Fluxoid formation: size effects and non-equilibrium universality

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 Ref. [1], 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.

Defect Formation in Superconducting Rings: External Fields and Finite-Size Effects

“…In Fig. 2, we show the crossover from KZ behaviour, indistinguishable from the falloff obtained previously 10 . Differing aspect ratios were tried for the central hole for the same perimeter, ranging from square to an elongated 4:1 rectangle, but no deviation from the perimeter law behaviour of Eq.…”

“…We have discussed this elsewhere 10 but, in brief, we assume that the winding number density is a Gaussian random variable. If C is the circumference of the ring the relevant quantity isξ /C.…”

“…With B ext = 0, we first sought to see if the exponential falloff in trapping probability predicted 10 by 1D simulations in Eq. (3) persisted for the more realistic theory.…”

Gaussianity revisited: exploring the Kibble–Zurek mechanism with superconducting rings

“…In Ref. [12] we showed that exponential damping does take place. However, we can go further in that, if we combine Eq.…”

“…To implement this in the approximation of Eq. (18), we need to replace f (x) by its periodic generalisation, the Jacobi ϑ function [12] f…”