Editor's Choice 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  106, issue 6 (2017) Long-lived quantum vortex knots In the bulk of a superfluid, besides well-known and experimentally observed quantum vortex rings, theoretically there can exist (developing in time) also solitary topologically non-trivial excitations as vortex knots [1-3]. The simplest of them are torus knots ${\cal T}_{p,q}$, where  $p$ and $q$ are co-prime integers, while parameters of torus are the toroidal (large) radius $R_0$ and the poloidal (small) radius $r_0$, both sizes being large in comparison with a width of quantum vortex core $\xi$. It was believed on the basis of previously obtained numerical results that such knots are unstable and they reconnect during just a few typical times, traveling a distance of several $R_0$ (the lifetime is somewhat longer for smaller ratios $B_0=r_0/R_0$). The mentioned results were obtained for not too large ratios $R_0/\xi\lesssim 20$, and with a very coarse step (about 0.1) on parameter $B_0$.  In this work it was numerically found that actually the situation is much more complicated and interesting. The dynamics of trefoil knot ${\cal T}_{2,3}$ was accurately simulated within a regularized Biot-Savart law using a small step on $B_0$. At fixed values of parameter $\Lambda=\log(R_0/\xi)$, the dependence of knot lifetime on parameter $B_0$ turned out to be drastically non-monotonic on sufficiently small $B_0\lesssim 0.2$. Moreover, at $\Lambda\gtrsim 3$ quasi-stability bands appear, where vortex knot remains nearly unchanged for many dozens and even hundreds of typical times. Qualitatively similar results take place also for  ${\cal T}_{3,2}$ knot. These observations essentially enrich our knowledge about dynamics of vortex filaments.  [1] D. Proment, M. Onorato, and C. F. Barenghi,  Vortex knots in a Bose-Einstein condensate, Phys. Rev. E 85, 036306 (2012).  [2] D. Proment, M. Onorato, and C. F. Barenghi, Torus quantum vortex knots in the Gross-Pitaevskii model for Bose-Einstein condensates, J. Phys.: Conf. Ser. 544, 012022, (2014).  [3] D. Kleckner, L. H. Kauffman, and W. T. M. Irvine, How superfluid vortex knots untie, Nature  Physics  12, 650 (2016).                                                                             V. P. Ruban, JETP Letters  107, issue 5 (2018). The spin kinetics of liquid 3He in contact with the microsized DyF3 powder at ferromagnetic ordering of Dy^{3+} For the first time the magnetic phase transition in DyF3 at low temperatures was observed by 3He NMR. The spin kinetics of liquid 3He in contact with a mixture of microsized powders LaF3 (99.67%) and DyF3 (0.33%) at temperatures 1.5-3 K was studied by pulse NMR technique. The DyF3 is a dipole dielectric ferromagnet with a phase transition temperature Tc = 2.55 K, while as the diamagnetic fluoride LaF3 used as a diluent for optimal conditions for observation of 3He NMR. The phase transition in DyF3 is accompanied by a significant changes in the magnetic fluctuation spectrum of the dysprosium ions. The spin kinetics of 3He in contact with the substrate is sensitive to this fluctuations. An significant change in the rates of the longitudinal and transverse nuclear magnetization of 3He in the region of magnetic ordering of solid matrix was observed. A technique is proposed for studying the static and fluctuating magnetic fields of a solid matrix at the low temperatures using liquid 3He as a probe. .. lakshin, .I. Kondratyeva, V.V. Kuzmin, .R. Safiullin, .. Stanislavovas, .V. Savinkov, .V. Klochkov,  .S. Tagirov JETP Letters 107 issue 2, 2018 Microparticles at the surface of liquid helium. Quantum version of Archimedes' principle Microspheres at the surface of liquid are widely used now for visualization of wave and vortex motion [1, 2]. The experiments of this kind had been performed recently to study of turbulence at the surface of liquid helium [3]. That’s why it is of interest to consider the corrections to a classic Archimedes' principle, because while the size of a particle floating at the surface decreases, the forces of surface tension and molecular interaction start to play a significant role.  We study the deviations from Archimedes' principle for spherical particles made of molecule hydrogen near the surface of liquid He4. Classic Archimedes' principle takes place if particle radius $R_0$ is greater than capillary length of helium $L_{k} \approx$ 500 µm and the height $h_+$  of the part of the particle above He is proportional to  $R_0$ . Over the range of $30 R_c...R_c$  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