Simulation of the Quantum Hall Effect in Samples with Weak Long-Range Disorder

The fine structure of the density of states is studied numerically in the quantum Hall effect mode during the ballistic transmission of an electron through an area of 1 µm2 of a two-dimensional electron gas with weak long-range disorder. The calculated widths of strict quantum plateaus agree with experimental data. Periodic conductance oscillations corresponding to the addition of two electrons to the simulated area are found in the central part of the lower Landau band. One-dimensional countercurrents are found inside the area and at its edge, which are separated by a magnetic length and explained by the motion of an electron with a low drift velocity.