The wave functions in the presence of constraints - Persistent Current in Coupled Rings

TL;DR

This paper introduces a new method for calculating wave functions under constraints, demonstrating its application to coupled metallic rings with magnetic fluxes, revealing even-odd effects on persistent currents and magnetization.

Contribution

A novel computational approach for wave functions with constraints, applied to coupled rings, highlighting even-odd electron effects on persistent currents and magnetization.

Findings

Even electron numbers lead to large persistent currents and magnetization.

Odd electron numbers suppress current at finite temperatures.

Reversing flux in one ring cancels currents and magnetization, enabling non-local control.

Abstract

We present a new method for computing the wave function in the presence of constraints. As an explicit example we compute the wave function for the many electrons problem in coupled metallic rings in the presence of external magnetic fluxes. For equal fluxes and an even number of electrons the constraints enforce a wave function with a vanishing total momentum and a large persistent current and magnetization in contrast to the odd number of electrons where at finite temperatures the current is suppressed. We propose that the even-odd property can be verified by measuring the magnetization as a function of a varying gate voltage coupled to the rings. By reversing the flux in one of the ring the current and magnetization vanish in both rings; this can be used as a non-local control device.