Convergence of the Lawrence-Doniach Energy for Layered Superconductors with Magnetic Fields near $H_{c_1}$

Abstract

We analyze minimizers of the Lawrence-Doniach energy for three-dimensional highly anisotropic superconductors with layered structure. For such a superconductor occupying a bounded generalized cylinder in ${\mathbb{R}}^3$ with equally spaced parallel layers, we assume an applied magnetic field that is perpendicular to the layers with intensity $h_{ex}\sim |\ln \epsilon |$ as $\epsilon \to 0$, where $\epsilon$ is the reciprocal of the Ginzburg-Landau parameter. We prove compactness results for various physical quantities of energy minimizers, and derive a Gamma-limit of the Lawrence-Doniach energy as $\epsilon$ and the interlayer distance $s$ tend to zero, under the additional assumption that the layers are weakly coupled (i.e., $s\gg \epsilon$).

References in corpus (1)

• Analysis of Minimizers of the Lawrence-Doniach Energy for Superconductors in Applied Fields