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.
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Søren Fournais, Bernard Helffer, Mikael Persson, Superconductivity between and . J. Spectr. Theory 1 (2011), no. 3, pp. 273–298