Localization problem of a two-dimensional lattice in a random magnetic field

Abstract

We calculate numerically the conductance of a square lattice of quantum wires (which is equivalent to a tight-binding model) in the presence of a random magnetic field. The magnetic flux per plaquette is uniformly distributed between -${\mathrm{\Phi }}_0$/2 and +${\mathrm{\Phi }}_0$/2, where ${\mathrm{\Phi }}_0$=hc/e is the unit of flux quanta. The existence of localized states is confirmed. Although we cannot reach a definite conclusion, inspection of the conductance distribution P(g) and an analysis of our results within a heuristic finite-size scaling hypothesis are consistent with the existence of extended states, and hence mobility edges.