M. V. Éntin

Spin orientation of electrons by lateral electric field in 2D system without inversion symmetry

Abstract Spin polarization in 2D system caused by a lateral electric field is studied taking into account both Rashba and Dresselhaus mechanisms of spin–orbit interaction.a

Quantum mechanics of graphene with a one-dimensional potential

Electron states in graphene with a one-dimensional potential have been studied. An approximate solution has been obtained for a small angle between vectors of the incident electron momentum and potential gradient. Exactly solvable problems with a potential of the smoothened step type U(x) = Utanh(x/a) and a potential with a singularity U(x) = −U/(|x| + d) are considered. The transmission/reflection coefficients and phases for various potential barriers are determined. A quasi-classical solution is obtained.

Spin Response of 2D Electrons to a Lateral Electric Field

The spin orientation of two-dimensional (2D) electrons by a lateral electric field is considered. The electron dispersion law is assumed to contain linear terms due to the spin-orbit band splitting in an asymmetric quantum well. The coefficient of spin orientation in a DC electric field is found. The mean electron spin is oriented in the sample plane perpendicularly to the electric field. The interaction of an AC electric field with spins of 2D electrons is studied. It is shown that transitions between different spin states give rise to a narrow absorption band. These states are mixed with 2D plasmons in the frequency range related to these transitions, with the result being that the plasmon spectrum is modified and a new type of oscillations arises (spin-plasmon polariton). The problem of the generation of spin-plasmon polaritons by an external field is solved.

Electrons in a curvilinear quantum wire

The adiabatic motion of electrons in curvilinear quantum wires was studied. It was assumed that the cross section of a wire was constant along its length. The potential that limited electron motion across a wire and the shape of the cross section of the wire were considered arbitrary, while the curvature and the torsion (defined as the derivative of the cross section rotation angle with respect to the length) were assumed to be small. An effective nonrelativistic Hamiltonian for the motion of electrons along a wire with the conservation of transverse quantum numbers was obtained. The spin-orbit coupling Hamiltonian related to the curvature and torsion of a wire was found. Particular cases of a rectilinear twisted quantum wire with a noncircular cross section and a curvilinear quantum wire on a plane were studied. Various transverse potential models limiting the motion of electrons were considered. In particular, the coefficients of the effective Hamiltonian for quantum wires with rectangular and circular cross sections and hard walls and for wires with a parabolic potential were found.

Theory of one-dimensional quantum pump based on a two-barrier structure

A 1D quantum pump based on a structure of two δ-functional harmonically oscillating potentials is considered. Such a structure can pump electrons from one bank to the other. An ac perturbation induces a steady-state current. The effect takes place in spatially asymmetric systems. Such an asymmetry is formed due to a difference in the initial heights of the barriers or in the amplitudes or phases of ac signals. The pump can operate in various modes depending on its parameters. It is shown that the current displays oscillations with a period such that the wavelength of incident or excited electrons is multiple to the separation of the δ-functions. Resonances at quasi-stationary states between the barriers, at zero energy, and with stationary states (in the case of wells) are investigated.

High-frequency blockade and related phenomena

Abstract We study systems with local vibrating potentials, one-dimensional (1D) single and double wells and the tight-binding 1D model with a single vibrating site. In general, these systems transmit or reflect particles inelastically with absorption or emission of several frequency quanta. Nevertheless, we have found that at some conditions these systems can perfectly and elastically reflect electrons. This high-frequency “blockade” give rise to unique possibility of near-ideal localization of electrons whose energy lies on the background of continuous energy spectrum. We discuss different consequences of this statement.

High-frequency resonant blockade in one-dimensional quantum pump with oscillating potential wells

The conductance and the stationary current are studied in a one-dimensional quantum wire with a harmonically oscillating delta-potential barrier or well. It is shown that, in the structure with a single well, the conductance vanishes at certain parameters. This phenomenon is associated with the occurrence of quasi-energy states corresponding to the total and elastic reflection of particles from the well. The stationary photovoltaic current under an alternating field in a double-well structure is considered. It is shown that the derivative of the photovoltaic current with respect to the Fermi energy vanishes under the same conditions. The results for a system with a single well are generalized to the case of a one-dimensional lattice in the tight binding model with an oscillating level of one of its sites. It is shown that the problem of particle scattering by a three-dimensional short-range center with an oscillating potential is reduced to the corresponding one-dimensional problem.

The surface energy of an electron gas in model crystals

The surface energy of an electron gas in a crystal is considered. The results obtained for a quadratic spectrum are generalized to an arbitrary energy spectrum in certain crystal models. The surface energy of an electron gas with a quadratic spectrum is found for a sample with a rough boundary when the height of irregularities is small compared with the electron wavelength.

The distribution of equilibrium magnetization currents in systems with dimensional quantization in a finite magnetic field

The distribution of equilibrium magnetization currents in two-dimensional bounded systems placed in an external magnetic field is studied. A half-plane, a quantum disk, and a wide quantum ring are considered. The passage from classical to quantizing magnetic fields is investigated. The edge currents near the boundary of the half-plane are shown to experience damped (far from the boundaries) spatial oscillations related to the Fermi electron wavelength. The region occupied by currents was found to narrow with increasing field. Apart from these oscillations, the current contains a component that smoothly changes with distance but oscillationally depends on the position of the Fermi level relative to the Landau levels. The suppression of the oscillations by temperature is studied. The spatial distribution of the current in a circular disk and a ring is shown to significantly depend on the position of the Fermi level.

Quantum corrections to the conductivity of a two-dimensional system with antidots

The quantum corrections to the conductivity of a two-dimensional electron system with antidots in the limit of a small antidot density are investigated. The corrections to the conductivity and magnetoconductivity due to the presence of antidots in a magnetic field perpendicular to the plane of the system are considered. It is assumed that the mean free path l of electrons on the impurities is far smaller than the antidot radius.