Persistent Current in Two Coupled Rings

TL;DR

This paper provides an exact solution for persistent current in two coupled rings with magnetic fluxes, revealing that their behavior can mimic a single ring and explaining experimental observations.

Contribution

It introduces an exact analytical solution for persistent current in coupled rings under magnetic flux, extending understanding of quantum coherence in mesoscopic systems.

Findings

Persistent current in coupled rings equals that in a single ring for large equal fluxes.

The magnetic fluxes alter the global phase of the electronic wave function.

The theory explains experimental results in multiple coupled rings.

Abstract

We report the solution of the persistent current in two coupled rings in the presence of external magnetic fluxes. We showed that the magnetic fluxes modify the global phase of the electronic wave function for multiple connected geometry formed by the coupled rings. We obtained an exact solution for the persistent current and investigated the exact solution numerically. For two large coupled rings with equal fluxes, we found that the persistent current in the two coupled rings is in fact equal to that in a single ring. This theory explains the experimental results observed in a line of sixteen coupled rings. (Phys. Rev. Lett. 86, 3124 (2001).)