Berry’s phase and persistent charge and spin currents in textured mesoscopic rings

We consider the motion of electrons through a mesoscopic ring in the presence of a classical, static, inhomogeneous, magnetic field. Zeeman interaction between the electron spin and this texture couples spin and orbital motion, and results in a Berry phase. As a consequence, the system supports persistent equilibrium spin and charge currents, even in the absence of conventional electromagnetic flux through the ring. We mention the possibility of analogous persistent mass and spin currents in normal ${}_{}{}^3{}_{}{}^{}\mathrm{He}$.