Analysis of Minimizers of the Lawrence-Doniach Energy for Superconductors in Applied Fields
Patricia A. Bauman, Guanying Peng · arXiv (Cornell University) · 2014
We analyze minimizers of the Lawrence-Doniach energy for layered superconductors occupying a bounded generalized cylinder, $ Ω\times[0,L]$, in $\mathbb{R}^3$, where $Ω$ 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 $\left|\lnε\right|\ll h_{ex}\llε^{-2}$ as $ε\rightarrow 0$, where $ε$ is the reciprocal of the Ginzburg-Landau parameter, we prove an asymptotic formula for the minimum Lawrence-Doniach energy as $ε$ and the interlayer distance $s$ tend to zero. Under appropriate assumptions on $s$ versus $ε$, 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 $ε$ tends to zero.