Semiclassical framework for the calculation of transport anisotropies

TL;DR

This paper introduces an exact solution method for the linear-response Boltzmann equation in anisotropic 2D systems, demonstrating its application to Rashba systems with magnetic scatterers and comparing it to approximate methods.

Contribution

It provides a novel exact solution framework for anisotropic transport calculations, improving upon previous approximate approaches.

Findings

Exact solutions for anisotropic magnetoresistance in Rashba systems.

Approximate methods can be unreliable in certain regimes.

Analytical evaluation of non-equilibrium distribution functions.

Abstract

We present a procedure for finding the exact solution to the linear-response Boltzmann equation for two-dimensional anisotropic systems and demonstrate it on examples of non-crystalline anisotropic magnetoresistance in a system with spin-orbit interaction. We show that two decoupled integral equations must be solved in order to find the non-equilibrium distribution function up to linear order in the applied electric field. The examples are all based on the Rashba system with charged magnetic scatterers, a system where the non-equilibrium distribution function and anisotropic magnetoresistance can be evaluated analytically. Exact results are compared to earlier widely-used approximative approaches. We find circumstances under which approximative approaches may become unreliable even on a qualitative level.