Localisation and the two-dimensional Hall effect

Abstract

The effect of a random substrate potential on electrons in a two-dimensional system in a strong magnetic field is examined. At zero temperature if the Fermi energy lies between Landau levels perturbation theory has a non-zero radius of convergence, and the substrate potential does not change the Hall voltage. Localised states may exist in the tails of the Landau levels, but these do not contribute to the transverse current. The nature of the extended states is examined, but no firm conclusions are reached.