Delocalization of Electrons in a Random Magnetic Field

Delocalization problem for a two-dimensional noninteracting electron system under a random magnetic field is studied. The Chern number is used to characterize the extended states in such a system, and by studying finite-size scaling of the density of extended states, an insulator-metal phase transition is revealed. The delocalization phase is found at the center of the energy band separated from the localized band tails by critical energies $\pm E_c$. Both the localization exponent and the critical energy $E_c$ are shown to be dependent on the strength of the random magnetic field.