  with  Ti:Sapphire laser systems centered at ~800 nm with pulse peak power of 1010–1013 W [3]. Ultrashort pulse filamentation is accompanied by supercontinuum conical emission [4]. The atmospheric transparency window [5] in the visible range ensures lossless propagation of supercontinuum blue wing in the course of backward propagation after reflection from the cloud [6]. However, the fingerprints of atmospheric molecular pollutants are in the mid- and far-infrared range [5]. Besides, the critical power for self-focusing is proportional to the squared wavelength and achieves several hundreds of gigawatts for mid-infrared pulse propagating in air. This requires the pulse energy of at least several tens of milliJoules (pulse duration of about 100 fs) to form a filament on an atmospheric path. In order to target the application of femtosecond lidar in the mid-infrared part of the spectrum, we suggested the generalized approach for identification of the optimum laser wavelength for supercontinuum remote sensing applications [7,8]. We also developed the gas cell [9] for pressures 10–3–120 bar and temperatures up to 150°C to reach the filamentation with sub-milliJoule pulses. Our long cell of 75-cm length provides the filamentation in high-pressure gas in the quasi-collimated geometry close to atmospheric path experiments. The gas dispersion in the cell can be continuously tuned from normal to anomalous in the vicinity of water absorption band at 1.35 mm. The reservoir with water is installed into the gas cell and is additionally heated. In our experiments the cell was filled with nitrogen (30 bar) and water vapor (200 Pa). The laser pulses of ~100-mJ energy and 1.3-mm central wavelength propagate in the cell. The nonlinearly enhanced linear absorption was revealed in the long-wavelength part of the supercontinuum spectrum; this observation confirmed the theoretical prediction [7] of launching the pulse on the red (long-wavelength) side of the absorption line to ensure the maximum transmission through gases.   [1] D. Strickland and G. Mourou, Opt. Commun. 55, 447 (1985). [2] A. Braun, G. Korn, X. Liu, D. Du, J. Squier, and G. Mourou, Opt. Lett. 20, 73 (1995). [3] S. L. Chin, S. A. Hosseini, W. Liu, Q. Luo, F. Théberge, N. Aközbek, A. Becker, V. P. Kandidov, O. G. Kosareva, and H. Schroeder, Can. J. Phys. 83, 863 (2005). [4] O. G. Kosareva, V. P. Kandidov, A. Brodeur, C. Y.Chien, and S. L. Chin, Optics letters 22, 1332 (1997). [5] L. Rothman et al., J. Quantum Spectrosc. Radiat. Transfer 130, 4 (2013), HITRAN2012 special issue. [6] J. Kasparian et al., Science 301, 61 (2003). [7] N. A. Panov, D. E. Shipilo, V. A. Andreeva, O. G. Kosareva, A. M. Saletsky, H. Xu, and P. Polynkin Phys. Rev. A 94, 041801 (2016). [8] N. A. Panov, D. E. Shipilo, A. M. Saletsky, W. Liu, P. G. Polynkin, and O. G. Kosareva Phys. Rev. A 100, 023832 (2019). [9] V. O. Kompanets, D. E. Shipilo, I. A. Nikolaeva, N. A. Panov, O. G. Kosareva, S. V. Chekalin “Nonlinear enhancement of resonant absorption under filamentation of mid-infrared laser pulse in high-pressure gas” JETP Lett. accepted for publication, December 2019. V. O. Kompanets, D. E. Shipilo, I. A. Nikolaeva, N. A. Panov, O. G. Kosareva, S. V. Chekalin JETP Letters 111, issue 1 (2020)     Non-quadratic transverse magnetoresistance in the nodal-line Dirac semimetal InBi   Quasiparticles with the Dirac spectrum arise in a number of materials. Well-known examples are graphene, topological insulators, Dirac semimetals. More recently, it has been found that there are also materials in which the vertices of the Dirac cone are not at one or more points of the Brillouin zone, but form a line [1]. A feature of nodal-line Dirac semimetals is the much higher density of Dirac states than in materials with Dirac points, which allows us to hope for a more vivid manifestation of the properties due to Dirac fermions.   ARPES study supported by first-principle calculations show that InBi is a Dirac semimetal in which the vertices of the Dirac cone form the lines in the momentum space along the directions MA and XR of the Brillouin zone, i.e. in the directions along the c axis [2]. Earlier studies of magnetoresistance in InBi indicate the presence of an extremely large positive transverse quadratic magnetoresistance, which exceeds 2 orders of magnitude and does not saturate in high magnetic fields [3]. The absence of saturation and its anomalously high value are associated with the equality of the concentrations of electrons and holes whose mobility at helium temperatures exceeds 104 cm2/V·s [3].      In this work, we present the results of high precision measurements of the transverse magnetoresistance in InBi. These enable us to distinguish features which were not observed previously. In particular, we found that the dependence of the resistance R on  magnetic field B does not follow the simple quadratic law  R(B) = R0 + bB2. Namely, at B < 0.1 T, it is characterized by high curvature,  at B > 1 T it approaches a quadratic law with a curvature several times smaller, and in the intermediate region it is described by the sum of linear and quadratic contributions. The observed deviation from the quadratic dependence corresponds to a linear contribution, which is expected for nodal-line Dirac semimetals [4]. We also proposed a simple formula                                                            R(B) = R0+R1(1+η2B2)1/2+bB2,             describing all the detected features of the magnetoresistance of the nodal-line Dirac semimetal InBi within the experimental accuracy of a few percent.   [1] A. A. Burkov, M. D. Hook, and L. Balents, Phys. Rev. B 84, 235126 (2011).        [2] S.A. Ekahana, Sh.-Ch. Wu, J. Jiang, K. Okawa, D. Prabhakaran, Ch.-C. Hwang, S.-K. Mo, T. Sasagawa, C. Felser, B. Yan, Zh. Liu and Yu. Chen, New J. Phys. 19, 065007 (2017).        [3] K. Okawa, M. Kanou, H. Namiki, and T. Sasagawa Phys. Rev. Materials 2, 124201 (2018).        [4] H. Yang and F. Wang, arXiv:1908.01625.   S.V. Zaitsev-Zotov and I.A. Cohn JETP Letters 111, issue 1 (2020) Manifestation of spin superfluidity at room temperature Superfluid 3He is a well-known condensed matter whose properties are described by quantum field theory. Upon transition to superfluid states, gauge and spin and orbital rotational symmetries are violated simultaneously, demonstrating the properties of antiferromagnetic superfluid liquid crystals. In these systems, spin superfluidity was discovered - quantum transfer of spins controlled by the gradient of the magnetization precession phase. Spin supercurrents provide coherence during the magnetization precession: the precession becomes coherent even in a strongly inhomogeneous magnetic field. This leads to a long-lived signal of free induction, which was observed experimentally, see Review [1]. An even more complex interaction between the spin and orbital degrees of freedom leads to the formation of an extremely long live signal, which was explained in terms of the Coleman Q-ball model [2]. For a long time, magnetic resonance in solid-state magnets was considered in the limit of small perturbations, which corresponds to a low concentration of no equilibrium magnons. However, at high concentrations, magnons can experience Bose condensation, as in superfluid 3He. Moreover, in the case of a repulsive interaction, magnons can form a superfluid state and exhibit spin superfluidity properties in a solid magnets [3]. In particular, manifestations of a superfluid spin state in yttrium iron garnet (YIG) at room temperature have recently been discovered [4]. This article presents the results of observations of a very long-lived induction decay signal obtained in a YIG at room temperature. Its properties are partially similar to the Q-ball observed in superfluid 3He. Nevertheless, there are some fundamental differences with the Q-ball, which require the correct theoretical explanation. The formation of this long-lived signal can be a manifestation of quantum field theory at room temperature.  [1]. Yu. M. Bunkov, G. E. Volovik  “Spin superfluidity and magnon BEC” Chapter IV of the book "Novel Superfluids", eds. K. H. Bennemann and J. B. Ketterson, Oxford University press, (2013) . [2].  S. Autti, Yu. M. Bunkov, V. B. Eltsov,   et al. “Self-trapping of magnon Bose-Einstein condensates in the ground and excited levels: from harmonic  to a box confinement”  Phys. Rev. Lett. 108, 145303 (2012). [3]. Yu. M. Bunkov,  E. M. Alakshin,2 R. R. Gazizulin, et al., “High-Tc Spin Superfluidity in Antiferromagnets” Phys. Rev. Lett. 108, 177002 (2012). [4]. Yu. M. Bunkov, A.Farhutdinov A. N. Kuzmichev, et al., “The magnonic superfluid droplet at room temperature”  https://arxiv.org/pdf/1911.03708.pdf     Yu.M.Bunkov, P.M.Vetoshko, A.N.Kuzmichev, G.V.Mamin. S.B.Orlinsky, T.R.Safin, V.I.Belotelov, M.S.Tagirov.   JETP Letters 111, issue 1 (2020)     Direct measurements of spin subsystem picosecond heating kinetics in diluted magnetic semiconductor nanostructures In recent years, a rapidly developing field of science and technology - spintronics - has attracted much attention. New principles for the operation of devices have been proposed, in which the electronic spin is used along with its charge to transmit and process information. The main tasks of semiconductor spintronics are the investigations of the carrier spins injection, orientation, accumulation and detection processes and the study of the possibilities of controlling them by optical and electrical methods. Diluted magnetic semiconductors and nanostructures based on II – VI materials with manganese ions are considered as model objects for possible applications in spintronics. In such structures, magnetic Mn2+ ions isoelectronically replace metal ions in cationic sublattices. The low-temperature spectra of magneto-optical photoluminescence provide quantitative information on the temperature and magnetization of the Mn ions subsystem. Indeed, the exciton luminescence line shift in external magnetic fields is directly proportional to the magnetization, which makes it possible to experimentally implement the internal thermometer of the magnetic ions spin temperature, since temperature increase leads to a decrease in the Zeeman shift of the emission band. Measurements of the low-temperature exciton luminescence spectra with time resolution in external magnetic fields also allow one to study the dynamics of changes in the spin subsystem magnetization and temperature of diluted magnetic semiconductor structures when non-equilibrium magnetization is created in them, for example, using high-power pulsed optical pumping [1]. To determine the real interaction time of carriers with magnetic ions, it is very important to study diluted magnetic semiconductor superlattices with type II band alignment. In such structures based on (Zn,Mn)Se/(Be,Mn)Te the type II band alignment makes it possible to experimentally change the interaction time of photoexcited carriers with magnetic ions. At high levels of optical excitation inside ZnSe/BeTe superlattices, due to the high concentration of spatially separated charges of electrons and holes, strong electric fields arise, which in turn lead to strong band bending [2]. Strong band bending leads to the formation of metastable above-barrier hole states [3], which increases the hole lifetimes in the ZnSe layer. In the present paper the magnetization kinetics in diluted magnetic semiconductor type II superlattices Zn0.99Mn0.01Se/Be0.93Mn0.07Te in external magnetic fields was studied using an optical technique with a high temporal resolution ~ 2 ps. For the first time, direct measurements of the picosecond kinetics of the process of energy and spin transfer from photoexcited carriers due to the exchange interaction with the localized spins of Mn2+ ions were performed and the energy and spin transfer time τ ≈ 17 ± 2 ps was determined. [1] M.K. Kneip, D.R. Yakovlev, M. Bayer, A.A. Maksimov, I.I. Tartakovskii, D. Keller, W. Ossau, L.W. Molenkamp, and A. Waag, Phys. Rev. B 73, 035306 (2006). [2] S.V. Zaitsev, V.D. Kulakovskii, A.A. Maksimov, D.A. Pronin, I.I. Tartakovskii, N.A. Gippius, M.Th. Litz, F. Fisher, A. Waag, D. R. Yakovlev, W. Ossau, and G. Landwehr, JETP Lett. 66, No. 5, 376-381 (1997). [3] A.A. Maksimov, S.V. Zaitsev, E.V. Filatov, A.V. Larionov, I.I. Tartakovskii, D.R. Yakovlev, and A. Waag, JETP Lett. 88, No. 8, 511–514 (2008). A.A. Maksimov, E.V. Filatov, I.I. Tartakovskii, D.R. Yakovlev, A. Waag JETP Letters 110, issue 12 (2019)   Optical Properties of $p_x + ip_y$ Superconductors with Strong Impurities Observation of the polar Kerr effect in $\mathrm{Sr_2RuO_4}$ [1], a layered material considered to realize the chiral $p_x+ip_y$ superconducting state, has lead to extensive theoretical investigations of the anomalous Hall response $\sigma_{xy}(\omega)$ in $p_x+ip_y$ superconductors. These studies consider either multi-band superconductor models or effects of potential disorder caused by weak impurities. This work generalizes existing theories of disorder-induced Hall response [2-5] to the case of strong impurities. We consider a low concentration of strong short-range potential impurities characterized by a scattering phase $\delta$. We show that such impurities in the $p$-wave superconductor lead to sub-gap bound states at energy $\Delta\cos\delta$ similar to Yu-Shiba-Rusinov states hosted by magnetic impurities in $s$-wave superconductors. These states form an impurity band which also governs the Hall response. We calculate $\sigma_{xy}(\omega)$ as function of temperature and frequency. It exhibits rich behaviour and sharp threshold features at frequencies $\omega=\Delta\pm\Delta\cos\delta$ which we identify with particular transition processes between the condensate, the impurity band and the continuous spectrum of the $p_x+ip_y$ superconductor. [1] J. Xia, Y. Maeno, P. T. Beyersdorf, M. M. Fejer, and A. Kapitulnik, Phys. Rev. Lett. 97, 167002 (2006).        [2] J.Goryo, Phys. Rev. B 78, 060501(R) (2008).        [3] R. M. Lutchyn, P. Nagornykh, V. M.Yakovenko, Phys. Rev. B 80, 104508 (2009).        [4] S. Li, A. V. Andreev, and B. Z.Spivak, Phys. Rev.B 92, 100506 (2015).        [5] E. J. König, A. Levchenko, Phys. Rev. Lett.118, 027001 (2017). Ioselevich P.A., Ostrovsky P.M. JETP Letters 110, issue 12 (2019)   Stimulated Raman scattering in metal-dielectric ENZ nanocomposites Most materials found in nature exhibit negligible nonlinear optical behaviors. To observe them, it is necessary to increase the interaction length  (for example, using optical fibers) and/or to amplify the pump intensity with high-powered pulse lasers. It means that the third-order nonlinear optical processes, for example, stimulated Raman scattering (SRS), optical Kerr effect, to name a few, do not appear within highly confined media or from single molecules exposed to continuous-wave low-powered laser light. Nonlinear enhancement of light becomes possible due to giant local electric fields and/or changes in higher-order nonlinear susceptibility. The nonlinear optical effects were found to occur in plasmonic and/or epsilon-near-zero (ENZ) materials [1-4]. In paper [5], the authors, for the first time, have succeeded to synthesize a metal-dielectric nanocomposite exhibiting the 2-ENZ behavior in the visible and near-infrared region. In such a medium, multiple plasmon resonances at different wavelengths are available. In this paper, we study SRS effects using a percolated 50 nm titanium oxynitride (TiON) thin film that exhibits the 2-ENZ behavior in the visible and near-infrared region. This film was fabricated using dc reactive magnetron sputtering in an argon-nitrogen environment at elevated temperature and post-oxidation in air. In order to enhance the SRS effect we have patterned the TiON thin film by making square-shaped planar nanoantennas with focused ion beam milling. Using tip-enhanced Raman scattering, we have proved that this nanocomposite film can be represented as the mixture of metallic TiN and dielectric TiO2 nanoparticles. The underlying mechanism to observe the SRS is linked to the enhanced effective third-order susceptibility due to plasmon resonances at the ENZ wavelengths. Earlier, we have experimentally demonstrated a far-field Raman color superlensing effect by showing a sub-wavelength resolution of l/6NA (l  is the excitation wavelength, NA - numerical aperture) at different SRS overtones using multi-walled carbon nanotubes of 40 nm in diameter directly dispersed on the TiON thin film [6]. This allows one to use this material for developing a multi-resonant meta-lens pushing a spatial resolution beyond the diffraction limit without post-recovery. The meta-lens serves as a SERS substrate that not only enhances a scattered light but provides the sub-wavelength resolution. The metal-dielectric 2-ENZ nanocomposite film can be used as a broadband perfect absorber for thermophotovoltaic cells.      [1] Reshef O., De Leon I., Alam M. Z., Boyd R. W. Nat. Rev. Mater. 4, 535 (2019). [2] Caspani, Kaipurath R. P. M., Clerici M.,et al.,  PRL 116, 233901 (2016) [3] Kharintsev S.S., Kharitonov A.V., Saikin S.K., Alekseev A.M., Kazarian S. G.  Nano Lett. 17, 5533 (2017). [4] Kharintsev S.S., Kharitonov A.V., Alekseev A.M., Kazarian S. G. Nanoscale 11, 7710 (2019). [5] Braic L., Vasilantonakis N., Mihai A.,et al., ACS Appl. Mater. Interfaces 9, 29857 (2017). [6] Kharintsev S.S.  Opt. Lett. 44 (24), 5909-5912 (2019).   Tyugaev M.D., Kharitinov A.V., Gazizov A.R., Fishman A.I., Salakhov M.Kh., Dedkova A.A., Alekseev A.M., Shelaev A.V., Kharintsev S.S. JETP Letters 110, issue 12 (2019)   Thermal Nieh-Yan anomaly in topological Weyl materials In 1982 Nieh and Yan introduced the quantum gravitational anomaly caused by the gravitational torsion field [1, 2]. Since that time the torsional anomaly has been debated, because the coefficient in the Nieh-Yan anomaly term contains the ultraviolet energy cut-off, which is not well defined. In this paper we discuss the temperature correction to the Nieh-Yan anomaly. As distinct from the zero temperature term, the $T^2$ temperature correction  does not depend on the ultraviolet cut-off and thus can be universal. Such $T^2$ Nieh-Yan term may exist not only in the relativistic quantum field theories, but also in condensed matter with Weyl fermions. In the topological  Weyl semimetals and in the chiral $p+ip$ superfluids and superconductors, this term is fully determined by the quasirelativistic physics in the vicinity of the Weyl nodes. [1] H. T. Nieh and M. L. Yan, J. Math. Phys. 23, 373  (1982). [2] H. T. Nieh and M. L. Yan, Ann. Phys.138, 237 (1982). Nissinen J., Volovik G.E. JETP Letters 110, issue 12 (2019) Superfluid $^3He$ in squeezed nematic aerogel Nematic aerogels consist of nearly parallel strands. In liquid 3He in such aerogels, the strands lead to anisotropy of 3He quasiparticles scattering that makes favorable new superfluid phases: polar, polar-distorted A (PdA) and polar-distorted B  [1]. A distinctive feature of this work is that experiments were performed with 3He in two samples of nematic aerogel one of which was squeezed by 30% in the direction transverse to the strands. The squeezing leads to anisotropy in a plane perpendicular to the strands that can affect superfluid phases. It was found that the superfluid transition of 3He in both samples occurred into the non-chiral polar phase, where no qualitative difference between properties of nuclear magnetic resonance in 3He in these samples was found. The difference, however, has appeared on further cooling, after a transition to the chiral PdA phase. The results agree with theoretical expectations and provide an additional proof of existence of the polar phase of 3He in nematic aerogels. The obtained quantitative characteristics of the observed phases also agree with recent theoretical paper [2] where it was stated that Anderson theorem for s-wave superconductors is applicable to superfluid 3He in ideal nematic aerogel.   [1] V.V. Dmitriev, A.A. Senin, A.A. Soldatov, and A.N. Yudin, Phys. Rev. Lett. 115, 165304 (2015). [2] I.A. Fomin, JETP 127, 933 (2018). V.V. Dmitriev, M.S. Kutuzov, A.A. Soldatov, A.N. Yudin JETP Letters 110, issue 11 (2019)   Stone-Wales graphane: structure, properties and its thermal stability After the discovery of graphene with its unique mechanical and electronic characteristics, a  number of other quasi-two-dimensional carbon structures were theoretically predicted, including octagraphene [1], pentagraphene [2], ψ-graphene [3], Stone-Wales (SW) graphene [4], as well as their various hydrogenated versions (graphane [5], pentagraphane [6], ψ-graphane [7] etc.). In this paper, SW graphane - a new allotropic modification of graphane is proposed. This quasi-two-dimensional structure is formed upon complete two-side hydrogenation of SW graphene. SW graphene is more thermodynamically stable than most other allotropic modification of carbon. This justifies possibility of the SW graphane formation. Unlike graphane, SW graphane is an anisotropic and soft material. Depending on the direction, its Young's modulus is 194 - 221 N/m, whereas in isotropic graphane it  is 249 N/m. The density of phonon states in SW graphane differs from that in graphane. There are no sharp peaks in the density of phonon states of SW graphane, which are typical for graphane. The densities of electronic states in SW graphane and pristine graphane slightly differ from each other. As well, as for graphane, the main channel of thermal decomposition of SW graphane is the separation of atomic hydrogen. The desorption energies of hydrogen atoms for graphane and SW graphane are also very close. 