
Editor's Choice
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 temperaturefield 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) Longlived quantum vortex knots
In the bulk of a superfluid, besides wellknown and experimentally observed quantum vortex rings, theoretically there can exist (developing in time) also solitary topologically nontrivial excitations as vortex knots [13]. The simplest of them are torus knots ${\cal T}_{p,q}$, where $p$ and $q$ are coprime 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 $B_0$. 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 DyF_{3} at low temperatures was observed by ^{3}He NMR. The spin kinetics of liquid ^{3}He in contact with a mixture of microsized powders LaF_{3} (99.67%) and DyF_{3} (0.33%) at temperatures 1.53 K was studied by pulse NMR technique. The DyF_{3} is a dipole dielectric ferromagnet with a phase transition temperature T_{c} = 2.55 K, while as the diamagnetic fluoride LaF_{3} used as a diluent for optimal conditions for observation of ^{3}He NMR. The phase transition in DyF_{3} is accompanied by a significant changes in the magnetic fluctuation spectrum of the dysprosium ions. The spin kinetics of ^{3}He in contact with the substrate is sensitive to this fluctuations. An significant change in the rates of the longitudinal and transverse nuclear magnetization of ^{3}He 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 ^{3}He as a probe. å.í. álakshin, å.I. Kondratyeva, V.V. Kuzmin, ë.R. Safiullin, á.á. Stanislavovas, á.V. Savinkov, á.V. Klochkov, í.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 He^{4}. Classic Archimedes' principle takes place if particle radius $R_0$ is greater than capillary length of helium $L_{k} \approx $ 500 µm and the height $h_+$ of the part of the particle above He is proportional to $R_0$ . Over the range of $30 <R_0 <500$ µm Archimedes' force is suppressed by the force of surface tension and $h_{+} \sim R^{3}_{0} / L^{2}_{k}$. When $R_0<30$µm, the particle is situated under the surface of liquid helium. In this case Archimedes' force competes with Casimir force which repels the particle from the surface to the depth of liquid. The distance from the particle to the surface $h_{} \sim R^{5/3}_c / R^{2/3}_0$ if $R_0>R_c...R_c$ can be expressed as $R_c \approx (\frac {\hbar c}{\rho g}) \approx $ 1µm, $\hbar $ is Planck's constant, c is speed of light, $\rho $ is helium density. For the very small particles ( $R_0<R_c)$ $h_{}$does not depend on their size: $h_{}$=$R_c$. 1. S. V. Filatov, S. A. Aliev, A. A. Levchenko, and D. A. Khramov, JETP Letters, , 104(10), 702 (2016). 2. S. V. Filatov, D. A. Khramov, A. A. Levchenko, JETP Letters, 106(5), 330 (2017). 3. A. A. Levchenko, L. P. MezhovDeglin, A. A. Pel’menev, JETP Letters, 106(4), 252 (2017). 4. E. V. Lebedeva, A. M. Dyugaev , and P. D. Grigoriev, JETP, 110(4), 693 (2010). 5. A. M. Dyugaev, P. D. Grigoriev, and E. V. Lebedeva, JETP Letters, 89(3), 145 (2009). Superconductorinsulator transition in disordered NbTiN films
One of the frontiers of quantum condensed matter physics seeks to analyze and classify scenarios of the superconductorinsulator quantum phase transition (SIT). Fermionic scenario [1] rules that disorder, when strong enough, breaks down Cooper pairs thus transforming a superconductor into a metal. The further cranking up disorder strength localizes quasiparticles turning the metal into an insulator. According to Bosonic scenario [2,3] disorder localizes Cooper pairs which survive on the insulating side of the SIT and provide an insulating gap. In the Fermionic scenario, the disorderdriven SIT is a twostage transition through the intermediate state that exhibits finite resistance R_{□} and is ordinarily referred to as quantum metal. In Bosonic scenario, the SIT this intermediate state shrinks into a single point in which the resistance assumes the universal quantum resistance per square R_{c} = 6.45 kΩ/□ [3]. The disorderdriven SIT was reported in films of InO_{x} [4, 5], Be [6], TiN [7]. However, the resistance R_{c }that separates superconducting and insulating states in these films is not universal. The access and detailed study of the phases in the critical vicinity of the SIT in different materials remains one of the major challenges. Here we observe the direct disorderdriven superconductorinsulator transition in NbTiN films with R_{c} = 2.7 kΩ/□ at room temperature. We show that the increasing the film's resistance suppresses the superconducting critical temperature T_{c} in accord with the Fermion model. We find that incrementally increasing R_{□} suppresses the BerezinskiiKosterlitzThouless temperature down to zero, while