Exact solution of the Lawrence-Doniach model in parallel magnetic fields

Abstract

For the first time, we obtain the complete and exact analytical solution of the Lawrence-Doniach model for layered superconductors in external parallel magnetic fields. By solving a nontrivial mathematical problem of exact minimization of the free-energy functional, we derive a closed, self-consistent system of mean-field equations involving only two variables. Exact solutions to these equations prove simultaneous penetration of Josephson vortices into all the barriers, yield a completely new expression for the lower critical field, refute the concept of a triangular Josephson vortex lattice and clarify the physics of Fraunhofer oscillations of the total critical Josephson current. PACS numbers: 74.80.Dm, 74.20.De, 74.50.+r