Spin transport in mesoscopic rings with inhomogeneous spin-orbit coupling

We revisit the problem of electron transport through mesoscopic rings with spin-orbit (SO) interaction. In the well-known path-integral approach, the scattering states for a quasi-one-dimensional (1D) ring with quasi-1D leads can be expressed in terms of spinless electrons subject to a fictitious magnetic flux. We show that spin-dependent quantum-interference effects in small rings are strongest for spatially inhomogeneous SO interactions, in which case spin currents can be controlled by a small external magnetic field. Mesoscopic spin Hall effects in four-terminal rings can also be understood in terms of the fictitious magnetic flux.