Self-Consistent Theory of Screening and Transport in Narrow, Translation-Invariant Hall Bars under the Conditions of the Integer Quantum-Hall-Effect

Abstract

We summarize and discuss a self-consistent screening and magneto-transport theory, developed to understand the results of scanning-force-microscope experiments on the current distribution in a two-dimensional electron system (2DES), located in a narrow Hall bar under the conditions of the integer quantum Hall effect (IQHE) and its breakdown. The theory explains why, at low temperatures, at certain intervals of the applied perpendicular magnetic field, the current density is confined to “incompressible stripes” (ISs), in which a fixed number of Landau levels is occupied, and the longitudinal and Hall resistivity assume quantized values. The theory also explains, how the position and shape of these ISs depend on magnetic field and temperature, and why the confinement of the current density on these ISs leads to precisely quantized values of the macroscopic longitudinal and Hall resistance. The theory, which leads, at high temperatures, to the well known Drude results for current density and resistance, shows that the IQHE is a consequence of the peculiar screening properties of a 2DES in a strong magnetic field at low temperatures, and that it can be understood without assumptions about special localization effects.