1. X.-L. Sheng, H.-J. Cui, et al., J. Appl. Phys. 112, 074315 (2012). 2. S. Zhang, J. Zhou, et al., Proc. Natl. Acad. Sci. U.S.A. 112, 2372 (2015). 3. X. Li, Q. Wang, P. Jena, The J. of Phys. Chem. Lett. 8, 3234 (2017). 4. H. Yin, X. Shi, et al., Phys. Rev. B 99, 041405 (2019). 5. J. O. Sofo, A. S. Chaudhari, and G. D. Barber, Phys.Rev. B 75, 153401 (2007). 6. H. Einollahzadeh, et al., Sci. Technol. Adv. Mater. 17, 610 (2017). 7. X. Huang, M. Ma, L. Cheng, and L. Liu Physica E 115, 113701(2020).   Podlivaev A.I.  JETP Letters 110, issue 10 (2019)     Relaxation times and population inversion of the excited states of As donors in germanium At present the interest to Coulomb impurity centers in semiconductors, particularly in silicon and germanium, is revived due to their natural zero-dimensional origin . The specific properties of such centers and advancement in modern technology allow one to create, a qubit with optically controlled coherent states [1], or a source of the THz coherent radiation which utilizes the conventional laser scheme or stimulated Raman scattering [2]. Such applications require accurate knowledge of optical excitation and relaxation processes within an impurity center. In weakly and moderately doped semiconductors, the lifetime of excited states for a shallow impurity center is controlled by phonon-assisted relaxation. Recently [3], the relaxation times for arsenic donor states in bulk germanium have been calculated; these values are encouraging and suggest that the population inversion and THz lasing can be realized under optical pumping. The present work is devoted to studying the low-temperature relaxation of the excited states of As donors in Ge crystal using a pump-probe technique. We show that the lifetime of lower odd parity 2p states are close to one ns. At the same time, experimental study of the inverse relaxation rate for the first excited state 1s(T2) yields value not longer than 160 ps. The data obtained are compared with the results of theoretical calculations [3] and confirm the possibility to reach THz amplification on the 2p – 1s(T2) transitions of optically excited As donors in Ge.   K.J. Morse, R. J. S. Abraham, A.D. Abreu et al., Sci. Adv. 3, e1700930, (2017). S. G. Pavlov, R. Kh. Zhukavin, V. N. Shastin et al., Phys. Stat. Sol. (b) 250, 9 (2013). V.V. Tsyplenkov, V.N. Shastin, Semiconductors, 52, 1573 (2018).     Zhukavin R. Kh., Kovalevskii K.A., Choporova Yu. Yu. et al. (Collaboration) JETP Letters 110, issue 10 (2019)   Observation of Electron Spin Resonance in the Microwave Induced Photovoltage Electron spin resonance (ESR) is one of the most fruitful approaches for the exploration of spin physics in a great deal of different materials including two-dimensional electron systems (2DES) confined in semiconductor heterostructures [1]. The conventional technique for the observation of spin resonance in a 2DES relies on the high sensitivity of a 2D electron channel resistance to the absorption of microwave radiation in the regime of integer quantum Hall effect. In the presented manuscript we propose the complementary experimental approach for the ESR detection as a sharp peak in the microwave induced photovoltage measured between the ohmic contacts to the 2DES. In the presented manuscript we have demonstrated that the suggested experimental approach works well in different semiconductor heterostructures and in various contact geometries. Detection of ESR in such a way requires no current flow through the sample, thereby protecting 2DES from potential overheating, and from resulting negative impact on  subtle physical phenomena like high-order fractional quantum Hall effect [3]. Furthermore, the flow of nonequilibrium charge carriers that is responsible for the generated voltage is at least partly spin polarized, as spin dephasing time in the quantum Hall regime [4] exceeds the transport scattering time. [1] M. Dobers, K. v. Klitzing, and G. Weimann, Phys. Rev. B 38, 5453 (1988). [2] D. Stein, K.v. Klitzing and G. Weimann, Phys. Rev. Lett. 51, 130 (1983). [3] R. Willett, J. P. Eisenstein, H. L. Stoermer, D. C. Tsui, A. C. Gossard, and J. H. English Phys. Rev. Lett. 59, 1776 (1987) [4] A. V. Shchepetilnikov, Y. A. Nefyodov, and I. V. Kukushkin, JETP Lett. 97, 574 (2013).       Destructive quantum interference and exceptional points in high-frequency response of two-state system   Periodic driving transforms the stationary energy spectrum into the Floquet modes spectrum (quasienergies). This can be associated with the so-called synthetic dimension introduced by the Floquet modes [1, 2]. Perturbation frequency in this case becomes an additional degree of freedom, which opens new ways of manipulating the quantum systems spectrum. In this context, periodic driving can introduce phenomena, which are typical for higher dimensional systems, in lower dimensional samples.   In a finite system, periodic driving can effectively change its topology (connectivity of tunneling paths). In present letter, we study interference features in the high-frequency conductance of a two-state model system within the Keldysh formalism for non-equilibrium Green functions in tight-binding basis. We provide a clear and illustrative correspondence between high-frequency response and stationary transmittance of spatially symmetric configurations of the model system considered. In particular, we show that the synthetic frequency dimension provides the possibility for effective degeneracy of eigenstates in a simply connected linear quantum conductor, which is impossible in statics. It turns to be the dynamical counterpart of the situation considered in [3] for stationary tunneling. In dynamical transport, this phenomenon manifests itself by the destructive quantum interference and resonance coalescence, described by an exceptional point of a generalized transmission coefficient. As a result, for instance, one can observe a dip in the real part of the conductance at resonant frequency. [1] E. Lustig, S.Weimann, Y. Plotnik et al. Nature 567, 356 (2019). [2] L.Yuan, Q. Lin, M. Xiao et al. Optica 5 (11), 1396 (2018). [3] A. A. Gorbatsevich, G.Ya. Krasnikov, and N. M. Shubin. Scientific Reports 8, 15780 (2018). Gorbatsevich A.A., Shubin N.M. JETP Letters 110, issue 9  (2019)   Electron spectrum and optical properties of transition metal dichalcogenides quantum wires  Specific features of the band structure of transition metal dichalcogenides (TMDCs) monolayers — the presence of two valleys, strong spin – orbit interaction — have recently become the subject of a large number of theoretical and experimental studies. Relatively few papers are available on the spatially inhomogeneous problems with  TMDCs – quantum dots and quantum wires (QW).    