On the Ginzburg–Landau Functional in the Surface Superconductivity Regime

M Correggi (1) , N Rougerie (2)

1 Dipartimento di Matematica e Fisica
2 LPM2C - Laboratoire de physique et modélisation des milieux condensés

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.

Domaines: Physique mathématique [math-ph]; Equations aux dérivées partielles [math.AP]; Supraconductivité [cond-mat.supr-con]

M Correggi, N Rougerie. On the Ginzburg–Landau Functional in the Surface Superconductivity Regime. 2013. ⟨hal-00859954v4⟩