Magnetic field influenced electron-impurity scattering and magnetotransport

Abstract

We formulate a classical theory (ωc1 with ωc as the cyclotron frequency and τ as the relaxation time) to study the influence of perpendicular magnetic field on the electron-impurity scattering process in two-dimensional electron gas. To describe the curved incoming and outgoing trajectories, we introduce a general recipe based on an abstraction of the actual impurity scattering process to define the scattering parameters such as the incoming and outgoing momentum and coordinate jump. In this picture, we can conveniently describe the skew scattering and coordinate jump, which will eventually modify the Boltzmann equation. We find an anomalous Hall resistivity different from the conventional Boltzmann-Drude result and a negative magnetoresistivity as a parabolic function of magnetic field. The origin of these results is analyzed. The relevance between our theory and recent simulation and experimental works is also discussed.