Anisotropic scattering in quantum magnetotransport calculations for two-dimensional electron systems in a one-dimensional superlattice

Based on the self-consistent Born approximation for the evaluation of Kubo formulas, we develop and evaluate a consistent approximation scheme that allows us to calculate the magnetoconductivity tensor for a high-mobility two-dimensional electron system, subjected to a weak periodic potential modulation in one lateral direction, under due consideration of anisotropic impurity scattering. We demonstrate that our approach avoids the inconsistencies observed with previous calculations based on a c-number approximation for the self-energy operator, and that it is able to reproduce, with reasonable assumptions for the finite-range impurity potentials, nearly quantitatively the experimental results for all components of the magnetoresistance tensor in the regime of moderate and strong magnetic fields, which are characterized by commensurability and Shubnikov-de Haas oscillations, respectively.