Spin-Hall edge spin polarization in a ballistic 2D electron system

Universal properties of spin-Hall effect in ballistic 2D electron systems are addressed. The net spin polarization across the edge of the conductor is second order, $\sim\lambda^2$, in spin-orbit coupling constant independent of the form of the boundary potential, with the contributions of normal and evanescent modes each being $\sim\sqrt{\lambda}$ but of opposite signs. This general result is confirmed by the analytical solution for a hard-wall boundary, which also yields the detailed distribution of the local spin polarization. The latter shows fast (Friedel) oscillations with the spin-orbit coupling entering via the period of slow beatings only. Long-wavelength contributions of evanescent and normal modes exactly cancel each other in the spectral distribution of the local spin density.