Anisotropic conductivity of disordered two-dimensional electron gases due to spin-orbit interactions

We show that the disorder-averaged conductivity tensor of a disordered two-dimensional electron gas becomes anisotropic in the presence of both Rashba and Dresselhaus spin-orbit interactions (SOIs). This anisotropy is a mesoscopic effect and vanishes with vanishing charge dephasing time. Using a diagrammatic approach including zero-, one-, and two-loop diagrams, we show that a consistent calculation needs to go beyond a Boltzmann equation approach. In the absence of charge dephasing and for zero frequency, a finite anisotropy σ_xy∝e²/p_Flh arises even for infinitesimal SOI, where p_F is the Fermi momentum and l is the mean free path of an electron.