Effects of Corners in Surface Superconductivity

Abstract

We study the Ginzburg-Landau functional describing an extreme type-II superconductor wire with cross section with finitely many corners at the boundary. We derive the ground state energy asymptotics up to $o(1)$ errors in the surface superconductivity regime, i.e., between the second and third critical fields. We show that, compared to the case of smooth domains, each corner provides an additional contribution of order $\mathcal{O}(1)$ depending on the corner opening angle. The corner energy is in turn obtained from an implicit model problem in an infinite wedge-like domain with fixed magnetic field. We also prove that such an auxiliary problem is well-posed and its ground state energy bounded and, finally, state a conjecture about its explicit dependence on the opening angle of the sector.

arXiv commentrevised version, presentation shortened and proof arguments streamlined; 54 pages, pdfLaTex

References in corpus (20)

• Influence of the confinement geometry on surface superconductivity
• Little Magnetic Book
• The Transition to a Giant Vortex Phase in a Fast Rotating Bose-Einstein Condensate
• Energy and Vorticity in Fast Rotating Bose-Einstein Condensates
• Phase transition curves for mesoscopic superconducting samples
• On the third critical field in Ginzburg-Landau theory
• Superconductivity in domains with corners
• Critical Rotational Speeds for Superfluids in Homogeneous Traps
• Boundary Behavior of the Ginzburg-Landau Order Parameter in the Surface Superconductivity Regime
• Local density approximation for the almost-bosonic anyon gas
• Surface Superconductivity in Presence of Corners
• Multi-component Ginzburg-Landau theory: microscopic derivation and examples
• Inhomogeneous Vortex Patterns in Rotating Bose-Einstein Condensates
• The breakdown of superconductivity in the presence of magnetic steps
• Effects of boundary curvature on surface superconductivity
• The density of superconductivity in domains with corners
• Universal and shape dependent features of surface superconductivity
• On the Third Critical Speed for Rotating Bose-Einstein Condensates
• Concentration Behavior and Lattice Structure of Surface Superconductivity
• Surface Effects in Superconductors with Corners

Cited by in corpus (1)

• Oscillatory patterns in the Ginzburg-Landau model driven by the Aharonov-Bohm potential (Derivation of the Aharanov-Bohm potential in the Ginzburg-Landau model)