Circulating currents and magnetic moments in quantum rings

TL;DR

This paper proposes a new method to calculate circulating currents in quantum rings connected to leads, revealing that these currents cannot always be derived from bond currents, especially when the rings are connected.

Contribution

It introduces a formula based on energy response to magnetic flux for calculating circulating currents in quantum rings, extending understanding beyond isolated systems.

Findings

The proposed method aligns with conventional results for isolated rings.

Connected rings exhibit circulating currents not reducible to bond currents.

The approach highlights differences in current calculation for connected versus isolated rings.

Abstract

In circuits containing closed loops the operator for the current is determined by charge conservation up to an arbitrary divergenceless current. In this work we propose a formula to calculate the magnetically active circulating current $I_{\rm ring}$ flowing along a quantum ring connected to biased leads. By {\em gedanken experiments} we argue that $I_{\rm ring}$ can be obtained from the response of the gran-canonical energy of the ring to an external magnetic flux. The results agree with those of the conventional approach in the case of isolated rings. However, for connected rings $I_{\rm ring}$ cannot be obtained as a linear combination of bond currents.