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\nelectric field in a paramagnetic two dimensonal electron gas with both Rashba\nand Dresselhaus spin-orbit coupling in the weak scattering regime. In the\nususal case where both spin-orbit-split bands are occupied, we find that the\nspin-Hall conductivity depends only on the sign of the difference in magnitude\nof the Rashba and Dresselhaus coupling strengths except within a narrow window\nwhere both coupling strengths are equal. We also find a new effect in which a\nspin current is generated in the direction of the driving field whenever the\nDresselhaus spin-orbit coupling is nonzero. We discuss experimental\nimplications of this finding taking into account the finite mobility and\ntypical parameters of current samples and possible experimental set ups for its\ndetection.\n