Phase transitions in isotropic extreme type-II superconductors

Using large-scale Monte Carlo simulations on a uniformly frustrated three-dimensional $\mathrm{XY}$ model, we report a first-order vortex lattice melting transition in clean, isotropic extreme type-II $\left(\overrightarrow{\kappa }\infty \right)$ superconductors. This work clarifies an important issue: the unpinned vortex liquid is always incoherent with no phase coherence in any direction for all anisotropies. Previous claims of a disentangled vortex liquid for isotropic superconductors based on simulations are due to finite-size effects. We explicitly show that the effective vortex-line tension vanishes precisely at the superconducting phase transition in zero magnetic field. This loss of line tension is accompanied by an abrupt change in the connectivity of the vortex tangle across the superconductor. We also obtain results indicating that the connectivity of the vortex tangle changes in a similar way even in a finite magnetic field, and suggest that this could also be associated with a genuine phase transition.