Spin separation and spin Hall effect in quantum wires due to lateral-confinement-induced spin-orbit-coupling

Abstract

We show that the spin-orbit coupling in two-dimensional (2D) electron systems with a potential gradient parallel to the 2D plane exerts a spin-dependent transverse force on moving electrons while conserving their spins. Due to the spin conservation, the standard continuity equation holds between spin density and spin current. Using numerical calculations based on the nonequilibrium Green's function formalism, we demonstrate for crossed quantum wires with a harmonic confining potential in the ballistic limit that transverse spin separation and spin Hall current are generated in response to a longitudinal charge current.