Transformation of the dimensionality of excitonic states in quantum wells with asymmetric barriers in an electric field

A transformation of the dimensionality of excitonic states from 2D to 3D with increasing external electric field is observed in single GaAs/Al_xGa_1−x As quantum-well structures with asymmetric barriers. The binding energy of a 2D exciton remains constant over a wide range of variation of the field, since the decrease in the binding energy is compensated by increasingly larger penetration of the electronic wave function into the barrier layer, where the exciton binding energy is higher because the effective mass is larger and the dielectric constant of AlGaAs is lower than that of GaAs. When the maximum of the electron wave function is displaced into the barrier as the field increases, the exciton binding energy decreases. As the field increases further, a 2D exciton transforms into a quasi-3D exciton, with a heavy hole in the quantum well and an electron in a resonant above-barrier state. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 3, 207–211 (10 February 1998)     

The role of auto-ionization transitions in the formation of the extended fine structure of high-energy secondary electron spectra

Extended fine structure (EFS) of secondary electron (SE) spectra has been detected beyond the high-energy (∼720 and ∼840 eV) LVV Auger lines in iron and nickel. Two mechanisms of its formation are considered: 1) direct transitions of electrons to the final state p according to Fermi’s “golden rule” and 2) second-order processes of auto-ionization type, passing through excitation of a core electron to an intermediate state q of the continuum with subsequent filling of the hole formed during this process by a valence electron and transition of the electron from the intermediate state q to the final state p. Interference of the direct wave with the wave reflected from neighboring atoms generates the EFS both in the final (p) and in the intermediate (q) state with two different periods determined by the wave numbers p and q. Comparison of calculated extended fine structures with the experimentally observed ones leads to the conclusion that the structure is formed by second-order auto-ionization processes. Fiz. Tverd. Tela (St. Petersburg) 40, 1589–1594 (September 1998)     

Semiclassical energy levels of electrons in metals with band degeneracy lines

We show that in calculating the semiclassical energy levels of electrons in metals located in a magnetic field, one must determine whether or not the corresponding electron paths in the space of wave vectors k are attached to a band degeneracy line. Calculations in the two possible cases, i.e., with and without such attachment, differ by |e|ℏ/2m*c, where e is the electron charge and m* is the cyclotron mass of the electron. This shift in the energy levels is of a topological nature, and its existence depends neither on the specific form of the electron dispersion relation ε(k) near the electron path nor on the shape or size of this path. The reason for this shift lies in the fact that the electron orbit is attached to the band degeneracy line, which is the line of singular points of the Bloch wave functions. In many respects this effect is similar to the Aharonov-Bohm effect if the band degeneracy line is considered an infinitely thin “solenoid.” This shift in energy levels should become apparent in studies of oscillation phenomena in metals. We give examples of metals in which the conditions for observing the shift is probably the most favorable. Zh. éksp. Teor. Fiz. 114, 1375–1392 (October 1998)     

Energy spectra and quantum crystallization in two-electron quantum dots in a magnetic field

Quantum crystallization of electrons in a quantum dot (QD) subjected to an external magnetic field is considered. Two-electron QDs with two-dimensional (2D) parabolic confining potential in an external transverse magnetic field are calculated. The Hamiltonian is numerically diagonalized in the basis of one-particle functions to find the energy spectra and wave functions for the relative motion of electrons with inclusion of electron-electron interaction for a broad range of the confining-potential steepness (α) and external magnetic fields (B). The region of the external parameters (α, B) within which a gradual transition to quantum crystalline order occurs is numerically determined. In contrast to a 2D unbounded system, a magnetic field acts nonmonotonically on “crystallization” in a quantum dot with several electrons because of a competition between two effects taking place with increasing B, namely, decreasing spread of the electron wave functions and increasing effective steepness of the confining potential, which reduces the average separation between electrons. Fiz. Tverd. Tela (St. Petersburg) 40, 1753–1759 (September 1998)     

Novel effects of electron-phonon interaction in quasi-two-dimensional structures located in a magnetic field

