Self-Consistent Treatment of Two-Dimensional Anderson Localization in Magnetic Fields

A self-consistent treatment of the Anderson localization by Vollhardt and Wölfle [Phys. Rev. B22 (1980) 4666] is extended to systems without time reversal symmetry by use of a diagrammatical method. In this paper magnetoresistance in two dimension is calculated for the case where the field effect can be treated quasiclassically. It is found that the magnetic field enhances the conductivity, though the system remains insulator in the absence of inelastic scatterings. The present investigation indicates that the one-parameter scaling theory cannot describe systems without the time reversal symmetry.