Spin Hall effect and zitterbewegung in an electron waveguide

We study spin-resolved probability distributions for electrons in a multichannel waveguide in the presence of a spin-orbit interaction. For a spin-polarized electron injection, a zitterbewegung pattern is predicted in the probability distribution of electrons in the waveguide. For a spin-unpolarized injection, the spin-resolved electron probability in the waveguide shows spin accumulations. In addition to the spin Hall phenomenon-namely, accumulations of opposite spins at the lateral edges of the waveguide-we predict the existence of a regular stripe pattern of spin accumulations in the internal region of the waveguide. We show that the predicted zitterbewegung and spin Hall effect stem from the same mechanism and are formed from coherent states of electrons in the waveguide.