Edge spin accumulation in a ballistic regime

We consider a mesoscopic ballistic structure with Rashba spin-orbit splitting of the electron spectrum. The ballistic region is attached to the leads with a voltage applied between them. We calculate the edge spin density which appears in the presence of a charge current through the structure due to the difference in populations of electrons coming from different leads. Combined effect of the boundary scattering and spin precession leads to oscillations of the edge polarization with the envelope function decaying as a power law of the distance from the boundary. The problem is solved with the use of scattering states. The simplicity of the method allows to gain an insight into the underlaying physics. We clarify the role of the unitarity of scattering for the problem of edge spin accumulation. In case of a straight boundary it leads to exact cancellation of all long-wave oscillations of the spin density. As a result, only the Friedel-like spin density oscillations with the momentum $2k_F$ survive. However, this appears to be rather exceptional case. In general, the smooth spin oscillations with the spin precession length recover, as it happens, e.g., for the wiggly boundary. We demonstrate also, that there is no relation between the spin current in the bulk, which is zero in the considered case, and the edge spin accumulation.