the critical temperature T_{c} remains finite, which complies with the Bosonic model. Upon further increase of R_{□}, the ground state of system becomes insulating. Finally, we demonstrate that the temperature dependence of the resistance of insulating films follows the Arrhenius law. [1] A. M. Finkel'stein, Superconducting transition temperature in amorphous films, JETP Lett. 45, 46 (1987). [2] A. Gold, Dielectric properties of disordered Bose condensate, Phys. Rev. A 33, 652 (1986). [3] M.P. A. Fisher, G. Grinstein, S. Grivin, Presence of quantum diffusion in two dimensions: Universal resistance at the superconductorinsulator transition, Phys. Rev. Lett. 64, 587 (1990). [4] A. F. Hebard, M. A. Paalanen, Magneticfieldtuned superconductorinsulator transition in twodimensional films, Phys. Rev. Lett. 65, 927 (1990). [5] D. Shahar, Z. Ovadyahu, Superconductivity near the mobility edge, Phys. Rev. B 46, 10917 (1992). [6] E. Bielejec, J. Ruan, W. Wu, Anisotropic magnetoconductance in quenchcondensed ultrathin beryllium films, Phys. Rev. B 63, 1005021 (2001). [7] T. I. Baturina et al., Localized superconductivity in the quantumcritical region of the disorderdriven superconductorinsulator transition in TiN thin films, Phys. Rev. Lett. 99, 257003 (2007).
M. V. Burdastyh, S. V. Postolova, T. I. Baturina, T. Proslier, V. M. Vinokur, A.Yu. Mironov JETP Letters 106 (11) (2017)
Detection of spin excitation transfer in a 2D electron system by photoluminescence of multiparticle exciton complexes
We demonstrate that nonequilibrium spin excitations drift to macroscopically large distances in
1. Yu.A. Bychkov, S.V. Iordanskii, and G.M. Eliashberg, Twodimensional electrons in a strong
Gorbunov A.V., Kulik L.V., Kuznetsov V.A., Zhuravlev á.S., JETP Letters 106, issue 10 (2017) Helical edge transport in the presence of a magnetic impurity
Twodimensional topological insulators are have attracted much recent interest since they feature helical edge states inside their band gap [1,2]. In the absence of timereversal symmetry breaking, spinmomentum locking prohibits elastic backscattering of these helical states, i.e., the helical edge is a realization of an ideal transport channel with conductance equal to e^{2}/h. However, this theoretical prediction was not confirmed by experiments on HgTe/CdTe [36] and InAs/GaSb [7,8] quantum wells. The timesymmetric interaction of the helical states with a "quantum magnetic impurity'' (an impurity which has its own quantum dynamics) is a leading candidate for explaining these experiments. In spite of recent theoretical studies of this problem [914], several key questions has not been addressed in details. We study theoretically the modification of the ideal currentvoltage characteristics of the helical edge in a twodimensional topological insulator by weak scattering off a single magnetic impurity. As a physical realization of such a system we have in mind the (001) CdTe/HgTe/CdTe quantum well (QW) with a Mn impurity that possesses spin S=5/2. Contrary to previous works, we allow for a general structure of the matrix describing exchange interaction between the edge states and the magnetic impurity. For S=1/2 we find an analytical expression for the backscattering current at arbitrary voltage. For larger spin, S>1/2, we derive analytical expressions for the backscattering current at low and high voltages. We demonstrate that the differential conductance may exhibit a nonmonotonous 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. GoldhaberGordon, 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 bandinverted 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 twodimensional 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 timereversal 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. [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, SelfOrganized 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 KuramotoBattogtokh 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 HeII.
Wellknown Faraday waves can be parametrically generated on a free surface of ordinary (classical) fluids such as water or on superfluid helium HeII surface when a sample cell is vibrated vertically. Standingwave patterns appear on the surface, and their frequencies are onehalf 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 HeII 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 2D vortices can be generated by Faraday waves on the surface of superfluid HeII also, more over one can observe formation of the vortex lattice in addition to the wave lattice on the surface of HeII 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 HeII, 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).
