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 ${\sigma }_{xy}\propto e^2/p_{F}lh$ arises even for infinitesimal SOI, where $p_F$ is the Fermi momentum and $l$ is the mean free path of an electron.

Figure 1

(Color online) Three relevant two-loop diagrams (out of nine) for the conductivity tensor ${\sigma }_{\alpha \beta }$. The matrix vertices $\tilde{\sigma }$ and $\overline{\sigma }$ are written assuming clockwise (in lower Hikami boxes) and counterclockwise (in upper Hikami boxes) direction of writing traces. Each diagram contains small-momentum singularities, which cancel each other in accordance with the theorem from Ref. 18.