Semiclassical framework for the calculation of transport anisotropies

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 noncrystalline anisotropic magnetoresistance in a system with spin-orbit interaction. We show that two decoupled integral equations must be solved in order to find the nonequilibrium 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 nonequilibrium 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.