Levchenko A.A., MezhovDeglin 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 highperformance nanoscale devices. Optimization of heterostructures requires experimental and theoretical analysis of their specific physical properties. Nanosystem consisting in gold 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 twolevel 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 plasmonpolariton 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 Sr_{2}FeSi_{2}O_{7} comes into focus as a possible compound with unusual magnetoelectric 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 spinorbit coupling. However the energy intervals between the lowlying 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 magnetoelectric coupling is described as follows. The odd crystal field from the tetrahedral environment induces the coupling of the orbital momentum of the Fe^{+2}( ^{5}D) 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 magnetoelectric 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.
M.V. Eremin JETP Letters 105 (11) (2017) Electrontopological transition in copperoxide highTC superconductors before superconducting transition
It is well known the conductivity of hightemperature superconductors (HTSCs) with T_{C} ~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=T_{C}+(~30 K) [2]. Hence it inevitably follows in the interval T_{C}<T<300 K the hole Fermi surface (FS) of these HTSCs transforms into an electron one as a result of a topological transformation (the Lifshitz transition (LT) [3]. There is one of the central questions in the problem of the pseudogap state [1] of copperoxide highT_{C} superconductors: how and at what temperatures this transformation occurs. To evidence the charge carrier conversion the Hall effect is used usually. As for the BiSrCaCuO and YBaCuO, their Hall coefficients (R_{H}) have several features in the temperature range T_{C}…300 K [4,5]. The most significant of them is observed before the T_{C} in the region of fluctuation conductivity and can be interpreted as a manifestation of a scale holeelectron (he) conversion in a system of charge carriers, i.e. as the LT. However, this point of view is not universally accepted. As for the data on the transformation of the FS obtained by the ARPES (Angle Resolved Photoemission Spectroscopy) method [7], they, like [4,5], support several rearrangements of the FS, including those occurring near T_{C}. Meanwhile, it is the possibility to evidence the he conversion in a hole HTSC (the last condition is sure), which does not require either electric or magnetic fields to create the Hall potential difference. The technique developed by us [7,8] is based on the phenomenon of rearrangement of the spectrum of charge carriers in the nearsurface layer of a hole HTSC being in contact with a normal metal (Me). This phenomenon is a consequence of the annihilation of "aboriginal" hole fermions in the HTSC/Me interface with electrons penetrated from Me. The essence of this technique is the registration of changes in the resistance of the HTSC/Me interface r_{ó}, which is characterized by a small number of hole carriers. The appearance of the temperature singularities of r_{C} and the sign of r_{C } variation (dr_{ó}) make it possible to obtain an idea of the character of the changes in the system of charge carriers of the HTSC array. The dependences r_{C}(T) of the Bi(Pb)SrCaCuO/Pb and YBaCuO/In interfaces have been studied and anomalies near the temperature of the pseudogap opening and before the superconducting transition have been observed. We are shown that in Bi(Pb)SrCaCuO and YBaCuO, when the temperature T=T_{C}+(~10 K) is reached, that do not concerns to fluctuating Cooper pairs condensation. So, there is due to changing the topology of the FS. As a result, significant piece of FS becomes electronic. The most probable reason for the topological transition is the achievement of the temperature of the 2D3D crossover (the temperature of the threedimensionality of HTSC), which is a consequence of a modification in the electronic subsystem that leads to a change in the interaction mechanisms of the fluctuation Cooper pairs [9, 10]. 1. The Physics of Superconductors, Vol.1. Conventional and HighT_{C} Superconductors. Ed. by K.H. Bennemann and J.B. Katterson, Berlin, Springer, (2003). 2. K. Kawabata, S. Tsukui, Y. Shono, O. Michikami, H. Sasakura, K. Yoshiara, Y. Kakehi, T. Yotsuya, Phys. Rev. B58, 2458 (1998). 3. I.M. Lifshits, JETP 38, 1569 (1960) (in Russian). 4. Q. Zhang, J. Xia, M. Fang, Z. He, S. Wang, Z. Chen, Physica C 162164, 999 (1989). 5. A.L. Solovjov, FNT 24, 215 (1998) (in Russian). 6. T. Kondo, A.D. Palczewski, Y. Hamaya, T. Takeuchi, J.S. Wen, Z.J. Xu, G. Gu, A. Kaminski, arXive: 1208.3448v1 (2012). 7. V.I. Sokolenko, V.A. Frolov, FNô 39, 134 (2013) (in Russian). 8. V.A. Frolov, VANô, Ser.: Vacuum, pure materials, superconductors, 1, 176 (2016) (in Russian). 9. Y.B. Xie, Phys. Rev., B46, 13997 (1992). 10. A.L. Solovjov, V.M. Dmitriev, FNT 35, 227 (2009) (in Russian).
