Fluctuation persistent current in small superconducting rings

TL;DR

This paper investigates how fluctuating Cooper pairs influence persistent currents in small superconducting rings under magnetic fields, revealing quantum critical points and the effects of ring size on superconductivity.

Contribution

It extends theoretical analysis of fluctuation effects on persistent currents, highlighting flux-tuned quantum critical points and mode interactions in small superconducting rings.

Findings

Identification of a flux-tuned quantum critical point in small rings.

Calculation of fluctuation persistent current across different regimes.

Analysis of pair-breaking mechanisms to observe flux-tuned transitions.

Abstract

We extend previous theoretical studies of the contribution of fluctuating Cooper pairs to the persistent current in superconducting rings subjected to a magnetic field. For sufficiently small rings, in which the coherence length $\xi$ exceeds the radius $R$, mean field theory predicts the emergence of a flux-tuned quantum critical point separating metallic and superconducting phases near half-integer flux through the ring. For larger rings with $R\gtrsim \xi$, the transition temperature is periodically reduced, but superconductivity prevails at very low temperatures. We calculate the fluctuation persistent current in different regions of the metallic phase for both types of rings. Particular attention is devoted to the interplay of the angular momentum modes of the fluctuating order parameter field. We discuss the possibility of using a combination of different pair-breaking mechanisms to simplify the observation of the flux-tuned transition in rings with $\xi>R$.