Equilibrium vortex-line configurations and critical currents in thin films under a parallel field

Abstract

Vortex-line equilibrium configurations and critical currents for type-II superconducting films at zero-temperature are studied theoretically. The films are assumed to be of thickness less than or equal to the penetration depth, free of pinning by imperfections, and to be subjected to a magnetic field parallel to the film surfaces and to a transport current perpendicular to the field. By numerical minimization of the exact London theory energy expression, using simulated annealing techniques, the equilibrium configurations are determined with great accuracy over a wide range of fields and currents. These consist of chains of straight vortex-lines whose number depends both on the field and on the current. Transitions involving a change by one in the chain number are found to take place either if the field is increased at zero transport current or if the transport current is increased at constant field. At the transitions, there is a considerable rearrangement in the vortex-line positions and a small, discontinuous, change in their number. The equilibrium configurations with chain numbers that are not too small form a nearly perfect triangular lattice, centered with respect to the film surfaces. However, small deviations from this arrangement are found to be important in determining the behavior near the transition and when the transport current approaches the critical current. It is found that the critical current has a a non-monotonic dependence on the field. The zero-temperature equilibrium phase diagram in the field-transport current plane is reported.