A. M. Kosevich

Peculiarities of dynamics of one-dimensional discrete systems with interaction extending beyond nearest neighbors, and the role of higher dispersion in soliton dynamics

In the analysis of dynamics of an ideal system as well as a system with point defects, the role of interaction is considered not only for the nearest neighbors. The Green’s function is constructed for steady-state vibrations of a chain at all possible frequencies. It is shown that, if the interaction with the next-to-nearest neighbors is taken into account, the Green’s function inevitably becomes double partial, the nature of its two components depending significantly on its eigenfrequency. It is found that the Green’s function for frequencies of the continuous spectrum of small vibrations has one component of the plane wave type, while the other component is localized near the source of perturbations. Such a Green’s function describes the so-called quasilocal vibrations. At certain discrete frequencies falling in the continuous spectrum, the quasilocal vibration is transformed into local vibration (that does not propagate to infinity). The conditions of applicability of differential equations with fourth...

Quantum levels and quasi-local states of SINIS structures

Quantum states of a superconductor–insulator–normal metal–insulator–superconductor sandwich (the SINIS structure) are investigated on the basis of the Bogoliubov–de Gennes equations. The dispersion equation is obtained for the quasiparticle spectrum for energies E<Δ (Δ is the energy gap in the superconductor) taking into account the Andreev scattering as well as conventional electron reflection at the interfaces of the SINIS structure. The spectrum makes it possible to calculate the Josephson current in the system. The transparency coefficient of the system for electrons with a continuous energy spectrum is calculated, and quasi-local states (“resonance levels” of transparency) are determined for the structure under investigation.

Surface and quasi-surface phonons and transformation waves in a hexagonal crystal

A simple model of the dynamics of a layered crystal having a hexagonal lattice with weak interaction of atoms in neighboring basal planes is formulated. Vibrations propagating in the basal plane with displacement vectors lying in the same plane are investigated. Energy–momentum relations are obtained for low-frequency (Rayleigh type) as well as high-frequency (gap-mode) vibrations localized at the free surface. The region of existence of quasi-surface phonons, whose boundaries are determined to a considerable extent by the shape of constant-frequency surfaces for two branches of bulk vibrations is determined. It is shown that peculiarities in the interaction of elastic waves with the crystal surface appear in the bulk spectrum at certain frequencies. The dispersion curves for surface vibrations separated from the continuous spectrum have a continuation in this spectrum in the form of dependences corresponding to transformation of a transverse wave into a longitudinal one. The effect of a surface monolayer...

Peculiarities of the resonant phonon scattering from a plane defect in an fcc crystal

Resonant peculiarities of phonon scattering from a plane defect in an fcc crystal with the central interaction between nearest neighbors are investigated. It is shown that resonance effects are associated with the interaction of phonons of two bulk branches on a plane defect. Dispersion curves for the frequencies of resonance transmission and reflection are derived. To clarify the physical nature of resonances under investigation, the dispersion relations of vibrations localized at the defect are calculated in a wide range of wavelengths. The frequency curves of localized symmetric vibrations continue in the bulk spectrum in the form of dispersion curves of the frequencies of resonant phonons transmitted through the defect.

Nonquantum oscillations associated with the dynamics of an electron in superlattice

Oscillations associated with the classical motion of a Bloch electron in a spatially periodic structure whose period considerably exceeds the atomic spacing are discussed. Such phenomena include the so-called Bloch oscillations, i.e., the vibrational motion of an electron in a constant uniform magnetic field, and the oscillatory dependence of magnetoresistance on a constant magnetic field, associated with the geometrical resonance at which the electron orbit diameter in the magnetic field is commensurate with the superlattice period.

Rayleigh-type vibrations localized at the free surface of a fcc crystal

The waves localized near the free surface (001) of a fcc crystal and propagating along the [110] direction are analyzed in the model of central interaction of nearest neighbors. The frequencies of these waves fall in the gaps of the frequency spectrum of bulk harmonic vibrations for a fixed value of the wave vector k along the surface. The long-wave limit and the case of wave vectors close to the Brillouin zone boundary are studied analytically. These limiting dependences are in accord with the results obtained earlier by other authors by numerical methods. The analytical calculations in the limiting intervals of vector k are supplemented with numerical calculations for arbitrary values of wave vectors. It is significant that the waves under investigation have a displacement component perpendicular to the crystal surface and hence can be studied by standard methods of inelastic scattering of helium atoms.