Continuous 3D Freezing Transition in Layered Superconductors

We use Ginzburg-Landau theory to study the $H_{c2\mathrm{}}$ transition in layered superconductors with field parallel to the layers, finding a continuous 3D freezing transition to a triangular vortex supersolid in the three-dimensional XY universality class. If screening effects are neglected, off-diagonal–long-range order survives only for $d>\mathrm{}{d}_{\mathrm{lc}}=5/2\mathrm{}$. The partial breaking of the lowest Landau level degeneracy induced by layering leads to a local selection of a triangular lattice structure, in contrast to the global free energy minimization in, e.g., Abrikosov's calculation. Our results are relevant to artificially layered superconductors and to strongly anisotropic high $T_c$ materials.