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

Abstract

We analyze minimizers of the Lawrence-Doniach energy for layered superconductors occupying a bounded generalized cylinder, $\Omega \times [0,L]$, in ${\mathbb{R}}^3$, where $\Omega$ is a bounded simply connected Lipschitz domain in ${\mathbb{R}}^2$. For an applied magnetic field ${\vec{H}}_{ex}=h_{ex}{\vec{e}}_3$ that is perpendicular to the layers with $\left|\ln \epsilon \right|\ll h_{ex}\ll {\epsilon }^{-2}$ as $\epsilon \to 0$, where $\epsilon$ is the reciprocal of the Ginzburg-Landau parameter, we prove an asymptotic formula for the minimum Lawrence-Doniach energy as $\epsilon$ and the interlayer distance $s$ tend to zero. Under appropriate assumptions on $s$ versus $\epsilon$, we establish comparison results between the minimum Lawrence-Doniach energy and the minimum three-dimensional anisotropic Ginzburg-Landau energy. As a consequence, our asymptotic formula also describes the minimum three-dimensional anisotropic energy as $\epsilon$ tends to zero.

Cited by in corpus (1)

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