Persistent spin current in spin-orbit coupling systems in the absence of an external magnetic field

The spin-orbit coupling systems with a zero magnetic field is studied under the equilibrium situation, {\it i.e.}, without a voltage bias. A persistent spin current is predicted to exist under most circumstances, although the persistent charge current and the spin accumulation are identically zero. In particular, a two-dimensional quantum wire is investigated in detail. Surprisingly, a persistent spin current is found to flow along the confined direction, due to the spin precession in accompany with the particle motion. This provides an interesting example of constant spin flowing without inducing a spin accumulation, contrary to common intuition.