In the present work we consider a QW made of TMDCs monolayer in the form of straight strip. Our analysis is based on the Dirac-type Hamiltonian with the finite gap and with accounting for the spin splitting both conduction and valence bands [1, 2, 3]. We use the boundary condition for the electron wave function proposed in [4] which is a special case of the more general consideration given in [5]. Our main findings are:  1.  There exists a certain critical value of the strip width L= Lcr that separates two types of the electron spectrum: for L> Lcr there are energy levels (subbands in which energy depends on the momentum along the wire) lying within the band gap of an infinite sample, while at L < Lcr such states are absent.  Note, that in conventional QW for particles with parabolic dispersion law there are no states in the forbidden gap for any value of width.  2.  The optical absorption of the QWs in question differs essentially from the one in conventional QWs. First of all, for the interband transitions there is no strict selection rule  Dn=0  where  n  is the number of the transversal subbands  in the valence band and the conduction band (cf. with conventional QWs where only interband  transitions at  Dn=0  are allowed). However in our case the transitions with  Dn=0  are still much more intensive than others. Second, depending on the mutual parity of the numbers of size quantization subbands in the valence and conduction bands, optical transitions are characterized by significantly different threshold behavior of the absorption intensity. Namely, for the transitions even – even or odd – odd types the threshold dependence of the absorption is I µ  (w-w0)-1/2  while for even – odd and odd – even cases we obtain  I µ  (w-w0)1/2.   [1]  D.Xiao et al., Phys.Rev.Lett., 108, 196802 (2012). [2]  A.Kormanyos et al., 2D Materials, 2, 022001 (2015). [3]  V.V.Enaldiev, Phys.Rev.B, 96, 235429 (2017). [4]  M.V.Berry and R.J.Mondragon, Proc.R.Soc.Lond., A412, 53 (1987). [5]  V. A. Volkov and T. N. Pinsker, Sov. Phys. Solid State 23, 1022 (1981).   R.Z.Vitlina, L.I.Magarill, A.V.Chaplik JETP Letters 110, issue 8  (2019)   Mossbauer spectroscopy study of the superconducting single crystals $FeSe_{0.91}S_{0.09}$ The discovery of superconductivity in iron-based pnictides and chalcogenides with a relatively high transition temperature has attracted considerable interest due to the unusual correlations between magnetism and superconductivity in these compounds [1-3]. Several theoretical models of superconductivity based on pair interactions associated with magnetic fluctuations have been proposed [3-7]. Much attention is paid to studying the interaction of superconductivity, nematicity of the electronic structure, and quantum paramagnetism in FeSe and FeSe1-xSx compounds [8,9]. The coexistence of ferromagnetism and superconductivity in FeSe crystals doped with Bi2Se3 was reported recently [10].  In the present work, the method of Mössbauer spectroscopy on 57Fe nuclei was used to study magnetic correlations and possible structural and electronic transformations that are expected in the temperature range of nematic and superconducting transitions in single crystals of iron selenide doped with sulfur Fe (Se0.91 ± 0.01S0.09 ± 0.01)1-δ. It was found that at room temperature, FeSe0.91S0.09 samples have a tetragonal β-FeSe structure of the PbO type (space group P4/mmm), which transforms into the orthorhombic phase when the crystal is cooled down to Ts ≈ 80 K. The temperature of the superconducting transition is  = 10.1 . The temperature dependence of the hyperfine interaction parameters obtained from the Mössbauer spectra revealed a number of anomalies in the temperature range of the superconducting Tc, structural Ts, and nematic T* phase transitions. It was established that iron atoms are in a nonmagnetic state even in the region of helium temperatures, which is explained by the low-spin state of Fe2+ ions (3d6, S = 0). It is shown that this state practically does not change at temperatures of transition to the superconducting state. This means that the low-spin state of iron ions is more likely a structural factor, and is not directly related to superconductivity. Thus, there is no effect of the suppression of magnetism by superconductivity. The electrical resistance and Mössbauer spectroscopy data show that in the Fe(Se0.91S0.09)1-δ crystal, the temperature of the nematic transition T* is about 200 K and is much higher than the temperature of the structural transition (Ts ≈ 80 K). The Debye temperature, obtained from Mössbauer data for the iron sublattice, is ΘM = 478 K, which turned out to be much higher than in the undoped FeSe1-δ compound (ΘM = 285 K).   [1] Y. Kamihara, T. Watanabe, M. Hirano, and H. Hosono, J. Am. Chem. Soc. 130, (2008) 3296. [2] X. H. Chen, T. Wu, G. Wu, R. H. Liu, H. Chen, and D. F. Fang, Nature 453, (2008) 761. [3] M.V Sadovskii. Physics-Uspekhi 59(10), (2016) 947. [4] Y. Mizuguchi, Y. Hara, K. Deguchi, et al., Supercond. Sci. Technol. 23, (2010) 054013. [5] J. Paglione and R. L. Greene, Nat. Phys. 6 (2010) 645. [6] V.A. Gasparov, JETP 111(2), (2010) 313. [7] A.A. Kordyuk, Low Temp. Phys. 38, (2012) 888. [8] K.K. Huynh, Y. Tanabe, T. Urata, et al., Phys. Rev. B 90, (2014) 144516. [9] Q. Wang, Y. Shen, B. Pan, et al., Nature Materials 15 (2016) 159. [10] Y. Liu, X.Y. Pu, K. Zhao, X.S. Yang, Y. Zhao, Solid State Comm. 281, (2018) 27.   K.V. Frolov, I.S. Lyubutin, D.A. Chareev and M. Abdel-Hafiez JETP Letters 110, issue 8 (2019)   Hall conductivity as the topological invariant in phase space in the presence of interactions and non-uniform magnetic field   The original TKNN invariant [1] responsible for the Hall conductivity has been derived for the uniform magnetic field (constant both as a function of time and space coordinates). The expression for the Hall  conductivity discussed in the present paper  is an extension of the TKNN invariant to the case of varying (in space) magnetic fields. Therefore, its consideration is important and should be interesting for the wide audience. The non - renormalization of the Hall conductivity (given by the original TKNN invariant) by interactions has been discussed earlier [2-6]. But this consideration was limited by the case of constant magnetic fields. Now we present the proof that the QHE conductivity (given by our extension of the TKNN invariant) is robust to the introduction of interactions in the case of varying magnetic field. This result has never been obtained in the past, to the best of our knowledge.   