Current Carrying States in a Random Magnetic Field

TL;DR

This paper investigates how noninteracting electrons in two dimensions transition between localized and extended states under the influence of random potentials and magnetic fields, using topological analysis and finite size scaling.

Contribution

It provides numerical evidence for a second order localization-delocalization transition driven by randomness, estimating critical parameters through finite size scaling.

Findings

Existence of a second order transition between localized and extended states.

Estimated critical randomness strength for the transition.

Determined localization length exponent.

Abstract

We report results of a numerical study of noninteracting electrons moving in two dimensions, in the presence of a random potential and a random magnetic field for a sequence of finite sizes, using topological properties of the wave functions to identify extended states. Our results are consistent with the existence of a second order localization-delocalization transition driven by the random potential. The critical randomness strength and localization length exponent are estimated via a finite size scaling analysis.