Spin Hall and spin-diagonal conductivity in the presence of Rashba and Dresselhaus spin-orbit coupling

We investigate the spin-current linear response conductivity tensor to an electric field in a paramagnetic two-dimensional electron gas with both Rashba and Dresselhaus spin-orbit coupling in the weak scattering regime within the Born approximation. In the usual sample parameters, and for cross-sectional size smaller than the spin-coherence length, the spin-Hall conductivity depends only on the sign of the difference in magnitude of the Rashba and Dresselhaus coupling except within a narrow window where both coupling strengths are equal. We also find that a spin current is generated in the direction of the driving field for a non-zero Dresselhaus term. Possible experimental setups for its detection, taking into account the finite mobility and typical parameters of current samples, are discussed.