In addition, the mathematical form of the topological invariant in phase space discussed here is somehow similar to the one of the topological invariant in momentum space composed of the two - point Green function. The latter topological invariant and its variations are used widely (see G.E. Volovik "Universe in a Helium droplet"). Now the Green function is substituted by its Wigner transformation depending on both space coordinates and momentum. The ordinary products are therefore changed to the Moyal (star) product, thus leading to the beautiful mathematical structure.  The resulting expression may be used in the presence of interaction for the calculation of Hall conductivity. One simply has to insert to it the interacting (Wigner transformed) two - point Green function. The Green functions with larger number of legs do not contribute to the Hall conductivity (this also has been proved in the presented paper).   We would also like to emphasize, that our proof is valid to all orders in the perturbation theory.   [1] D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Phys. Rev. Lett. 49, 405(1982). [2] Ryogo Kubo, Hiroshi Hasegawa, Natsuki Hashitsume, Journal of the Physical Society of Japan 14(1) (1959) 56-74 DOI: 10.1143/JPSJ.14.56 [3] Q. Niu, D. J. Thouless, and Y. Wu, Phys. Rev. B 31, 3372 (1985). [4] B. L. Altshuler, D. Khmel'nitzkii, A. I. Larkin and P. A. Lee, Phys.Rev.B 22, 5142 (1980). [5] B.L. Altshuler and A.G. Aronov, Electron-electron inter-action in disordered systems (A.L.Efros, M. Pollak, Ams-terdam, 1985). [6] S. Coleman and B. Hill, Phys. Lett. B159 (1985) 184 T. Lee, Phys. Lett. B171 (1986) 247 C.X.Zhang, M.A.Zubkov JETP Letters 110, issue 7 (2019) Modulation of magneto-intersubband oscillations in a one-dimensional lateral superlattice Landau quantization in a two-subband Fermi electronic system placed in an external perpendicular magnetic field B leads not only to the well-known Shubnikov – de Haas (SdH) oscillations, but also to another type of quantum resistance oscillations — the magneto-intersubband oscillations (MISO) [1, 2]. MISO are not suppressed by the temperature broadening of the Fermi distribution function and therefore allow one to study quantum transport under conditions when SdH oscillations cannot be used for these purposes [3, 4]. The present work is devoted to the study of MISO in a one-dimensional (1D) lateral superlattice (LSL), where 1D periodic potential is applied to a two-subband electronic system. The 1D LSL was created on the basis of a selectively doped GaAs/AlAs heterostructure [5, 6]. The measurements were carried out using Hall bars fabricated by means of optical lithography and wet etching. The 1D LSL of period a = 300 nm was created as an array of metal strips on a planar surface of Hall bars using electron beam lithography and the method of exploding an Au/Ti bilayer metallic film. The potential modulation in the studied LSL arises without applying voltage to the metal strips. One of the reasons for this modulation is elastic mechanical stresses between metal strips and a heterostructure [7]. The measurements were carried out at the temperature T = 4.2 K in magnetic fields B < 2 T. It has been shown that commensurability oscillations (CO) of resistance co-exist with MISO in the studied LSL. It has been found that 1D periodic potential in a two-subband electron system leads not only to COs but also to MISO amplitude modulation, which is caused by periodic modulation of Landau level width in a 1D LSL in external inverse magnetic field. It has been shown that increased intersubband scattering time in a two-subband system under 1D periodic potential modulation is one of the reasons of MISO amplitude damping in a 1D LSL. [1] V. M. Polyanovskii, Sov. Phys. Semicond. 22, 1408 (1988). [2] D. R. Leadley, R. Fletcher, R. J. Nicholas, F. Tao, C. T. Foxon, and J. J. Harris, Phys. Rev. B 46, 12439 (1992). [3] A. A. Bykov, A. V. Goran, and S. A. Vitkalov, Phys. Rev. B 81, 155322 (2010). [4] O. E. Raichev, Phys. Rev. B 81, 195301 (2010). [5] K.-J. Friedland, R. Hey, H. Kostial, R. Klann, and K. Ploog, Phys. Rev. Lett. 77, 4616 (1996). [6] D. V. Dmitriev, I. S. Strygin, A. A. Bykov, S. Dietrich, and S. A. Vitkalov, JETP Lett. 95, 420 (2012). [7] Ivan A. Larkin, John H. Davies, Andrew R. Long, and Ramon Cuscó, Phys. Rev. B 56, 15242 (1997).   A.A. Bykov, I.S. Strygin, A.V. Goran, D.V. Nomokonov, I.V. Marchishin, A.K. Bakarov, E.E. Rodyakina, A.V. Latyshev JETP Letters 110, issue 5 (2019).     Experimental verification of the principle of microscopic reversibility in the photoluminescence decay kinetics It has been shown in [1] that any photoluminescent body in thermal equilibrium obeys the following relation: $P(\lambda_1, T) F(\lambda_1, \lambda_2, t) = P(\lambda_2, T) F(\lambda_2, \lambda_1, t)$ (1) where P(λ, T) is the Planck function, which describes the spectral density of thermal radiation at wavelength λ and temperature T, and F(λ1, λ2, t) is the time-resolved excitation-emission matrix, which describes the probability density of emitting a photon with wavelength λ2 at time t as a result of absorption of a photon with wavelength λ1 at time t = 0. For fixed λ1, the function F(λ1, λ2, t) is the photoluminescence spectrum PL(λ; λ0, t) at time t after a short-pulse excitation at wavelength λ0: PL(λ; λ0, t) = F(λ0, λ, t). For fixed λ2, the function F(λ1, λ2, t) is the photoluminescence excitation spectrum PLE(λ; λ0, t) detected at wavelength λ0 at time t after a short-pulse excitation at wavelength λ: PLE(λ; λ0, t) = F(λ, λ0, t). Equation (1) rearranged to $\frac{ PL(\lambda;\lambda_0, t) }{ PLE(\lambda;\lambda_0, t) } = \frac{ P(\lambda, T) }{ P(\lambda_0, T) }$ (2) is a new universal photoluminescence law stating that for any luminophore in thermal equilibrium, the ratio of the corresponding time-resolved photoluminescence and photoluminescence-excitation spectra, PL(λ; λ0, t) and PLE(λ; λ0, t), is equal to the ratio of black-body radiation spectra at wavelengths λ and λ0. For fixed λ1 and λ2, the function F(λ1, λ2, t) is the kinetics of decay of photoluminescence excited instantaneously at λ1 and detected at λ2. Since the right-hand side of equation (2) does not depend on time, the left-hand side is also time-independent. This means that the photoluminescence decay kinetics is invariant under interchange of the excitation and detection wavelengths up to a time-independent factor. The aim of the present study is to test the relation (2) experimentally by measuring the photoluminescence decay kinetics with interchanging the excitation and detection wavelengths. This implies that when the forward process is a Stokes photoluminescence, then the reverse process is an anti-Stokes photoluminescence. Colloidal solutions of InP/ZnS quantum-dot nanoclusters, which do not obey the Vavilov law about the independence of the photoluminescent properties of a luminophore of  the excitation wavelength, have been used in the study to test the invariance of the decay kinetics under interchange of the excitation and emission wavelengths. [1]. S. A. Tovstun, V. F. Razumov, et all. // J. Lumin. 