Localization phase diagram for a disordered two-dimensional system in a magnetic field

The phase diagram for the Anderson transition of a two-dimensional disordered system with variable impurity concentration and a perpendicular magnetic field is investigated. A phase boundary is found, separating localized from extended states. It is calculated by means of a finite-size-scaling approach. The shape of the phase boundary and the change in the magnetoresistance are explained in terms of quantum interference effects, i.e., weak localization. A critical exponent for the correlation length and the onset of the delocalized phase are determined.