Persistent currents in mesoscopic metallic rings: Ensemble average

Abstract

A magnetic flux induces a persistent current in a mesoscopic metallic ring with period ${\mathrm{\phi }}_0$, the flux quantum. We show that the ensemble average of the current (on disorder or on the number of particles) is finite with a ${\mathrm{\phi }}_0$/2 periodicity. We find from numerical calculations that in the diffusive regime, this average is reduced compared with the typical current ${\mathit{ev}}_{\mathit{D}}$/L by a factor (${\mathit{M}}_{\mathrm{eff}}$ ${)}^{\mathrm{-}1/2}$ where ${\mathit{v}}_{\mathit{D}}$ is the diffusion velocity along the ring and ${\mathit{M}}_{\mathrm{eff}}$ is the number of conducting channels in the ring. The recent experimental discovery of the persistent currents, which shows the ${\mathrm{\phi }}_0$/2 periodicity, is in reasonable agreement with our results.