Electron Localization in a 2D System with Random Magnetic Flux

TL;DR

This study investigates how disorder and random magnetic fields affect electron localization in a 2D system, revealing a universal critical exponent and implications for fractional quantum Hall experiments.

Contribution

It introduces a finite-size scaling method to analyze localization in disordered 2D electron systems with random magnetic flux, highlighting universality of the critical exponent.

Findings

Localization length diverges near critical energy

Critical energy shifts with disorder strength

Critical exponent remains approximately 4.8

Abstract

Using a finite-size scaling method, we calculate the localization properties of a disordered two-dimensional electron system in the presence of a random magnetic field. Below a critical energy $E_c$ all states are localized and the localization length $\xi$ diverges when the Fermi energy approaches the critical energy, {\it i.e.} $\xi(E)\propto |E-E_c|^{-\nu}$. We find that $E_c$ shifts with the strength of the disorder and the amplitude of the random magnetic field while the critical exponent ($\nu\approx 4.8$) remains unchanged indicating universality in this system. Implications on the experiment in half-filling fractional quantum Hall system are also discussed.