Electron Localization in a 2D System with Random Magnetic Flux

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 $ξ$ diverges when the Fermi energy approaches the critical energy, {\it i.e.} $ξ(E)\propto |E-E_c|^{-ν}$. We find that $E_c$ shifts with the strength of the disorder and the amplitude of the random magnetic field while the critical exponent ($ν\approx 4.8$) remains unchanged indicating universality in this system. Implications on the experiment in half-filling fractional quantum Hall system are also discussed.