Surface Superconductivity in Presence of Corners

Abstract

We consider an extreme type-II superconducting wire with non-smooth cross section, i.e., with one or more corners at the boundary, in the framework of the Ginzburg-Landau theory. We prove the existence of an interval of values of the applied field, where superconductivity is spread uniformly along the boundary of the sample. More precisely the energy is not affected to leading order by the presence of corners and the modulus of the Ginzburg-Landau minimizer is approximately constant along the transversal direction. The critical fields delimiting this surface superconductivity regime coincide with the ones in absence of boundary singularities.

20 pages, pdfLaTex, 2 figures

References in corpus (3)

• Superconductivity in domains with corners
• Critical Rotational Speeds in the Gross-Pitaevskii Theory on a Disc with Dirichlet Boundary Conditions
• Effects of boundary curvature on surface superconductivity

Cited by in corpus (13)

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• The breakdown of superconductivity in the presence of magnetic steps
• The density of superconductivity in domains with corners
• Universal and shape dependent features of surface superconductivity
• Surface Effects in Superconductors with Corners
• Microscopic Derivation of Ginzburg-Landau Theory and the BCS Critical Temperature Shift in a Weak Homogeneous Magnetic Field
• Magnetic steps on the threshold of the normal state
• Effects of Corners in Surface Superconductivity
• Microscopic Derivation of Ginzburg-Landau Theory and the BCS Critical Temperature Shift in General External Fields
• On the Ginzburg-Landau Energy of Corners
• On the bound states of magnetic Laplacians on wedges
• Oscillatory patterns in the Ginzburg-Landau model driven by the Aharonov-Bohm potential (Derivation of the Aharanov-Bohm potential in the Ginzburg-Landau model)
• Almost Flat Angles in Surface Superconductivity