Nature of the low-field transition in the mixed state of high-temperature superconductors

Abstract

We have numerically studied the statics and dynamics of a model three-dimensional (3D) vortex lattice at low magnetic fields. For the statics we use a frustrated 3D $\mathrm{XY}$ model on a stacked triangular lattice. We model the dynamics as a coupled network of overdamped resistively shunted Josephson junctions with Langevin noise. At low fields, there is a weakly first-order phase transition, at which the vortex lattice melts into a line liquid. Phase coherence parallel to the field persists until a sharp crossover, conceivably a phase transition, near $T_{\mathcal{l}}>T_m$ which develops at the same temperature as an infinite vortex tangle. The calculated flux flow resistivity in various geometries near ${T=T}_{\mathcal{l}}$ closely resembles experiment. The local density of field induced vortices increases sharply near $T_{\mathcal{l}},$ corresponding to the experimentally observed magnetization jump. We discuss the nature of a possible transition or crossover at $T_{\mathcal{l}}$(B) which is distinct from flux lattice melting.