Effective field theory of electron motion in the presence of random magnetic flux

Abstract

We construct a nonlinear σ model to describe a system of noninteracting electrons propagating in the presence of random magnetic flux. We find a term describing the long range logarithmic interaction between the topological density of the nonlinear sigma model, and argue that this could give rise to a Kosterlitz-Thouless transition from the localized phase to a phase with power law correlations and continuously varying conductances. We provide a physical interpretation of our results in terms of the scattering of edge states of the magnetic domains in different regions.