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

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.

Kibble-Zurek Scaling and its Breakdown for Spontaneous Generation of Josephson Vortices in Bose-Einstein Condensates

“…Moreover, by varying the circumference, we verify that the KZM departure is not due to the finite-size effects discussed in Ref. [31][32][33].…”

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

“…These linearized equations generally lead to KZ scaling behaviour for fast quenches in large systems, both non-relativistic and relativistic [9][10][11]. More recently, preliminary simulations which further support underlying Gaussian behaviour explicitly for superconductors were performed by us in [12,13], and this paper builds on this analysis.…”

“…However, we have seen previously (in Ref. [13]) that this secondary mechanism, the Hindmarsh-Rajantie (HR) mechanism [20,21], does not seem to be important for our small systems and we shall not pursue it further.…”

“…To test the approximations outlined in the previous sections we simulated the superconducting ring in a 3D box [13]. Although the superconductor is thereby taken to be a thin planar film, the three-dimensional simulation allows for nontrivial correlations of the magnetic field.…”

“…More recently, preliminary simulations which further support underlying Gaussian behaviour explicitly for superconductors were performed by us in Refs. [12,13], and this paper builds on this analysis.…”