Coexistence of diffusive resistance and ballistic persistent current in disordered metallic rings with rough edges: Possible origin of puzzling experimental values

Typical persistent current ($I_{typ}$) in a mesoscopic normal metal ring with disorder due to rough edges and random grain boundaries is calculated by a scattering matrix method. In addition, resistance of a corresponding metallic wire is obtained from the Landauer formula and the electron mean free path ($l$) is determined. If disorder is due to the rough edges, a ballistic persistent current $I_{typ} \simeq e v_F/L$ is found to coexist with the diffusive resistance ($\propto L/l$), where $v_F$ is the Fermi velocity and $L \gg l$ is the ring length. This ballistic current is due to a single electron that moves almost in parallel with the rough edges and thus hits them rarely (it is shown that this parallel motion exists in the ring geometry owing to the Hartree-Fock interaction). Our finding agrees with a puzzling experimental result $I_{typ}\simeq e v_F/L$, reported by Chandrasekhar et al. [Phys. Rev. Lett. \textbf{67}, 3578 (1991)] for metallic rings of length $L \simeq 100 l$. If disorder is due to the grain boundaries, our data reproduce theoretical result $I_{typ}\simeq (e v_F/L) (l/L)$ that holds for the white-noise-like disorder and has been observed in recent experiments. Thus, result $I_{typ}\simeq e v_F/L$ in a disordered metallic ring of length $L \gg l$ is as normal as result $I_{typ}\simeq (e v_F/L)(l/L)$. Which result is observed depends on the nature of disorder. Experiments that would determine $I_{typ}$ and $l$ in correlation with the nature of disorder can be instructive.