Semiclassical Electron Transport in case of Spin-Orbit Interaction: a Way to Spin-Polarize the Current

Semiclassical solutions of a 2-dimensional Schr\"{o}dinger equation with the Rashba spin-orbit interaction and a smooth potential are considered. We argue that the electron motion in the semiclassical approximation follows the evolution of one of the spin-orbit-split energy subbands. Within a given subband the in-plane electron spin orientation is automatically adjusted to the momentum orientation. This allows to generate spin-polarized currents with the help of a Quantum Point Contact open for transmission only in a single subband. Out of plane spin polarization, proportional to the electric field, appears as a quantum correction.