The fate of the Lifshitz tails of high Landau levels

Abstract

The density of states in the tails of the disorder-broadened nth Landau level of a two-dimensional electron gas in a strong magnetic field is calculated asymptotically for large n by considering the non-trivial (instanton) saddle-point configurations of an effective field theory. The controlling factor is found to be of the form ϵ 2 exp{−Cn 1 2 (ϵ 2−ϵ 0 2)} where ϵ is the energy relative to the Landau level of the pure system. The Lifshitz tails of the Landau level are therefore exponentially suppressed in the large- n limit.