Theory of electric-field-induced spin accumulation and spin current in   the two-dimensional Rashba model
  Based on the spin-density-matrix approach, both the electric-field-induced spin accumulation and the spin current are systematically studied for the two-dimensional Rashba model. Eigenmodes of spin excitations give rise to resonances in the frequency domain. Utilizing a general and physically well-founded definition of the spin current, we obtain results that differ remarkably from previous findings. It is shown that there is a close relationship between the spin accumulation and the spin current, which is due to the prescription of a quasi-chemical potential and which does not result from a conservation law. Physical ambiguities are removed that plagued former approaches with respect to a spin-Hall current that is independent of the electric field. For the clean Rashba model, the intrinsic spin-Hall conductivity exhibits a logarithmic divergency in the low-frequency regime. 
V. V. Bryksin, P. Kleinert