Bogolyubov Institute for Theoretical Physics
of the National Academy of Sciences of Ukraine

Department of Theory of Nonlinear Processes in Condensed Matter
  • Based on the solutions of the Dirac equation, it is shown that the system of quasi-two-dimensional electrons confined in the potential layer, for instance, in layered semiconducting heterostructures, can be in one of the three possible spin states. These states differ by spin polarization and by the spectrum of the two-dimensional energy zones. One of these states is a well-known Rashba state which is characterized by the spin splitting of energy zones. In the other spin state the spin splitting is anisotropic, and in the third state the energy zones are degenerate with respect to spin. Respectively, there are the three systems of eigenfunctions of the Dirac equation that correspond to the three spin states. The functions of each of these systems are also eigenfunctions of three different spin operators, which commute with the Hamiltonian of the Dirac equation, but do not commute with each other. These spin operators do determine the spin polarization of electrons.
    A. Eremko, L. Brizhik, V.M. Loktev
  • We study the thermodynamic properties of the two-component 2+1-dimensional massive Dirac fermions in an external magnetic field. The violation of the time-reversal symmetry is shown to give rise to a term in the thermodynamic potential that is linear in the magnetic field, while the famous problem of Landau diamagnetism suggests that the leading field-dependent term is quadratic in the field. Accordingly, the leading term of the explicitly calculated magnetization is anomalous, viz. it is independent of the strength of the magnetic field.
    S.G. Sharapov
  • The theory is developed for sound waves emitted by Au, Ag and Cu nanoparticles embedded in the plexiglass matrix under ultrashort laser pulses irradiation. Analytical expressions are obtained for the amplitude and power of the longitudinal spherical acoustic oscillations as functions of density and elastic properties of the medium, the laser pulse duration, electron temperature, particle radii, and electron-phonon coupling constant. The factors affecting the dynamics of the power damping of these waves are studied in detail.
    N.I. Grigorchuk
  • Two- and three-terminal devices consisting of a single barrier surrounded by one or two potential wells were studied. The zero-thickness limit for these objects has been considered and it was shown that point interactions obtained in this limit can be described by a family of diagonal matrices, which are a subclass of four-parameter family of point interactions. Tunneling through such structures is absent almost everywhere except several points controlled by external voltage. Analytical expressions for resonant tunneling through such a kind of hetero-structures have been obtained.
    A.V. Zolotaryuk, Y.А. Zolotaryuk
  • The sensitivity of the surface plasmon resonance wavelength position in prolate and oblate metal nanoparticles to the refractive index of an embedding solution, nanoparticle shape, and temperature was studied theoretically. The influence of dissipation factor on plasmon resonance was discussed as well. The new approach specifying the optimal nanoparticle shape to reach the maximal sensitivity has been proposed. It was found that the ratio of the sensitivity to the half-width of the resonance line in the dependence on the refractive index as well as the nanoparticle radius has oscillatory character. The calculations were illustrated on the example of K, Na and Ag nanoparticles.
    N. Grigorchuk
  • Temperature influence on the ratchet solitons drift induced by periodic with mean zero value force that takes place in molecular chain with broken inverse symmetry has been studied. It was shown that the temperature improves the conditions of the drift, namely, with its increasing the critical value of the intensity of the external electric field, above which the ratchet phenomenon takes place, decreases. The temperature decreases also the lower critical value of the electric field period. It was found that there is a temperature range where the drift velocity is larger than that at zero temperature and was demonstrated the existence of stochastic resonance, i.e. an optimal temperature at which the solitons drift is maximum.
    L.S. Brizhik, A.A. Eremko
  • The tunneling of a particle with non-zero spin through the potential barrier of the finite width, which has a chiral symmetry, is studied with the account of the spin-orbit interaction. Based on the exact solution of the Shroedinger equation, the trnasition and reflection coefficients are calculated and it is shown that such barriers posses a property of spin selectivity. This means that non-magnetic barriers can lead to a spin current in the absence of their mirror symmetry. These expressions are used to describe quantitatively the experiments on the transfer of photoelectrons through the layers of DNA moleculers on a substrate.
    O.O. Eremko, V.M. Loktev
  • The propagation is studies of a soliton (fluxon) in a two-dimensional Josephson contact with a strip-like in-homogeneity , which belongs to the class of a short-cuts and is a line oriented perpendicular to the propagation of fluxons. The radiation , caused by scattering of a fluxon on in-homogeneity, is calculated and shown to have a resonant dependence on the fluxon velocity. which is qualitatively different from the case of point-like impurity, for which such a dependence is a monotonously increasing function.
