A Unified Model for Two Localisation Problems: Electron States in Spin-Degenerate Landau Levels, and in a Random Magnetic Field

Abstract

A single model is presented which represents both of the two apparently unrelated localisation problems of the title. The phase diagram of this model is examined using scaling ideas and numerical simulations. It is argued that the localisation length in a spin-degenerate Landau level diverges at two distinct energies, with the same critical behaviour as in a spin-split Landau level, and that all states of a charged particle moving in two dimensions, in a random magnetic field with zero average, are localised.