Symmetry properties of spin currents and spin polarizations in multiterminal mesoscopic spin-orbit-coupled systems

We study theoretically some symmetry properties of spin currents and spin polarizations in a multiterminal mesoscopic spin-orbit-coupled system. Based on the scattering wave function approach, we show rigorously that no finite equilibrium terminal spin currents and/or finite equilibrium spin polarizations can survive in the equilibrium state. By use of a typical two-terminal structure as the example, we show explicitly that the nonequilibrium terminal spin currents in a multiterminal mesoscopic spin-orbit-coupled system may be nonconservative in general, and this nonconservation is intrinsic but not caused by the use of an improper definition of spin current in the calculations. We also show that the nonequilibrium lateral edge spin accumulation induced by a longitudinal charge current in a thin strip of finite length of a ballistic two-dimensional electronic system with intrinsic spin-orbit coupling may be nonantisymmetric in general, suggesting that some cautions need to be taken when attributing the occurrence of nonequilibrium lateral edge spin accumulation induced by a longitudinal charge current in such a system to a spin Hall effect.