Defective vortex lattices in layered superconductors with point pins at the extreme type-II limit

Abstract

The mixed phase of layered superconductors with no magnetic screening is studied through a partial duality analysis of the corresponding frustrated $\mathrm{XY}$ model in the presence of weak random point pins. Isolated layers exhibit a defective vortex lattice at low temperature that is phase coherent. Sufficiently weak Josephson coupling between adjacent layers results in an entangled vortex solid that exhibits weak superconductivity across layers. The corresponding vortex liquid state shows an inverted specific-heat anomaly that we propose accounts for that seen in yttrium barium copper oxide. A three-dimensional vortex lattice with dislocations occurs at stronger coupling. This crossover sheds light on the apparent discrepancy concerning the observation of a vortex-glass phase in recent Monte Carlo simulations of the same $\mathrm{XY}$ model.