Sokolenko V.I., Frolov V.A. JETP Letters 105, issue 10 (2017)
QUANTUM GENERALIZATION OF THE THOMAS  FERMI APPROACH : EXACTLY SOLVABLE EXAMPLE
Correct allowing for the interparticle interaction in manybody systems faces considerable mathematical difficulties. The most frequently used approximation in such problems is the mean field approximation (MFA) which neglects fluctuations and the particles are considered as a continuous medium of inhomogeneous density. If , moreover, the system is described by the classical distribution function ( the statistics can be a quantum one) we obtain the well known Thomas  Fermi approach .However there are situations when at least some of the degrees of freedom of the system have to be treated in accord with quantum mechanics. Such examples are electrons in quantum wells or dipolar excitons in an electrostatic trap. In such cases the density of particles appearing in MFA is to be expressed via wave functions of a particle in the effective potential. The latter, in its turn, depends on the wave functions and occupation numbers, so one has to solve a selfconsistent problem. In case of a shortrange interparticle pair potential (2D gas of dipolar excitons) a nonlinear wave equation arises while for the longrange ( Coulomb) pair interaction the corresponding equation becomes integrodifferential (nonlocal effects). Two different systems are considered: bose  gas of dipolar excitons in a ring shape trap and fermigas of electrons in a quantum well of a MOSstructure. The trapped excitons are described by the GrossPitaevskyi nonlinear equation and for the very simple case of the rectangular potential of the “empty” trap the exact analytical solution is found. The most interesting result of this problem is criterion for existence of bound state in the effective potential ( in the one particle problem a 1D symmetric potential well always contains at least one bound state) . Methodologically instructive is the way of obtaining the eigenvalue of the GrossPitaevskyi equation: the ground state energy is found from the normalization condition. In case of electrons in a quantum well one deals with nonlinear integrodifferential equation for which the exact solution is unknown. The direct variational method was used to find the frequency of the intersubband transition. This frequency turned out to be scaled with the electron concentration N as $N^{2/3}$.
Chaplik A.V. JETP Letters 105 (9) (2017) Toward a selfconsistent theory of Fermi systems with flat bands
A model of fermion condensation, advanced more than 25 years ago, still remains the subject of hot debates, due to the fact that within its frameworks, nonFermiliquid (NFL) behavior, ubiquitously exhibited by strongly correlated Fermi systems, including electron systems of solids, is properly elucidated. The model is derived with the aid of the same Landau postulate that the ground state energy $E$ is a functional of its quasiparticle momentum distribution $n$, giving rise to the conventional Landau state. However, the model discussed deals with completely different solutions, emergent beyond a critical point, at which the topological stability of the Landau state breaks down, and therefore relevant solutions of the problem are found from the wellknown variational condition of mathematical physics $\delta E(n)/\delta n({\bf p})=\mu$ where $\mu$ is the chemical potential. Since the left side of this condition is nothing but the quasiparticle energy $\epsilon({\bf p})$, the variational condition does imply formation of the flat band or, in different words, a fermion condensate (FC). In fact, variational condition furnishes an opportunity to find solely the FC quasiparticle momentum distribution $n_*({\bf p}\in \Omega)$. New allotropes of carbon based in the C60 and C20 fullerenes with outstanding mechanical properties
Materials harder than diamond are always attract great attention from the scientists all over the world. Many attempts were made towards the synthesis especially of carbon material harder than diamond, which is the hardest possible material nowadays. A special interest belongs to materials called as fullerites. There are several experimental and theoretical works, where the synthesis and investigation of superhard fullerite were carried out. [1]–[4] Such materials reveal outstanding mechanical properties with the bulk modulus of several times higher than that of diamond. In this case the computational approaches and methods allow the theoretical investigations and prediction of a new materials with desired properties without using very expensive experimental equipment. Here we used the stateoftheart theoretical methods of computational predictions to predict new carbon phases based on the fullerene molecules of different sizes (C_{60} and C_{20}). Using the evolutionary algorithm, implemented in USPEX package, [5] we considered more than 3000 possible crystal structures to find the most stable ones. The important point, that predicted phases are based on the polymerized fullerites, displaying the superior mechanical properties. We defined the crystal structure of predicted 4 stable allotropes by simulating the XRD patterns. All predicted structures are highly symmetric. The mechanical properties were studied in details in terms of elastic tensor, bulk and shear moduli and velocities of acoustic waves. All predicted structures display elastic constants and bulk modulus very close to diamond, which allows to say that we indeed predict new superhard phases. The possible way of synthesis of such phases was proposed consisting in the cold compression of a mixture of graphite and C_{60} fullerenes. The important feature of predicted phases (besides the mechanical properties) is that they have relatively small band gap ~2.5 eV, while the cI24 phase has the direct gap of 0.53 eV. All obtained data allows the conclusion that predicted superhard semiconducting phases based on the polymerized fullerenes reveal necessary properties for applications in the electronic as basic elements.
