Coulomb corrections to the extrinsic spin-Hall effect of a two-dimensional electron gas

We develop the microscopic theory of the extrinsic spin-Hall conductivity of a two-dimensional electron gas, including skew-scattering, side-jump, and Coulomb interaction effects. We find that while the spin-Hall conductivity connected with the side jump is independent of the strength of electron-electron interactions, the skew-scattering term is reduced by the spin-Coulomb drag, so the total spin current and the total spin-Hall conductivity are reduced for typical experimental mobilities. Further, we predict that in paramagnetic systems the spin-Coulomb drag reduces the spin accumulations in two different ways: (i) directly through the reduction of the skew-scattering contribution, and (ii) indirectly through the reduction of the spin diffusion length. Explicit expressions for the various contributions to the spin-Hall conductivity are obtained using an exactly solvable model of the skew scattering.