    Ya.O. Zolotaryuk
  • The effect of electron temperature on absorption and scattering of light by metallic nanoparticles during the excitation of a surface plasmon, is studied. Expressions for the tensors of electroconductivity and polarizability at finite electron temperatures are obtained. Electroconductivity and shape of resonance of the surface plasmon are obtained for a spherical metallic nanoparticle. These results allow to describe various kinetic phenomena in such spherical particles, place in a dielectric medium.
    M.I. Grigorchuk
  • Superconducting properties of the two-dimensional model of a metal with a spectrum that contains an insulating gap which can lay either below or above Fermi level has been studied. It has been shown that presence of this gap influences the superconducting gap as well as the critical temperatures Tc and TcMF . In particular, jumps of the derivatives of these temperatures have been identified as functions of doping or Fermi level position.
    V.M. Loktev
  • The experimental data on the influence of the spin-polarized current on the dynamics of the magnetization vector of an antiferromagnetic layer have been analyzed. A precessional regime of motion of this vector with the linear dependence of its frequency on the current has been found. The intensity of the pulses that excite such precession and the influence of the external magnetic field has been estimated. The results appear to be in accordance with the available observation.
    V.M. Loktev
  • A possibility of binding of two excess electrons in a solitonic state in anharmonic molecular lattices with electron-phonon interaction has been proven. The energy, mass and the localization length of such bisolitonic states has been calculated.
    L.S. Brizhik
  • Dynamics of large charged polarons in one-dimensional diatomic lattices under the influence of an external periodic electromagnetic field with zero mean has been investigated. The possibility of rectification of polaron motion if the field intensity and its period exceed certain critical value has been demonstrated.
    L.S. Brizhik, A. A. Eremko
  • The role of the interlayer exchange interactions in the formation of magnetic structures with different packing sequences of the dense-packed molecular planes in the δ-phase of solid oxygen has been investigated. It has been shown that the temperature- or pressure-induced variation in the intermolecular distances gives rise to the change of the exchange coupling between the nearest close-packed planes and, as a result, causes transitions between different magnetic phases of δ-oxygen. The interpretation of the recently experimentally measured phase diagram of δ-oxygen has been done on the basis of the proposed model.
    H.V. Gomonay
  • A theory of optoacoustic phenomena for metallic nanoclusters incorporated in a insulating matrix that has been developed. It makes possible to determine the amplitude of the sound oscillations of the matrix when the clusters are excited by a laser. In the field of plasmonic resonances a considerable difference between the optoacoustic properties of discrete and continuous metal films on the surface of the transparent insulating matrix has been obtained.
    N.I. Grigorchuk
  • The investigation of the regularity of the electric field penetration into the structured system of electrolytes, in particular into a biological structure. The equations that describe such a process have been obtained and the characteristics of the electric fields that can effectively penetrate into the living objects. The obtained results have been used during the experimental investigation of the electric field influence on the bacteria. In particular, a sharp hydrophobicity rise (sevenfold) in such objects after the action of weak electric field has been detected experimentally.
    V.N. Ermakov
  • The scattering processes on the point-dipole one-dimensional potentials that can be defined as a weak limit of the regular finitely separated well- and barrier-shaped functions. It has been shown that resonant tunneling across the point potentials depends on the regularization of these potentials.
    A.V. Zolotaryuk
  • Directed motion of domain walls (DWs) in a classical biaxial ferromagnet placed under the influence of periodic unbiased external magnetic fields has been obtained. The symmetry approach for the analysis of the equations of motion has been developed and the necessary conditions for the directed DW motion have been found. With the help of the soliton perturbation theory and numerical simulations, the average DW velocity as a function of different system parameters such as damping constant, amplitude, and frequency of the external field, is computed.
    Y. Zolotaryuk
  • Longitudinal magnetic susceptibility of a two-dimensional quantum Ising model in a transversal magnetic field in the wide temperature range and near the quantum critical point has been investigated. The asymptotic scaling behavior of the longitudinal magnetic susceptibility has been obtained.
    O.B. Kashuba
  • The average first passage time during which the intensity of the electron flow across the tunneling system rises from the initially low value to the value that guarantees transition to the new stationary state has been computed with the help of numerical simulations. This time has been obtained for the different noise parameters: its intensity and the correlation time. Numerical simulations have shown that the process slows down in the sense that the relaxation time increases monotonically as a function of the correlation time, while at the same time the rise of the noise intensity accelerates the transition.
    O.O. Ponezha
  • The model with optical phonons that can describe the phonon spectrum of graphene with sufficiently high precision. It has been shown how the electron-phonon interaction renormalizes the electron motion on the Fermi surface due to the presence of the effective mass renormalization parameter. In the case of graphene this parameter depends on the chemical potential has the physical meaning of the velocity renormalization. It has been shown that the chemical potential value is shifted with respect to its value in the free zone. The relative position of the Dirac point is also being renormalized respectively.
    S.G. Sharapov