Periodic vortex lattices for the Lawrence-Doniach model of layered superconductors in a parallel field

We consider the Lawrence-Doniach model for layered superconductors, in whic h stacks of parallel superconducting planes are coupled via the Josephson e ffect. We assume that the superconductor is placed in an external magnetic field oriented parallel to the superconducting planes and study periodic la ttice configurations in the limit as the Josephson coupling parameter tau - -> 0. This limit leads to the "transparent state" discussed in the physics literature, which is observed in very anisotropic Egh-T-c superconductors a t sufficiently high applied fields and below a critical temperature. We use a Lyapunov-Schmidt reduction to prove that energy minimization uniquely de termines the geometry of the optimal vortex lattice: a period-2 (in the lay ers) array proposed by Bulaevskii & Clem. Finally, we discuss the apparent conflict with previous results for finite-width samples, in which the minim izer in the small coupling regime takes the form of "vortex planes" (introd uced by Theodorakis and Kuplevakhsky).