Phase diagram of localization in a magnetic field

The phase diagram of localization is numerically calculated for a three-dimensional disordered system in the presence of a magnetic field using the Peierls substitution. The mobility-edge trajectory shifts in the energy-disorder space when increasing the field. In the band center, localized states near the phase boundary become delocalized. The obtained field dependence of the critical disorder is in agreement with a power-law behavior expected from scaling theory. Close to the tail of the band the magnetic field causes localization of extended states.