Journal of Spectral Theory

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Volume 1, Issue 3, 2011, pp. 273–298
DOI: 10.4171/JST/12

Published online: 2011-07-13

Superconductivity between $H_{C_2}$ and $H_{C_3}$

Søren Fournais[1], Bernard Helffer[2] and Mikael Persson[3]

(1) University of Aarhus, Denmark
(2) Université de Nantes, France
(3) University of Aarhus, Denmark

Superconductivity for Type II superconductors in external magnetic fields of magnitude between the second and third critical fields is known to be restricted to a narrow boundary region. The profile of the superconducting order parameter in the Ginzburg–Landau model is expected to be governed by an effective one-dimensional model. This is known to be the case for external magnetic fields sufficiently close to the third critical field. In this text we prove such a result on a larger interval of validity.

Keywords: Spectral theory, Ginzurg–Landau functional, Ordinary differential operator

Fournais Søren, Helffer Bernard, Persson Mikael: Superconductivity between $H_{C_2}$ and $H_{C_3}$. J. Spectr. Theory 1 (2011), 273-298. doi: 10.4171/JST/12