[1] V.D. Blank, S.G. Buga, G.A. Dubitsky, N. R Serebryanaya, M.Y. Popov, and B. Sundqvist, Carbon 36, 319 (1998). [2] M. Popov, V. Mordkovich, S. Perfilov, A. Kirichenko, B. Kulnitskiy, I. Perezhogin, and V. Blank, Carbon 76, 250 (2014). [3] Y.A. Kvashnina, A.G. Kvashnin, M.Y. Popov, B.A. Kulnitskiy, I.A. Perezhogin, E.V. Tyukalova, L.A. Chernozatonskii, P.B. Sorokin, and V.D. Blank, J. Phys. Chem. Lett. 6, 2147 (2015). [4] Y.A. Kvashnina, A.G. Kvashnin, L.A. Chernozatonskii, and P.B. Sorokin, Carbon 115, 546 (2017). [5] C.W. Glass, A.R. Oganov, and N. Hansen, Comput. Phys. Commun. 175, 713 (2006).
Kvashnina Yu.A., Kvashnin D.G., Kvashnin A.G., Sorokin P.B. JETP Letters 105 ( 7) (2017)
Stochastic clustering of materials by plasma  surface interaction
Recently stochastic clustering with statistical selfsimilarity (fractality) has been found on material surface exposed under extreme plasma thermal loads in fusion devices (see [1]). In such devices, multiple processes of erosion and redeposition of the eroded material, surface melting and motion of the surface layers lead to a stochastic surface growth on the scales from tens of nanometers to hundreds of micrometers. The moving of eroded material species during redeposition from plasma and agglomeration on the surface is governed by stochastic electric fields generated by the hightemperature plasma. The specific property of the nearwall plasma in fusion device is the nonGaussian statistics of electric field fluctuations with longrange correlations [2]. It leads to the stochastic agglomerate growth with a selfsimilar structure (hierarchical granularity  fractality) of nonGaussian statistics contrary to a trivial roughness observed in ordinary processes of stochastic agglomeration. The dominant factor in such process in fusion device is the collective effect during stochastic clustering rather than the chemical element composition and physical characteristics of the solid material. In support of this view it is reported in this Letter, that such similar stochastic fractal structure with hierarchical granularity and selfsimilarity is formed on various materials, such as tungsten, carbon materials and stainless steel exposed to hightemperature plasma in fusion devices. In the literature it is discussed hypotheses of universal scalings of stochastic objects and processes with multiscale invariance property (statistical selfsimilarity), see e.g. [3]. The kinetic models propose the describing of the stochastic clustering with a selfsimilar structure and considering the power law solutions for the number N of agglomerating clusters with mass m (see e.g. [4]), N(m)=Cm^{(3+}^{h}^{)/2}, where h is a selfsimilarity exponent of the agglomeration kinetic model, C is a constant factor. It is surprisingly found in this Letter that such the power laws (with power exponents from 2.4 to 2.8) describing the roughness of the test specimens from fusion devices are strictly deviated from that of the reference samples formed in a trivial agglomeration process forming Brownianlike rough surface (such as samples exposed to lowtemperature glow discharge plasma and rough steel casting with the power law exponent in the range of 1.97 to 2.2). Statistics of stochastic clustering samples from fusion devices is typically nonGaussian and has a "heavy" tails of probability distribution functions (PDF) of stochastic surface heights (of the Hurst exponent from 0.68 to 0.86). It is contrary to the Gaussian PDF of the reference samples with trivial stochastic surface. Stochastic clustering of materials from fusion devices is characterised by multifractal statistics. Quantitative characteristics of statistical inhomogeneity of such material structure, including multifractal spectrum with broadening of 0.5 ¾ 1.2, are in the range observed for typical multifractal objects and processes in nature. This may indicate a universal mechanism of stochastic clustering of materials under the influence of hightemperature plasma.
