Fluxoid formation: size effects and non-equilibrium universality

TL;DR

This paper investigates fluxoid formation in superconducting loops, examining size effects and non-equilibrium universality, and challenges previous interpretations of high Kibble-Zurek scaling exponents through analytic and simulation approaches.

Contribution

It provides a detailed analysis of fluxoid density scaling in small superconducting loops, questioning earlier high exponent claims and clarifying the role of system size and quench dynamics.

Findings

Small loops exhibit fluxoid densities influenced by size, not scaling.

High Kibble-Zurek exponents are likely due to finite-size effects.

Slow quenches differ physically from small ring experiments.

Abstract

Simple causal arguments put forward by Kibble and Zurek suggest that the scaling behaviour of condensed matter at continuous transitions is related to the familiar universality classes of the systems at quasi-equilibrium. Although proposed 25 years ago or more, it is only in the last few years that it has been possible to devise experiments from which scaling exponents can be determined and in which this scenario can be tested. In previous work, an unusually high Kibble-Zurek scaling exponent was reported for spontaneous fluxoid production in a single isolated superconducting Nb loop, albeit with low density. Using analytic approximations backed up by Langevin simulations, we argue that densities as small as these are too low to be attributable to scaling, and are conditioned by the small size of the loop. We also reflect on the physical differences between slow quenches and small rings, and derive some criteria for these differences, noting that recent work on slow quenches does not adequately explain the anomalous behaviour seen here.