Vortex interactions and thermally induced crossover from type-I to type-II superconductivity

Abstract

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 what appears to be a crossover, from an attractive to a repulsive effective vortex interactions in an intermediate range of Ginzburg-Landau parameters $\ensuremath{\kappa}\ensuremath{\in}[0.76,1]/\sqrt{2}$ upon increasing the temperature in the superconducting state. This corresponds to a thermally induced crossover from type-I to type-II superconductivity around a temperature ${T}_{\mathrm{Cr}}(\ensuremath{\kappa}),$ 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 Ta and Nb elemental superconductors which have low-temperature values of $\ensuremath{\kappa}$ in the relevant range.