Electron Scattering in High Magnetic Field

Electrical conductivity in a strong magnetic field is calculated for the case of scattering by delta-function impurities. The impurity concentration is taken as sufficiently weak that collision broadening may be neglected. The scattering by an individual center is solved exactly rather than by perturbation theory. As a result, transition probabilities for an electron at the bottom of a Landau level vanish, rather than diverge. Expressions are given for the longitudinal and transverse conductivities in the oscillatory range, and in the quantum limit range for degenerate and nondegenerate statistics. The relation of this theory to those employing collision broadening is discussed.