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 ${\sigma }_{sH}$ is found by direct microscopic calculation. Within the semiclassical approximation $\hslash /\tau \ll {\epsilon }_F$ and $\Delta \ll {\epsilon }_F$ the value of ${\sigma }_{sH}$ is zero for arbitrary ratio of the spin-orbit splitting $\Delta$ and the inverse elastic scattering time $1/\tau$.

4 pages, 3 figures. An error corrected in the calculation of the spin-Hall conductivity, leading to contrary effect