Magnetic field influenced electron-impurity scattering and magnetotransport

TL;DR

This paper develops a quasiclassical theory to analyze how magnetic fields affect electron-impurity scattering and magnetotransport in two-dimensional electron gases, revealing anomalous Hall resistivity and negative magnetoresistivity.

Contribution

It introduces a general framework for describing skew scattering and coordinate jumps, modifying the Boltzmann equation to better understand magnetotransport phenomena.

Findings

Discovery of anomalous Hall resistivity deviating from classical results.

Identification of negative parabolic magnetoresistivity in magnetic fields.

Relevance of the theory to dilute impurity systems and recent experiments.

Abstract

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 has been analyzed. The relevance between our theory and recent simulation and experimental works is also discussed. Our theory dominates in dilute impurity system where the correlation effect is negligible.