Localization in a random magnetic field: The semiclassical limit.

Abstract

We study the two-dimensional electron gas in the presence of a random perpendicular magnetic field. We examine, in particular, the limit in which the correlation length of the random field is large compared to the typical magnetic length. In this limit, a semiclassical approach can be used to understand a large part of the energy spectrum. To investigate localization, we introduce a simplified model, in which electrons propagate coherently on a random network derived from the classical trajectories. The same network model (with different parameters) also represents electron motion in a uniform magnetic field and a random scalar potential, in a spin-degenerate Landau level. Requiring that the global phase diagram of our model be consistent with Khmelnitskii's scaling flow for the quantum Hall effect, we argue that all electron states in a random magnetic field are localized in the semiclassical limit. We present the results of numerical simulations of the model in support of this conclusion.