This paper studies the interaction of electrons and acoustic phonons in a quasi-two-dimensional system with an asymmetric quantizing potential in a magnetic field that is parallel to the structure’s plane. It is demonstrated that the electron-phonon interaction in such a system generates an emf when there is a standing acoustic wave, as well as when the structure is heated uniformly. These phenomena are macroscopic manifestations of a universal quantum effect, which amounts to an emf being generated by any isotropic perturbation of any electron system in which the energy depends asymmetrically on the velocity υ, i.e., ε(υ)≠ε(−υ). Zh. éksp. Teor. Fiz. 115, 959–969 (March 1999)     

Electronic resonances in a quantum well having a periodically uneven boundary

The spectrum of the electronic states in an infinitely deep two-dimensional potential well, where one wall is periodically uneven, is investigated theoretically. It is shown that in non-Bragg type resonances — standing electron wave resonances, which are modes of different spatial harmonics of the electron wave function — arise in such a well. The resonances occur in a wide range of energies, starting at values close to the bottom in each 2D subband. The resonance interaction splits the energy spectrum and results in the appearance of gaps, giving the electron spectrum a miniband character. The properties of the electron gas vary substantially in accordance with the new characteristics of the spectrum. Fiz. Tverd. Tela (St. Petersburg) 41, 1867–1870 (October 1999)     

Anisotropic momentum transfer in low-dimensional electron systems in a magnetic field

In low-dimensional systems with an asymmetric quantizing potential, an asymmetric electron energy spectrum ε(p)≠ε(−p), where p is the electron momentum, arises in the presence of a magnetic field. A consequence of such an energy spectrum is that momentum transfer to the electron system in mutually opposite directions in the presence of an external perturbation is different. Therefore, in the presence of a standing electromagnetic wave momentum is transferred from the wave to the electrons, which gives rise to a new type of electromotive force. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 8, 551–555 (25 October 1997)     

Quasi-one-dimensional transport of nondegenerate electrons in two-dimensional systems with a fluctuation potential

A threshold vanishing of the Hall emf with decreasing gate voltage is observed at ≈ 77 K in semiconductor systems which are disordered as a result of a high built-in charge density near the plane of the 2D-electron channel. The effect is observed at a channel conductivity σ ≈e ²/h and is due to a transition to nondegenerate-electron transport via a 2D percolation cluster having a quasi-1D character of the conduction. We have established that the conductance of “short” structures, having a length of the order of the correlation length of a percolation cluster, equals ≈e ²/h per electron and is determined by isolated percolation paths having a lowered percolation threshold. These phenomena are a general property of disordered 2D systems. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 10, 633–638 (25 November 1997)     

Magnetoquantum de Haas-van Alphen oscillations in spin-split two-dimensional Fermi liquid

Theory of magnetoquantum oscillations with spin-split structure in strongly anisotropic (two-dimensional (2D)) metal is developed in the formalism of level approach. Parametric method for exact calculation of oscillations wave forms and amplitudes, developed earlier for spin degenerate levels is generalized on a 2D electron system with spin-split levels. General results are proved: 1) proportionality relation between magnetization and chemical potential oscillations accounting for spin-split energy levels and magnetic field unperturbed levels (states of reservoir), 2) basic equation for chemical potential oscillations invariant to various models of 2D and 1D energy bands (intersecting or overlapping) and localized states. Equilibrium transfer of carriers between overlapping 2D and 1D bands, characterizing the band structure of organic quasi 2D metals, is considered. Transfer parameter, calculated in this model to be of the order of unity, confirms the fact that the wave form of oscillations in organic metals should be quasisymmetric up to ultralow temperature. Presented theory accounts for spin-split magnetization oscillations at magnetic field directions tilted relative to the anisotropic axis of a metal. Theoretical results are compared with available experimental data on organic quasi-2D metal α-(BEDT-TTF)₂KHg(SNC)₄ explaining the appearance of clear split structure under the kink magnetic field and absence above by the corresponding change in the electron g-factor rather than cyclotron mass. Received 20 December 2000 and Received in final form 13 July 2001     

(e, 2e) triple differential cross section for ionization-excitation of helium

Simultaneous ionization and excitation of helium by electron impact is considered in an improved second Born approximation. The wave function of the low energy ejected electron is obtained in the field of residual He⁺ ion in 2s-state. The calculation has been done for the processe ⁻+He→e ⁻+He⁺(2s)+e ⁻ in the coplanar asymmetric geometry with Hartree-Fock wave function of Byron and Joachain for the helium ground state and the results are compared with the absolute experimental data of Dupreet al [J. Phys. B25, 259 (1992)] at ∼ 5.5 keV incident energy. Our results are found to increase the ratio of the recoil peak to binary peak intensity by about 30% over the first Born results and thus to bring it closer to the experimental data.     