1. V.P. Budaev et al., JETP Letters vol. 95, 2, 78 (2012). 2. V.P. Budaev, S.P. Savin, L.M. Zelenyi, PhysicsUspekhi 54 (9), 875 (2011) 3. A. L. Barabasi and H. E. Stanley, Fractal Concepts in Surface Growth (Cambridge Univ. Press, Cambridge, 1995). 4. C. Connaughton, R. Rajesh, O. Zaboronski, PRL 94 (19), 194503 (2005).
V.P. Budaev, JETP Letters vol. 105, issue 5 (2017) Fluctuational shift of nematic  isotropic phase transition temperature
Modern physics of liquid crystals is much younger than its traditional condensed matter material counterparts. Therefore the field is not yet completely elaborated and exhausted, and one may still expect discoveries of new mesogen materials exhibiting of new types of liquidcrystalline ordering. A few years ago such a discovery of socalled bentcore or dimer mesogens which can form short pitch heliconical nematic state (also known as twistbend nematics, $N_{TB}$) [1, 2], attracted a lot of interest to this new state of matter with nanoscale orientational modulation. First, to understand the nature of the phase, basically different from conventional uniform nematics and from modulated in mass density smectics (see e.g., Landau theory approach, [3,4]). Second, to exploit potentially very perspective applications of the $N_{TB}$ liquid crystals. Along this way, very recently S.M.Saliti, M.G.Tamba, S.N. Sprunt, C.Welch, G.H.Mehl, A.Jakli, J.T.Gleeson [5] observed of the unprecedentedly large magnetic field induced shift $\Delta T_c(H)$ of the nematic  isotropic transition temperature. What is even more surprising $\Delta T_c(H)$ does not follow the thermodynamics textbook wisdom prediction $H^2$ scaling. Our interpretation of such a behavior is based on singular longitudinal fluctuations of the nematic order parameter. Since these fluctuations are governed by the Goldstone director fluctuations they exist only in the nematic state. External magnetic field suppresses the singular longitudinal fluctuations of the order parameter. The reduction of the fluctuations changes the equilibrium value of the modulus of the order parameter in the nematic state, and leads to additional (with respect to the mean field contribution) fluctuational shift of the nematic  isotropic transition temperature. The mechanism works for any nematic liquid crystals, however the magnitude of the fluctuational shift increases with decrease of the Frank elastic moduli. Since some of these moduli supposed to be anomalously small for the bentcore or dimer mesogen formed nematic liquid crystals, just these liquid crystals are promising candidates for the observation of the predicted fluctuational shift of the phase transition temperature. Paradox of photons disconnected trajectories being located by means of "weak measurements" in the nested MaxZehnder interferometer
In a recent letter A. Danan et al. [A. Danan, D. Farfurnik, S. BarAd et al., Phys. Rev. Lett. 111, 240402 (2013)] have experimentally demonstrated an intriguing behavior of photons in an interferometer. Simplified layout of the experimental setup represents a nested MachZehnder interferometer (MZI) and is shown below. The surprising result is obtained when the inner MZI is tuned to destructive interference of the light propagating toward mirror F. In that case the power spectrum shows not only peak at the frequency of mirror C but two more peaks at the frequencies of mirrors A and B, and no peaks at the frequencies of mirrors E and F. From these results authors conclude that the path of the photons is not represented by connected trajectories, because the photons are registered inside the inner MZI and not registered outside it. These unusual results have raised an active discussion. Nevertheless, until now there was no comprehensive and clear analysis of the experiment within the framework of the classical electromagnetic waves approach. In this letter, we calculate the signal power spectrum at the output of the nested MZI, based on traditional concept of the classical electromagnetic waves (or quantum mechanics). This concept imply the continuity of the wave (photon) trajectories. We give intuitive clear and comprehensive explanation of paradoxical results. So, there is no necessity for a new concept of disconnected trajectories.
