Numerical simulation of diffusive conductivity in Rashba split two-dimensional gas

We numerically model the conductivity of a two-dimensional electron gas (2DEG) in the presence of the Rashba spin-orbit (SO) interaction in the diffusive transport regime. We performed simulation using samples which width W and length L are up to 200 and 30 000, respectively, on a tight-binding square lattice. When the system is in the diffusive regime, the quadratic increase of the conductivity with SO interaction strength λSO derived previously by Born approximation is reproduced except for very weak SO interaction. In order to obtain satisfactory agreement between numerical and analytical results, the sample width and length should be much larger than the mean free path ℓ but the length should be shorter than the localization length ξ, e.g. 4ℓ≲W and 10ℓ≲L⪡ξ. The anomaly at weak SO interaction is also observed in the conductance fluctuation and the localization length, and is attributed to the finite size crossover from symplectic to orthogonal class with decreasing SO interaction. The typical values of the SO interaction characterizing the crossover obtained for ℓ∼48 are λSO∼1.0/W and 0.2/W when we impose open and periodic boundary conditions, respectively.