Energy spectrum of a GaAs (δ-Sn) structure on a vicinal face

The potential profile, electron energy levels, and corresponding wave functions are calculated for a gallium-arsenide structure with a δ-doped tin vicinal face GaAs(0.3°, δ-Sn). Calculated values of the electron densities in the subbands agree well with the quantities obtained from an analysis of the Shubnikov-de Haas oscillations and photoluminescence spectra of the structure. On the basis of the calculated band diagram the lines observed in the photoluminescence spectrum of the GaAs(0.3°, δ-Sn) structure are identified here for the first time as associated with electron transitions on the size-quantization levels in the tin δ-layer. Fiz. Tverd. Tela (St. Petersburg) 39, 1853–1856 (October 1997)     

Integrable chain of electrons coupled with squeezed phonons

The exact wave function for a one-dimensional chain of electrons coupled with squeezed phonons is obtained. The ground state energy and the gap in the electron spectrum are calculated. It is shown that there exists an optimal phonon number n ^ph≠0 for the ground state of the system. The results are generalized for a system of correlated electrons. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 3, 140–145 (10 August 1996) On leave from Institute of General and Inorganic Chemistry of the Russian Academy of Sciences, 31 Leninskii prosp., GSP-1, Moscow, 117907, Russia Published in English in the original Russian journal. Edited by Steve Torstveit.     

3D Visualization of the separated fluid flows

For the detailed investigation of the 3D unsteady incompressible viscous separated fluid flows around a sphere (for 200≤Re≤700) and a circular cylinder (for 200≤Re≤400) the direct numerical simulation and 3D visualization are used. For 3D visualization of the fluid flows around a sphere the definition of vortex core as a connected region containing two negative eigenvalues of theS ²+Ω ² tensor is used (whereS _i,j andΩ _ij are the rate of strain and the rate of rotation tensors). The formation mechanism of vortices in the sphere wake for Re=500 is described in detail. For 3D visualization of the fluid flows around a circular cylinder the 3D isosurfaces of the streamwise component of vorticity ω _x are used.     

Topological Berry phase and semiclassical quantization of cyclotron orbits for two dimensional electrons in coupled band models

The semiclassical quantization of cyclotron orbits for two-dimensional Bloch electrons in a coupled two band model with a particle-hole symmetric spectrum is considered. As concrete examples, we study graphene (both mono and bilayer) and boron nitride. The main focus is on wave effects – such as Berry phase and Maslov index – occurring at order (^h/_2p)\hbar in the semiclassical quantization and producing non-trivial shifts in the resulting Landau levels. Specifically, we show that the index shift appearing in the Landau levels is related to a topological part of the Berry phase – which is basically a winding number of the direction of the pseudo-spin 1/2 associated to the coupled bands – acquired by an electron during a cyclotron orbit and not to the complete Berry phase, as commonly stated. As a consequence, the Landau levels of a coupled band insulator are shifted as compared to a usual band insulator. We also study in detail the Berry curvature in the whole Brillouin zone on a specific example (boron nitride) and show that its computation requires care in defining the “k-dependent Hamiltonian” H(k), where k is the Bloch wavevector.     

