On the Ginzburg--Landau Functional in the Surface Superconductivity Regime
Abstract
We present new estimates on the two-dimensional Ginzburg-Landau energy of a type-II superconductor in an applied magnetic field varying between the second and third critical fields. In this regime, superconductivity is restricted to a thin layer along the boundary of the sample. We provide new energy lower bounds, proving that the Ginzburg-Landau energy is determined to leading order by the minimization of a simplified 1D functional in the direction perpendicular to the boundary. Estimates relating the density of the Ginzburg-Landau order parameter to that of the 1D problem follow. In the particular case of a disc sample, a refinement of our method leads to a pointwise estimate on the Ginzburg-Landau order parameter, thereby proving a strong form of uniformity of the surface superconductivity layer, related to a conjecture by Xing-Bin Pan.
Keywords
Cite
@article{arxiv.1309.2268,
title = {On the Ginzburg--Landau Functional in the Surface Superconductivity Regime},
author = {M. Correggi and N. Rougerie},
journal= {arXiv preprint arXiv:1309.2268},
year = {2019}
}
Comments
Revision of the version published in Communications in Mathematical Physics 332 (3), 1297-1343 (2014). Minor mistakes corrected and Theorem 2.4 reformulated accordingly