Vanishing Spin-Hall Conductivity in 2D disordered Rashba electron gas

Abstract

For the two-dimensional ideal electron gas with the Rashba spin-orbit interaction and in the presence of non-magnetic short-ranged potential impurities the spin-Hall conductivity $σ_{sH}$ is found by direct microscopic calculation. Within the semiclassical approximation $\hbar/τ\ll ε_F$ and $Δ\ll ε_F$ the value of $σ_{sH}$ is zero for arbitrary ratio of the spin-orbit splitting $Δ$ and the inverse elastic scattering time $1/τ$.