Vortex Interactions and Thermally Induced Crossover from Type-I to Type-II Superconductivity

We have computed the effective interaction between vortices in the Ginzburg-Landau model from large-scale Monte-Carlo simulations, taking thermal fluctuations of matter fields and gauge fields fully into account close to the critical temperature. We find a change, in the form of a crossover, from attractive to repulsive effective vortex interactions in an intermediate range of Ginzburg-Landau parameters $\kappa \in [0.76-1]/\sqrt{2}$ upon increasing the temperature in the superconducting state. This corresponds to a thermally induced crossover from \typeI to \typeII superconductivity around a temperature $T_{\rm{Cr}}(\kappa)$, which we map out in the vicinity of the metal-to-superconductor transition. In order to see this crossover, it is essential to include amplitude fluctuations of the matter field, in addition to phase-fluctuations and gauge-field fluctuations. We present a simple physical picture of the crossover, and relate it to observations in \metal{Ta} and \metal{Nb} elemental superconductors which have low-temperature values of $\kappa$ in the relevant range.