  We investigate the spin-current linear response conductivity tensor to an
electric field in a paramagnetic two dimensonal electron gas with both Rashba
and Dresselhaus spin-orbit coupling in the weak scattering regime. In the
ususal case where both spin-orbit-split bands are occupied, we find that the
spin-Hall conductivity depends only on the sign of the difference in magnitude
of the Rashba and Dresselhaus coupling strengths except within a narrow window
where both coupling strengths are equal. We also find a new effect in which a
spin current is generated in the direction of the driving field whenever the
Dresselhaus spin-orbit coupling is nonzero. We discuss experimental
implications of this finding taking into account the finite mobility and
typical parameters of current samples and possible experimental set ups for its
detection.
