Persistent current in small superconducting rings

TL;DR

This paper theoretically investigates how fluctuating Cooper pairs contribute to persistent currents in small superconducting rings, revealing significant currents due to fluctuations even when mean field theory predicts suppressed superconductivity.

Contribution

It provides an analytical study of persistent currents caused by Cooper pair fluctuations in small superconducting rings, especially near the critical flux and size regimes.

Findings

Persistent currents remain large due to fluctuations even when mean field theory predicts suppression.

Analytical expressions for susceptibility in the critical fluctuation region are derived.

Competition between two complex order parameters influences the fluctuation behavior.

Abstract

We study theoretically the contribution of fluctuating Cooper pairs to the persistent current in superconducting rings threaded by a magnetic flux. For sufficiently small rings, in which the coherence length $\xi$ exceeds the radius $R$, mean field theory predicts a full reduction of the transition temperature to zero near half-integer flux. We find that nevertheless a very large current is expected to persist in the ring as a consequence of Cooper pair fluctuations that do not condense. For larger rings with $R\gg \xi$ we calculate analytically the susceptibility in the critical region of strong fluctuations and show that it reflects competition of two interacting complex order parameters.