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 σsHR=e∕8π for the reactive response, which cancels however with the dissipative part σsHD=-e∕8π.
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Raimondi et al. (2005) studied this question.
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