Vortex-Loop Unbinding and Flux-Line Lattice Melting in Superconductors

We study the interplay between a novel vortex-loop unbinding in finite magnetic field at ${T=T}_V$ and flux-line-lattice (FLL) melting at ${T=T}_M$ in type-II superconductors. The FLL melts due to nucleation of vortex loops parallel to the $\hat{c}$ axis, connected to flux lines. For moderate anisotropy, phase coherence parallel to $\hat{c}$ is lost at $T_V>T_M$ due to an $\mathrm{ab}$-plane vortex-loop unbinding with loops located close to thermal FLL fluctuations. For large anisotropy, phase coherence parallel to $\hat{c}$ is lost at $T_V<T_M$ due to nucleation of vortex loops uncorrelated to flux lines, predominantly in the $\mathrm{ab}$ plane.