On the Spin-Hall effect in a dirty Rashba semiconductor

The impact of the boundary condition on the solution of the spin diffusion equations in a dirty Rashba semiconductor is reinvestigated. To this end diffusion equations, which take into account the coupling between spin and charge, are derived. The investigation of the solution to the spin diffusion equations near the boundary shows that the spin-current tensor vanishes discontinuously at the boundary. As a consequence, there is non spin-Hall effect in a dirty Rashba semiconductor.