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 L0=1 μm and cross-section A=0.02×0.02 μm2, the persistent current due to the self-inductance is IL=0.2I0 where I0 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.