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 ??Ec. Both the localization exponent and the critical energy Ec are shown to be dependent on the strength of the random magnetic field