Spin-Hall effect in a disordered two-dimensional electron system

We calculate the spin-Hall conductivity for a two-dimensional electron gas within the self-consistent Born approximation, varying the strength and type of disorder. In the weak disorder limit we find both analytically and numerically a vanishing spin-Hall conductivity even when we allow a momentum dependent scattering. Separating the reactive from the dissipative current response, we find the universal value ${\sigma }_{sH}^R=e∕8\pi$ for the reactive response, which cancels however with the dissipative part ${\sigma }_{sH}^D=-e∕8\pi$.