190, 436 (2017).   Razumov V.F., Tovstun S.A., Kuzmin V.A. JETP letters 110, Issue 5 (2019)       Specific features of magneto-intersubband oscillations in HgTe quantum wells Studies of oscillatory magnetotransport effects are one of the most reliable methods for investigating energy spectrum of 2D carrier systems. A magnetic field normal to the plane of a 2D gas leads to orbital quantization of the spectrum and, as a consequence, to the appearance of oscillations of the magnetoresistance (ρxx) at low temperatures (Shubnikov de Haas oscillations). These oscillations are periodic in the inverse magnetic field and their frequency f is determined by the carrier concentration.   In systems in which two (or several) branches of the spectrum E1,2 (k) are filled, the oscillations are observed with frequencies f1 and f2, determined by the carrier concentration in its branch. The sum of these oscillations manifests itself as a beating of oscillations of ρxx,, causing nodes and antinodes at certain magnetic fields. In the presence of transitions between the branches, new oscillations arise with a difference frequency, f1 - f2. They are called magneto-intersubband oscillations (MISO) [1,2]. The simplest qualitative examination shows that the positions of the antinodes in magnetic field must coincide with the ρxx maxima of MISO. Such mutual positions of the antinodes and the MISOs were investigated for the structures based on wide-gap semiconductors with double quantum wells, for wide quantum wells where two branches of the spectrum are formed due to the Coulomb repulsion of electrons, and for structures with two filled subbands of the size quantization. Along with the cases described above, the two branches of the spectrum for a single quantum well can arise due to the strong spin-orbit (SO) interaction. The large SO splitting can occur for the quantum wells of narrow-gap (InAs, InSb) and gapless (HgTe, HgSe) semiconductors, as well as for many new topological insulators. Such MISO oscillations were considered only theoretically [3, 4], but were never observed experimentally. This work reports an experimental study of rxx  in  the gated structures with HgTe quantum wells of 8-20 nm widths with an inverted spectrum. It was found that, unlike all other cases and theoretical predictions, the mutual position of the antinodes and MISO is quite opposite. Namely, the positions of the antinodes in a magnetic field coincide with the ρxx minima of MISO. A possible reason for such unusual behavior is discussed. 1. .. , , 22, 2230. (1988) 2. D.R Leadly, R. Fletcher and R. J. Nicholas, Phys. Rev.B, 46, 12439- (1992) 3. M. Langenbuch, M. Suhrke and U. Ro^¨ssler, Phys. Rev. B  69, 125303 (2004) 4. S. G. Novokshonov, Low Temperature Physics 39, 378 (2013) G.M. Minkov, O.E. Rut, A.A. Shestobitov, S.A.Dvoretski, N.N. Mikhailov JETP Letters 110, issue 4 (2019)       Chiral Estimate of QCD Pseudocritical Line Precisely mapping the phase diagram of strongly-interacting matter is a challenging problem. Lattice simulations of QCD, the field theory of strong interactions, are reliable at zero density, but become less precise when the density is finite and at the moment are not capable to map the whole phase diagram of strong interactions. The most dramatic phenomenon that happens when strongly interacting matter is heated to extreme temperatures is restoration of chiral symmetry, a key symmetry of QCD that largely determines properties of hadrons and interactions among them. Chiral symmetry restoration is a sharp crossover at zero density that happens at temperature $T_{0}\simeq 157\,{\rm Mev}$ accurately known  from lattice simulations \cite{Bazavov:2018mes}.  Various model estimates predict that at larger baryon densities the crossover becomes sharper and eventually merges into a line of first-order phase transitions at a critical endpoint whose precise location on the $T-\mu$ plane is not entirely known. Model estimates vary by a factor of a few  \cite{Stephanov:2004wx} depending on the model assumptions. The order parameter of the chiral symmetry breaking is the quark condensate $\bar{\psi }\psi$, which has a non-zero expectation value in the vacuum. The pseudo-Goldstone modes that arise from the chiral phase of the condensate: $\bar{\psi }\psi \sim \Sigma\,{\rm e}\,^{\gamma ^5 T^{a}\pi _{a}}$ are identified with pions, kaons and the $\eta$-meson, which are substantially lighter than other hadrons. Chiral symmetry restoration is typically associated with melting of the quark condensate, but can also proceed via disordering of the condensate's phase. Strong pion fluctuations, such that $\left\langle \mathop{\mathrm{tr}}\,{\rm e}\,^{iT^{a}\pi _{a}}\right\rangle=0$, will restore chiral symmetry even if condensate's modulus is non-zero. This paper studied this slightly unconventional scenario of chiral symmetry restoration. Following \cite{Zarembo:2001wr} the shape of the pseudocritical line on the $T-\mu$ plane can then be predicted from the low-energy effective field theory. An interesting consequence of this scenario is an absence of the critical endpoint. The symmetry restoration always proceeds through a crossover which moreover becomes weaker with growing baryon density.   1. A. Bazavov et al., 1812.08235. 2. M. A. Stephanov, Prog. Theor. Phys. Suppl. 153, 139 (2004). 3. K. Zarembo, JETP Lett. 75, 59 (2002). K. Zarembo JETP Letters 110, issue 3 (2019). Layered Superconductor in a Magnetic Field: Breakdown of the Effective Masses Model   Recently, a number of quasi-two-dimensional (Q2D) high-temperature and intermediate-temperature superconductors have been discovered. The anisotropic upper magnetic critical fields in some of them can be described by the Lawrence-Doniach model, which is relevant to Q2D superconductors with high anisotropic properties. On the other hand, there are many Q2D superconductors with intermediate anisotropy of the upper critical magnetic fields, which are usually described by the so-called effective masses (EM) model, partially based on the anisotropic Ginzburg-Landau equations. The most popular such Q2D compounds are MgB2 and Fe-based superconductors [1]. It is possible to define anisotropic ratio in Q2D superconductors, g, as the ratio of the parallel and perpendicular upper critical magnetic fields, which is always bigger than 1, g > 1. In accordance with EM model, the ratio g doesn’t have to depend on temperature. Meanwhile recent experiments show strong temperature dependence of anisotropy g, which in the case of superconductor MgB2 increases with decreasing temperature.    The previous explanations of this phenomenon were based on some approximate many-band calculations of the upper critical magnetic fields and were prescribed to many-band effects. In this Letter, we investigate anisotropy ratio, g, more carefully by using derivation and investigation of an integral equation for the so-called superconducting nucleus, using the Gor’kov equations for non-uniform superconductivity (see, for example, the corresponding derivations for a 3D isotropic case in Ref.