Ballistic persistent currents in disordered metallic rings: Origin of puzzling experimental values

Abstract

Typical persistent current ($I_{typ}$) in a normal metal ring with disorder due to random grain boundaries and rough edges is calculated microscopically. If disorder is due to the rough edges, a ballistic current $I_{typ}\simeq e v_F/L$ is found in spite of the diffusive resistance ($ \propto L/l$), where $v_F$ is the Fermi velocity, $l$ is the mean free path, and $L \gg l$ is the ring length. This ballistic current has a simple interpretation: It is due to a single coherent electron that moves in parallel with the edges and thus does not feel the roughness. Our calculations explain a puzzling experimental result $I_{typ}\simeq e v_F/L$, reported by Chandrasekhar et al. [Phys. Rev. Lett. 67, 3578 (1991)] for metal rings of length $L \simeq 100 l$. If disorder is due to the grain boundaries, our results agree with diffusive result $I_{typ}\simeq (e v_F/L) (l/L)$, derived by Cheung et al. [Phys. Rev. Lett. 62, 587 (1989)] and observed by Bluhm et al. [Phys. Rev. Lett. 102, 136802 (2009)] and Bleszynsky-Jayich et al. [Science 326, 272 (2009)].