V. B. Shikin

Stationary soliton on a charged surface of liquid helium and hydrogen films

A change in the shape of a charged surface of liquid hydrogen and helium — the formation of a solitary wave (a positively charged hump for hydrogen and a negatively charged dimple for helium)-is observed in an electric field exceeding a critical value under conditions of total compensation of the applied field by the surface charge.

Photoconductivity of 2D Electron Systems in Magnetic Field

According to recent photoconductivity measurements in 2D electron semiconductor systems in magnetic fields normal to the 2D plane, the photoconductivity as a function of magnetic field exhibits oscillations in the region of fields much weaker than those necessary for the observation of the Shubnikov-de Haas effect. In this paper, the aforementioned oscillations are interpreted as a two-dimensional analogue of magnetophoton (phonon) oscillations studied in detail by different authors on 3D samples.

Two-Fraction Electron System on a Thin Helium Film

A systematic theoretical investigation of microwave absorption of 2-dimensional electron systems above a thin helium film in the presence of a cyclotron resonance magnetic field is presented. To explain the measured data, a two-fraction structure of the electron system is introduced. One component corresponds to the free electron motion, the second one takes into account electron localization near the potential minimum caused by the roughness of the substrate. Within this model the general dependence of microwave absorption becomes understandable. The details of the observed cyclotron resonance line-shift are discussed.

Reconstruction of a charged helium film on a metallic substrate

Peculiarities of the reconstruction of a charged helium film surface on a metallic substrate are considered. Instability evolution in this case resembles the generation of a solitary wave in hydrodynamics of a free liquid surface and leads to the formation of charged solitons under certain conditions. Basic characteristics of such solitons are obtained in the one-dimensional approximation under the conditions of weak nonlinearity of the problem.

Elliptical multielectron dimples on liquid and solid helium surfaces

Abstract The structure of multielectron dimples on helium substrates is investigated for conditions deviating from axial symmetry. Main sources for an ellipticity of dimples are an anisotropy of the surface tension, as for the liquid-solid He interface, or anisotropic boundary conditions, as for liquid He between vertical parallel plates.

Electrons on liquid helium in a resonator

An investigation of the microwave absorption for 2-dimensional electron layers in a resonator cavity are presented. The difference in the eigenmodes of the resonator in case of an empty cavity and in presence of a 2-dimensional electron layer on a helium film within the cavity are calculated. When introducing electrons into the cavity a pronounced frequency dependence is found. The expected shift in the resonance frequency is compared to previous and new data of resonance response measurements.

Screening and edge states in two-dimensional metals in a magnetic field

The length λ0 at which the lateral electric-field component E⊥ perpendicular to the boundary is conserved near the boundary of two-dimensional (2D) samples, which is covered by 2D electrons, has been determined. The existence of the finite such length follows from the self-consistent process of the screening of the external fields forming the boundaries of real 2D systems by the electrons of the metal. The effect of E⊥ on the structure of magnetic edge states has been taken into account in the mean field approximation in a wide range of the external field from the semiclassical limit (ɛF ≫ ħωc), where ɛF is the Fermi energy of the 2D system and ħωc is the cyclotron energy to the quantum Hall effect (QHE) region (ɛF ≪ ħωc). The positions of the magnetic edge state peaks against the background of their ideal distribution along the perimeter of the 2D circle in the known problem of transverse magnetic focusing have been determined in the semiclassical limit. The systematic description of the structure of the skin layer with λH ≥ λ0, consisting of the set of the so-called integer strips (overlapping or independent), which are carriers of the universal quantum conductance, has been proposed in the QHE regime. A relatively large probability of the overlapping of the fields of adjacent strips, as well as the possibility of describing coupled integer cascades, is remarkable. The existing data on the tunneling current through integer strips in the λH layer providing suitable information on the actual state of the boundary of the 2D system have been commented. A natural analogy between the properties of magnetic edge states and a well-known problem of the details of the ballistic conductance σ‖(H) of narrow electron channels in the magnetic field H has been noticed. The formalisms of both problems are identical under the conditions λH ≥ w, where 2w is the effective width of the quasi-one-dimensional channel. The existing information on the σ‖(H) dependence in a wide range of the magnetic field has been systematized. The attributes of the QHE observed in σ‖(H) convincingly indicate the reality of the formation of various modifications of integer strips in inhomogeneous 2D systems in the quantizing magnetic field.

Breakdown of the quantum hall effect in regularly inhomogeneous 2D electron systems

A breakdown mechanism is discussed for the current-voltage characteristic of the system of integer Hall channels in a 2D sample with a regularly inhomogeneous 2D electron density. It has been shown that the appearance of an external potential V on the “edges” of such strips leads to two alternatives: as V increases, the strip width decreases to zero or increases geometrically but “deteriorates qualitatively.” In both cases with their (different) thresholds, integer strips lose their properties inherent in them in the quantum Hall effect regime. These thresholds are attributed here to the asymmetric breakdown of the quantum Hall effect for the system of integer channels.

Minimum energy of a free electron in inert gases

The properties of the minimum energy W of a low-energy free electron in an inert gas are discussed. This quantity is one of the basic characteristics of the electron in problems of the formation of various charged clusters (bubbles or compacts) in low-dimensional electronic states along interfaces. A relation between the energy W and a similar energy W0 determined in the so-called optical approximation, where the energy W0 is proportional to the gas density ng, has been obtained. Comparison makes it possible to determine the ng dependence of the scattering length a0 introduced in the “optical” description of the gaseous medium and to reveal the conditions under which a0(ng) may change sign, which behavior, by definition, is beyond the framework of the optical approximation and is observed experimentally.

Stationary nonlinear waves at the surface of a thin liquid layer under inverted gravitation conditions

Instability of the flat surface of a thin liquid layer wetting a solid substrate under inverted gravitation conditions is discovered. The development of this instability leads to the formation of a new stationary nonuniform liquid surface state. It looks like a solitary hill with characteristics sensitive to the liquid film parameters, particularly to the layer thickness at which the instability begins to develop. By application of a variational approach the mechanical stability of such a hill (droplet) in the one-dimensional approximation is proved. A variational picture of the shape evolution for a cylindrical charged droplet in an external electric field is constructed, too. The results obtained are compared with an experiment on liquid hydrogen droplets [A. A. Levchenko, G. V. Kolmakov, L. P. Mezhov-Deglin, M. G. Mikhailov, and A. B. Trusov, Low Temp. Phys. 25, 242 (1999)]. The theory developed is in good agreement with the results of experiments.