No abstract

We calculate the spin-Hall conductivity for a two-dimensional electron gas within the selfconsistent 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 disspative current response, we find the universal value σ R sH = e/8π for the reactive response, which cancels however with the dissipative part σ D sH = −e/8π.

We present a microscopic derivation of the generalized Boltzmann and Eilenberger equations in the presence of non-Abelian gauges for the case of a nonrelativistic disordered Fermi gas. A unified and symmetric treatment of the charge ͓U͑1͔͒ and spin ͓SU͑2͔͒ degrees of freedom is achieved. Within this framework, just as the U͑1͒ Lorentz force generates the Hall effect, so does its SU͑2͒ counterpart gives rise to the spin Hall effect. Considering elastic and spin-independent disorder we obtain diffusion equations for charge and spin densities and show how the interplay between an in-plane magnetic field and a time-dependent Rashba term generates in-plane charge currents.