Single electron in a random potential and a strong magnetic field

Abstract

An electron in an infinitely extended plane is subject to a strong transverse magnetic field. The degenerate states pertaining to a single Landau level are coupled by a random potential. We develop a matrix algorithm that maps this problem onto a path-integral problem in two dimensions. For a class of random potentials, we calculate the average level density for an arbitrary Landau level, and we show that the problem differs from the localization problem without magnetic field only by the presence of the topological term. The coefficient multiplying this term is given explicitly.