Almost flat angles in surface superconductivity. (28th September 2021)

• Record Type: Journal Article
• Authors: Correggi, Michele; Giacomelli, Emanuela L
• Is Part Of: Nonlinearity. Volume 34:Number 11(2021)
• Page Start: 7633
• Page End: 7661
• Publication Date: 2021-09-28
• Subjects: Ginzburg–Landau theory -- superconductivity -- domains with corners; 35Q56; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/ac24e0
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: Type-II superconductivity is known to persist close to the sample surface in presence of a strong magnetic field. As a consequence, the ground state energy in the Ginzburg–Landau theory is approximated by an effective one-dimensional model. As shown by Correggi and Giacomelli (2021 Calc. Var. Partial Differential Equations in press), the presence of corners on the surface affects the energy of the sample with a non-trivial contribution. In (Correggi and Giacomelli 2021 Calc. Var. Partial Differential Equations in press), the two-dimensional model problem providing the corner energy is implicitly identified and, although no explicit dependence of the energy on the corner opening angle is derived, a conjecture about its form is proposed. We study here such a conjecture and confirm it, at least to leading order, for corners with almost flat opening angle.