Electron Delocalization by a Magnetic Field in Two Dimensions

Abstract

The problem of two-dimensional localization in the presence of a magnetic field is reconsidered. The existence of extended electronic states is demonstrated by use of the replica formalism and duality arguments. These states are analogs of $\ensuremath{\theta}=\ensuremath{\pi}$ vacua in four-dimensional Yang-Mills theories, and occur at the center of each Landau band. The present results complete the explanation of the integrally quantized Hall effect.