Spin Currents and Intrinsic Spin-Hall Effect in Low Dimensional Systems

We consider the spin-Hall effect in two-dimensional electron systems (2DES) with Rashba and Dresselhaus spin-orbit couplings (SO). We find nonzero diagonal spin conductivity provided that Dresselhaus coupling is finite. In addition we consider the influence of disorder on spin conductivities in these systems. By comparing with the exact diagonalization method the finite quasiparticle lifetime (Born) approximation we argue that the latter one seems to be sufficient to describe the case when spin-orbit coupling is stronger or comparable with disorder strength. Furthermore, in the framework of Landauer–Buttiker formalism we show that the transverse and diagonal spin conductivities in Rashba plus Dresselhaus SO systems are robust against disorder for finite size systems.