Persistent current in superconducting nanorings

TL;DR

This paper investigates how quantum phase slips suppress persistent currents in superconducting nanorings, transforming their flux dependence from sawtooth to sinusoidal, and models this behavior via a quantum particle in a sinusoidal potential.

Contribution

It introduces a novel theoretical model linking persistent current behavior in nanorings to a quantum particle in a sinusoidal potential with twisted boundary conditions.

Findings

Persistent current amplitude decreases exponentially with quantum phase slips.

Current-flux relationship transitions from sawtooth to sinusoidal shape.

The problem reduces to solving a Schrödinger equation with twisted boundary conditions.

Abstract

The superconductivity in very thin rings is suppressed by quantum phase slips. As a result the amplitude of the persistent current oscillations with flux becomes exponentially small, and their shape changes from sawtooth to a sinusoidal one. We reduce the problem of low-energy properties of a superconducting nanoring to that of a quantum particle in a sinusoidal potential and show that the dependence of the current on the flux belongs to a one-parameter family of functions obtained by solving the respective Schrodinger equation with twisted boundary conditions.