Quantum transport of vortices in a weakly dissipative ring threaded by an Aharonov-Casher flux: A tight-binding model

Based on the tight-binding model and taking into account the effect of dissipation as well as the disorder, we study quantum interference via the Aharonov-Casher effect for fluxons in a ring-shaped superconductor. The electrical resistance in terms of the transmission probability for a quantum vortex to traverse the ring is calculated. It is shown that a quantum interference effect is exhibited in the resistance in the presence of weak dissipation. Our analysis may also be applied to a Josephson-junction array system. In particular, by including the disorder effect, we are able to explain the experimental measurements in the dissipative regime done by Elion et al. [Phys. Rev. Lett. 71, 2311 (1993)].