Defect formation in superconducting rings: external fields and finite-size effects

TL;DR

This paper investigates fluxoid formation in superconducting rings during temperature quenches, highlighting finite-size effects and external fields, supported by large-scale simulations that align with simplified analytical models.

Contribution

It provides detailed 3D simulations of superconducting ring quenches considering electromagnetic dynamics and external flux, clarifying when simplified models are sufficient.

Findings

Finite-size effects influence fluxoid production.

External magnetic fields cause deviations from canonical behavior.

Simplified Gaussian models accurately predict outcomes in many cases.

Abstract

Consistent with the predictions of Kibble and Zurek, scaling behaviour has been seen in the production of fluxoids during temperature quenches of superconducting rings. However, deviations from the canonical behaviour arise because of finite-size effects and stray external fields. Technical developments, including laser heating and the use of long Josephson tunnel junctions, have improved the quality of data that can be obtained. With new experiments in mind we perform large-scale 3D simulations of quenches of small, thin rings of various geometries with fully dynamical electromagnetic fields, at nonzero externally applied magnetic flux. We find that the outcomes are, in practice, indistinguishable from those of much simpler Gaussian analytical approximations in which the rings are treated as one-dimensional systems and the magnetic field fluctuation-free.