Persistent Current for a genus g=2 structure

TL;DR

This paper presents the first exact calculation of persistent current in a genus g=2 structure formed by two coupled rings, revealing behaviors similar to a single ring and chaotic energy structures under opposite fluxes.

Contribution

It introduces an exact solution for persistent current in a coupled rings structure with genus g=2, extending Dirac's method to fermionic constraints.

Findings

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

Chaotic energy structures occur under opposite fluxes.

Periodicity of the current is $h/e$ in both cases.

Abstract

We report the first calculation of persistent current in two coupled rings which form a character ``8'' genus g=2 structure. We obtain an exact solution for the persistent current and investigated the exact solution numerically. For two large coupled rings with equal fluxes, we find that the persistent current in the two coupled rings is equal to that in a single ring. For opposite fluxes the energy has a chaotic structure. For both cases the periodicity is $h/e$. This results are obtained within an extension of Dirac's second class method to fermionic constraints. This theory can be tested in the ballistic regime.