Spin-orbit-induced anisotropic conductivity of a disordered two-dimensional electron gas

We present a semiautomated computer-assisted method to generate and calculate diagrams in the disorder-averaging approach to disordered two-dimensional (2D) conductors with intrinsic spin-orbit interaction (SOI). As an application, we calculate the effect of the SOI on the charge conductivity for disordered 2D systems and rings in the presence of Rashba and Dresselhaus SOI. In an infinite-size 2D system, anisotropic corrections to the conductivity tensor arise due to phase coherence and the interplay of Rashba and Dresselhaus SOI. The effect is more pronounced in the quasi-one-dimensional case, where the conductivity becomes anisotropic already in the presence of only one type of SOI. The anisotropy further increases if the time-reversal symmetry of the Hamiltonian is broken.