Simplified experimental setup with two nested MachZehnder interferometers. A, B, C, E, and F stands for mirrors; BS1 and BS2, and PBS1 and PBS2 stands for ordinary and polarized beam splitters respectively. The elements BS1, A, B, and BS2 form an inner MZI whereas the elements PBS1, C, E, F and PBS2 form an outer MZI. Various mirrors inside the MZI vibrate with different frequencies. The rotation of a mirror causes a vertical shift of the light beam reflected off that mirror. The shift is measured by a quadcell photodetector QCD. When the vibration frequency of a certain mirror appears in the power spectrum, authors conclude that photons have been near that particular mirror
G.N.Nikolaev JETP Letters 105 (3) (2017) Dark matter from dark energy in qtheory
The dynamics of the quantum vacuum is one of the major unsolved problems of relativistic quantum field theory and cosmology. The reason is that relativistic quantum field theory and general relativity describe processes well below the Planck energy scale, while the deep ultraviolet quantum vacuum at or above the Planck energy scale remains unknown. Following the condensed matter experience we develop a special macroscopic approach called qtheory, which incorporates the ultraviolet degrees of freedom of the quantum vacuum into an effective theory and allows us to study the dynamics of the quantum vacuum and its influence on the evolution of the Universe. The vacuum in our approach is considered as the Lorentzinvariant analog of a condensedmatter system (liquid or solid) which is stable in free space. The variable q is the Lorentzinvariant analog of the particle number density, whose conservation regulates the thermodynamics and dynamics of manybody systems. This approach is universal in the sense that the same results are obtained using different formulations of the qfield. In the paper, we choose the qfield in terms of a 4form field strength, which has, in particular, been used by Hawking for discussion of the main cosmological constant problem  why is the observed value of the cosmological constant many orders of magnitude smaller than follows from naive estimates of the vacuum energy as the energy of zeropoint motion. In qtheory, the huge zeropoint energy is naturally cancelled by the microscopic (transPlanckian) degrees of freedom, as follows from the GibbsDuhem identity, which is applicable to any equilibrium ground state including the one of the physical vacuum. In the paper, we consider a further extension of qtheory. We demonstrate that, in an expanding Universe, the variable effectively splits into two components. The smooth part of the relaxing vacuum field is responsible for dark energy, while the rapidly oscillating component behaves as cold dark matter. In this way, qtheory provides a combined solution to the missingmass problem and the cosmological constant problem. If this scenario is correct, the implication would be that direct searches for darkmatter particles remain unsuccessful in the foreseeable future. F.R. Klinkhamer and G.E. Volovik, JETP Letters 105, issue 1 (2017) NEW METHOD OF INVESTIGATIONS
The ability to detect nonequilibrium spin accumulation (imbalance) by all electrical means is one of the key ingredients in spintronics . Transport detection typically relies on a nonlocal measurement of a contact potential difference induced by the spin imbalance by means of ferromagnetic contacts or spin resolving detectors . A drawback of these approaches lies in a difficulty to extract the absolute value of the spin imbalance without an independent calibration. An alternative concept of a spintocharge conversion via nonequilibrium shot noise was introduced and investigated in experiment recently . Here, the basic idea is that a nonequilibrium spin imbalance generates spontaneous current fluctuations, even in the absence of a net electric current. Being a primary approach , the shot noise based detection is potentially suitable for the absolute measurement of the spin imbalance. In addition, the noise measurement can be used for a local noninvasive sensing. In this letter, we calculate the impact of a spin relaxation on the spin imbalance generated shot noise in the absence of inelastic processes. We find that the spin relaxation increases the noise up to a factor of two, depending on the ratio of the conductor length and the spin relaxation length. The design of the system. A diffusive normal wire of the length L is attached to normal islands on both ends. Nonequilibrium energy distribution on the left hand side of the wire generates the shot noise at a zero net current. The spin imbalance on the lefthand side of the wire is due to the electric current flowing from one ferromagnetic lead (red) to another one with opposite magnetization (blue).
V.S. Khrapai and K.E. Nagaev JETP Letters 105, №1 (2017)