[2]) . For the first time, we show that the superconducting nucleus is not of the Gaussian shape for the parallel upper critical magnetic field and even changes its sign with space coordinate. This circumstance breaks down the EM model and predicts a factor of 1.3 increase of the upper critical magnetic fields ratio, g, with decreasing temperature. We prescribe the experimentally observed increase of the parameter g in the superconductor MgB2 [1] to the breakdown of the EM model suggested in the Letter. This issue is an important one since Q2D high-temperature and intermediate-temperature superconductors are good candidates for some scientific and industrial applications in high magnetic fields. [1] See, for example, review V.G. Kogan and R. Prozorov, Rep. Prog. Phys. 75, 114502 (2012). [2] L.P. Gor’kov, Sov. Phys. JETP, 37(10), 42 (1960).                                                                                                                                                        Lebed A.G.                                                                                                                       JETP Letters 110, issue 3 (2019).   Metastable conducting crystalline hydrogen at high pressures The formation of metallic hydrogen, predicted in [1], was observed experimentally in [2]. It is also assumed that this state of solid hydrogen is a superconductor at room temperature. However, the possibility of practical application of the metallic hydrogen is significantly limited by the pressure of formation of this state. The properties of stability and metastability of metallic hydrogen depend on the structure, which determines the relevance of the theoretical study of this issue. As it was shown in [3 - 6], atomic metallic hydrogen at zero temperature exists in a metastable state up to normal pressure. In the present work, the quantum molecular dynamics method within the framework of the density functional theory is applied for the calculation of the equation of state, the pair correlation function, and the static electrical conductivity of solid hydrogen in the region of the possible formation of the conducting phase. A hysteresis of the dependence of pressure on density is observed under compression and following expansion in the pressure range from 350 GPa to 625 GPa, corresponding to the region of existence of metastable states of molecular and non-molecular solid hydrogen. Thus, the magnitude of the metastability region is 275 GPa. An estimate of the equilibrium pressure of the transition to the non-molecular state 487.5 GPa was obtained. During compression, the transition of molecular hydrogen with the C2/c symmetry to a conducting non-molecular state with the C2221 symmetry through an intermediate conducting molecular phase with Cmca-4 symmetry was detected. Under expansion, the transition of the non-molecular structure of C2221 to the molecular Cmca-4 occurs through an intermediate non-molecular state with the P21/c symmetry group. The possibility of the existence of conductive non-molecular crystalline hydrogen with P21/c symmetry under expansion up to a pressure of 350 GPa is shown. [1] E. Wigner, H. B. Huntington, J. Chem. Phys. 3, 764 (1935). [2] R. Dias, I. F. Silvera, Science 355, 715 (2017). [3] Yu. Kagan and E. G. Brovman, Sov. Phys. Usp. 14, 809 (1971). [4] E. G. Brovman, Yu. Kagan, and A. Kholas, Sov. Phys. JETP 34, 1300 (1972). [5] E. G. Brovman, Yu. Kagan, and A. Kholas, Sov. Phys. JETP 35, 783 (1972). [6] Yu. Kagan, V. V. Pushkarev, and A. Kholas, Sov. Phys. JETP 46, 511 (1977). I.M. Saitov JETP Letters 110, №3 (2019) A new type of charge-density-wave pinning in orthorhombic TaS$_3$ crystals with quenching defects There are a number of physical systems in which, under certain conditions, spatially ordered electronic superstructures are formed. Charge and spin density waves (CDW and SDW), Wigner crystals and vortex lattices in type-II superconductors in a magnetic field are examples of such systems. The interaction of the superstructure with local lattice imperfections (various point defects, impurities, etc.) leads to its  pinning. In the simplest case, such a pinning (let's call it local) is divided into collective (weak) and individual (strong). In the present work, it is experimentally shown that, in the Peierls conductor {\it o}-TaS$_3$, a new type of CDW pinning appears as a result of samples quenching. It is characterized by a number of fundamental differences from pinning by local pinning centres, namely:     Pinning by quenching defects is not described by the $\sqrt {E_T} \propto \Delta T_P$ law typical for both weak and strong local pinning centres. ere $E_T$ is  the threshold field for onset of CDW sliding and $\Delta T_P$ is pinning-induced change of the Peierls transition temperature.   In the case of pinning by quenching defects, only a slight smoothing of the Peierls transition occurs even for a large  $\Delta T_P$, whereas in the case of local pinning  with similar changes in $\Delta T_P$, the Peierls transition is almost completely suppressed due to the loss of three-dimensional ordering.  Pinning provided by quenching defects is unstable and can be eliminated  by thermocycling in the temperature range  $T 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}$, \label{Helmholtz} \frac{\partial {\bf B}}{\partial t} =\mbox{rot}[{\bf v}\times {\bf B}],\,\,\mbox{div}\,{\bf v}=0, whence one can see that${\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. C. Kallin and B.I. Halperin, Phys. Rev. B 30, 5655 (1984). S. Dickmann and I.V. Kukushkin, Phys. Rev. B 71, 241310(R) (2005). S. Dickmann, Phys. Rev. Lett. 110, 166801 (2013). 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. B.P. Abbott, R. Abbot, T.D. Abbot et al. (LIGO and VIRGO Collaborations), Phys. Rev. Lett., 119, 161101 (2017). A.D. Avrorin, A.V. Avrorin, V.M. Aynutdinov et.al. (Baikal Collaboration) PoS (ICRC2017),1034, (2017) A.D. Avrorin, A.V. Avrorin, V.M. Aynutdinov et.al. (Baikal Collaboration) JETP Letters 108, issue 12 (2018) 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]]. A.Yu.Kotov 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. F.S. Bergeret, A.F. Volkov, and K.B. Efetov, Rev. Mod. Phys. 77, 1321 (2005). A.I. Buzdin, Rev. Mod. Phys. 77, 935 (2005). A.A. Golubov, M.Yu. Kupriyanov, and E. Il'ichov, Rev. Mod. Phys. 76, 411 (2004). Matthias Eschrig, Rep. Progr. Phys. 78 , 104501 (2015). 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) NON-WIENER DYNAMICS OF THE GENERALIZED DIKE MODEL AS A BROADBAND ONE-PHOTON PACKET DETECTOR 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 107, 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$30 R_c...R_c$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_01/2, 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.     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) 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