Electron localization in a two-dimensional 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 ${\mathit{E}}_{\mathit{c}}$ all states are localized and the localization length ξ diverges when the Fermi energy approaches the critical energy, i.e., ξ(E)∝‖E-${\mathit{E}}_{\mathit{c}}$ ${\mathrm{\Vert }}^{\mathrm{-}\nu }$. We find that ${\mathit{E}}_{\mathit{c}}$ shifts with the strength of the disorder and the amplitude of the random magnetic field while the critical exponent (ν≊4.5) remains unchanged indicating universality in this system. Implications on the experiment in the half-filling fractional quantum Hall system are also discussed.