2-DIMENSIONAL ELECTRON-GAS UNDER STRONG MAGNETIC-FIELDS - PROPERTIES NEAR ABRUPT EDGES

According to mechanism of electron confinement within the plane, the effective confinement barriers at system edges can be classified as smooth and abrupt. Here, less studied abrupt barriers will be investigated. For simple finite rectangular step barriers, Landau level bending in the step vicinity exhibits pronounced structures in the form of electron dispersion plateaus above the barrier tops, accompanied by regions with a substantial reduction of energy gaps between neighbouring Landau branches [1]. The enhanced density of electron states should be observable in optical and nuclear spin relaxation phenomena. Distortions of electron wave functions, consisting in systematical lagging of electron center of mass behind the orbital center are described. Diamagnetic current density, and in particular, development of diamagnetic edge channels as a function of the position of the Fermi level of the 2-dimensional electron gas (2DEG) is investigated. Total currents along the individual edges are found to be quantized. From the Kubo formula, very simple expressions for Hall conductivity have been derived for a general confinement barrier. Application to a system with a simple rectangular confinement elucidates the problem of space distribution of tile current throughout the Hall bar. Total deviation of the Hall conductivity from the integer values is found to be given by the product of two factors. The geometrical factor is inversely proportional to the sample width. The edge factor is proportional to the derivative of the electron dispersion relation at the Fermi level and in this way it relates the Hall conductivity deviation to the shape of the confinement barrier. The deviations have been evaluated for several channel widths and found to be in qualitative agreement with recent experimental results for quantum wires.