Effective Field Theory of Electron Motion in the Presence of Random Magnetic Flux

TL;DR

This paper develops a nonlinear sigma model to analyze electron behavior under random magnetic flux, predicting a possible phase transition from localization to a phase with power-law correlations and variable conductance.

Contribution

It introduces a novel sigma model incorporating long-range interactions due to random magnetic flux, suggesting a new type of phase transition in disordered electron systems.

Findings

Prediction of a Kosterlitz-Thouless transition

Identification of a phase with power-law correlations

Physical interpretation via edge state scattering

Abstract

We construct a nonlinear $\sigma$ model to describe a system of non-interacting electrons propagating in the presence of random magnetic flux. We find a term describing the long ranged logarithmic interaction between the topological density of the non-linear 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.