Almost flat angles in surface superconductivity

Correggi, Michele and Giacomelli, Emanuela L. (2021): Almost flat angles in surface superconductivity. In: Nonlinearity, Vol. 34, No. 11: pp. 7633-7661

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.

• Item Type: Journal article
• Faculties: Mathematics, Computer Science and Statistics > Mathematics
• Subjects: 500 Science > 510 Mathematics
• ISSN: 0951-7715
• Language: English