Spectrum of polariton excitations of a two-dimensional electron plasma in a magnetic field

Polariton excitations associated with magnetoplasma and cyclotron oscillations in a two-dimensional (2D) electron plasma are studied. In contrast to previous works by other authors, it is concluded that there exists a low-frequency nontransmission band in the spectrum of 2D surface magnetoplasma polaritons. Radiative polariton excitations associated with nonuniform cyclotron oscillations of electrons in a 2D system are investigated. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 3, 200–204 (10 August 1998)     

Contribution to the theory of “incompressible” regions in an inhomogeneous magnetized 2D electronic system

A modification of the theory of “incompressible” regions in an ideal spinless inhomogeneous magnetized 2D electronic system near points on the electron density profile n(x) with an integer filling factor is proposed. Such regions leads to the appearance of a finite capacitance between the parts of the 2D system that are separated by an incompressible channel, so that capacitive methods can be used to investigate such a system. The Corbino configuration is especially convenient for these purposes. The parameters of the “incompressible” channel in a Corbino disk with a spatially inhomogeneous 2D electronic system in the presence of an individual point, near the channel, on the electron density profile with an integer magnetic filling factor are determined. The magnetocapacitance between the edges of the Corbino disk separated by an incompressible interlayer is found for cases of practical interest. It is shown that this magnetocapacitance contains direct information about the width of the integer strip. Fiz. Tverd. Tela (St. Petersburg) 41, 1103–1109 (June 1999)     

Theory of superfluidity of nuclear matter based on the Fermi-liquid approach

This paper discusses how an electromagnetic field consisting of a superposition of a constant magnetic field and a field of laser type can affect nuclear beta decay. In general it is not assumed that the intensities of the two types of fields are small compared to the characteristic field H _cr*=β ₁ H _cr, where H _cr=m ² c ³/eℏ and the quantity β ₁ depends on the energy liberated in the decay and the configuration of the electromagnetic field. For nonrelativistic decays the quantity β ₁ is found to be of the same order as the maximum kinetic energy of an electron referenced to its rest energy β ₁∼I≪1. It is assumed that the frequency of the wave field satisfies ℏω/mc ²⩽I. The behavior of the probability for the process is studied over a wide range of the fundamental parameters that characterize the fields. Corresponding asymptotic expressions are derived in the “weak”-and “strong”-field regimes. Also discussed are so-called interference corrections to the unperturbed decay probability, which cannot in principle be studied by the methods of perturbation theory. It is shown that the times and distances that are important in generating these contributions exceed the parameters of the unperturbed processes, just as in the case of a plane-wave field previously investigated in detail by Nikishov and Ritus. However, in contrast to the case of a pure wave field, when a system is simultaneously subjected to a constant magnetic field and a wave field, the degree to which these characteristic regions are enlarged can depend not only on the intensities of the electromagnetic fields but also on their rates of change, even in the limit in which the wave field is slowly varying. Zh. éksp. Teor. Fiz. 111, 3–24 (January 1997)     

On the state of supersaturation of a 2D electron system on a liquid-helium surface

The reasons why supersaturated states appear for a 2D electron system on a liquid-helium surface and the possibility of stationary existence of such states are discussed. The main characteristics of a 2D electron system on helium under stationary saturation conditions are calculated. It is shown that the well-known saturation state for electrons above helium is one of a continuum of supersaturated states. The experimental possibilities for observing and identifying supersaturated states for electrons on a helium surface are noted. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 4, 274–278 (25 August 1999)     

Temperature dependence of magnetophonon resistance oscillations in GaAs/AlAs heterostructures at high filling factors

The temperature dependence of the magnetic-field resistance oscillations induced by acoustic phonons in a 2D system with a moderate mobility and a high electron density in the range T = 7.4–25.4 K has been studied. It has been established that the amplitude of the magnetophonon resistance oscillations in the system under study is determined by the quantum lifetime modified by the electron-electron scattering, in accordance with the results recently obtained in a GaAs/AlGaAs heterostructure with an ultrahigh mobility and a low electron density [A. T. Hatke et al., Phys. Rev. Lett. 102, 086808 (2009)]. The shift of the main maximum of the magnetophonon resistance oscillations to higher magnetic fields with increasing temperature is observed.     

Quasistationary states of an electron in a spherical β-HgS/β-CdS/β-HgS nanoheterosystem

The electron scattering matrix for spherically symmetric states in a spherical β-HgS/β-CdS/β-HgS nanoheterosystem is calculated. The positions of the energy levels and the lifetimes of an electron in the corresponding states are found as functions of the geometric parameters of the system and analyzed. Fiz. Tverd. Tela (St. Petersburg) 41, 2081–2083 (November 1999)