Abstract
We carry out numerical simulations of a temperature quench in a Hamiltonian system that models a superconducting film in three-dimensional (3D) space. Theoretical arguments suggest that vortices are spontaneously formed by two separate mechanisms: the Kibble–Zurek mechanism, which is based on the dynamics of the order parameter, and the flux trapping mechanism, which is based on the dynamics of the electromagnetic field. We find that fast quenches are in agreement with the predictions of the flux trapping scenario, but the results from slow quenches appear to point to the Kibble–Zurek mechanism. Our results demonstrate the crucial role the electromagnetic field plays in this phenomenon, making it very different from vortex formation in fully 2D systems or in superfluids.
Highlights
When a superconductor in rapidly cooled from the normal to the superconducting phase in the absence of an external magnetic field, vortices form
We investigate vortex formation in the case of a two-dimensional film in three-dimensional space
The plot shows that the linearized result works very well in fast quenches
Summary
When a superconductor in rapidly cooled from the normal to the superconducting phase in the absence of an external magnetic field, vortices (and antivortices) form This phenomenon has been observed in several experiments[1,2,3,4,5,6,7,8] and has analogues in other condensed matter systems such as superfluids[9,10,11] and liquid crystals.[12,13,14,15] In the latter cases, the order parameter is electrically neutral and defect formation can be understood in terms of the Kibble-Zurek mechanism.[16,17,18] In contrast, the Cooper pairs in superconductors are electrically charged, which means that the electromagnetic field plays an important role.[19,20]. We do not believe the qualitative phenomena we are interested in are sensitive to the specific choice, but quantitative details may well be different
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