Analysis of minimizers of the Lawrence-Doniach energy for superconductors in applied fields

We analyze minimizers of the Lawrence-Doniach energy for layered superconductors with Josephson constant lambda and Ginzburg-Landau parameter 1/epsilon in a bounded generalized cylinder D = Omega x [0, L] in R-3, where Omega is a bounded simply connected Lipschitz domain in R-2. Our main result is that in an applied magnetic field (H) over right arrow (ex) = h(ex)e(3) which is perpendicular to the layers with vertical bar ln epsilon vertical bar << h(ex) << epsilon(-2), the minimum Lawrence-Doniach energy is given by vertical bar D vertical bar/2h(ex) ln 1/epsilon root h(ex) (1+o(epsilon,s) (1)) as epsilon and the interlayer distance s tend to zero. We also prove estimates on the behavior of the order parameters, induced magnetic field, and vorticity in this regime. Finally, we observe that as a consequence of our results, the same asymptotic formula holds for the minimum anisotropic three-dimensional Ginzburg-Landau energy in D with anisotropic parameter lambda and o(epsilon,s) (1) replaced by o(epsilon)(1).d