Boundary spin Hall effect in a two-dimensional semiconductor system with Rashba spin-orbit coupling

We derive boundary conditions for the coupled spin-charge diffusion equations at a transmitting interface between two-dimensional electron systems with different strengths of the Rashba spin-orbit (SO) coupling alpha and an electric field parallel to the interface. We consider the limit where the spin-diffusion length l(s) is long compared to the electron mean-free path l and assume that alpha changes discontinuously on the scale of l(s). We find that the spin density is also discontinuous on the scale of l(s). In the case where the electron mobility is constant across the interface, this leads to the complete suppression of the expected spin injection from a region with alpha not equal 0 into a non-SO region with alpha=0.