Magnetic Field Influenced Electron-Impurity Scattering and Magnetotransport

We formulate a quasiclassical theory ($\omega_c\tau \lesssim 1$ with $\omega_c$ as the cyclotron frequency and $\tau$ as the relaxation time) to study the influence of magnetic field on electron-impurity scattering process in the two-dimensional electron gas. We introduce a general recipe based on an abstraction of the detailed impurity scattering process to define the scattering parameter 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 parabolic in magnetic field. The origin of these results will be analyzed. The relevance between our theory and recent simulation and experimental works will be discussed. Our theory dominates in dilute impurity system where the correlation effect is negligible.