On the shape of interlayer vortices in the Lawrence--Doniach model

We consider the Lawrence--Doniach model for layered superconductors, in which stacks of parallel superconducting planes are coupled via the Josephson effect. To model experiments in which the superconductor is placed in an external magnetic field oriented {\it parallel} to the superconducting planes, we study the structure of isolated vortices for a doubly periodic problem. We consider a singular limit which simulates certain experimental regimes in which isolated vortices have been observed, corresponding to letting the interlayer spacing of the superconducting planes tend to zero and the Ginzburg--Landau parameter \kappa\to\infty simultaneously, but at a fixed relative rate.