Spontaneous vortex formation on a superconducting film

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.