Crossover from hc/e to hc/2e current oscillations in rings of s-wave superconductors

TL;DR

This paper investigates the transition from hc/e to hc/2e flux periodicity in persistent currents of superconducting rings, identifying the mechanisms and conditions under which the periodicity changes, especially near the critical temperature.

Contribution

The study provides a detailed model explaining the flux periodicity crossover in superconducting rings, incorporating multi-channel effects and coherence length considerations.

Findings

Flux dependence becomes strictly hc/2e periodic when ring circumference exceeds coherence length.

The model captures the crossover behavior near the critical temperature.

Multi-channel effects influence the flux periodicity in superconducting rings.

Abstract

We analyze the crossover from an hc/e-periodicity of the persistent current in flux threaded clean metallic rings towards an hc/2e-flux periodicity of the supercurrent upon entering the superconducting state. On the basis of a model calculation for a one-dimensional ring we identify the underlying mechanism, which balances the hc/e versus the hc/2e periodic components of the current density. When the ring circumference exceeds the coherence length of the superconductor, the flux dependence is strictly hc/2e periodic. Further, we develop a multi-channel model which reduces the Bogoliubov - de Gennes equations to a one-dimensional differential equation for the radial component of the wave function. The discretization of this differential equation introduces transverse channels, whose number scales with the thickness of the ring. The periodicity crossover is analyzed close the critical temperature.