Aharonov-Bohm effect induced by mutual inductance for an array of mesoscopic rings.

Abstract

The effect of mutual inductance on the persistent currents in N mesoscopic rings placed periodically on a plane is investigated. The persistent currents for the situations with mutual inductance between the nearest-neighbor rings are calculaed in detail. We find that while the self-inductance suppresses the persistent current, the effect of the mutual inductance is to enhance it. For example, for a metal ring (Au or Cu) of length ${\mathit{L}}_{0}$=1 \ensuremath{\mu}m and cross-section A=0.02\ifmmode\times\else\texttimes\fi{}0.02 \ensuremath{\mu}${\mathrm{m}}^{2}$, the persistent current due to the self-inductance is ${\mathit{I}}_{\mathit{L}}$=0.2${\mathit{I}}_{0}$ where ${\mathit{I}}_{0}$ is the persistent current without the self-inductance. For a pair of rings, the contribution of the persistent current due to the mutual inductance is about 10%. The results can be understood as entirely due to self-consistency of the equilibrium properties in the nanostructure.