Article

Communications in Mathematical Physics

, Volume 266, Issue 1, pp 153-196

First online:

On the Third Critical Field in Ginzburg-Landau Theory

  • S. FournaisAffiliated withLaboratoire de Mathématiques UMR CNRS 8628, Université Paris-Sud - Bât 425CNRS and Laboratoire de Mathématiques UMR CNRS 8628, Université Paris-Sud - Bât 425 Email author 
  • , B. HelfferAffiliated withCNRS and Laboratoire de Mathématiques UMR CNRS 8628, Université Paris-Sud - Bât 425

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Abstract

Using recent results by the authors on the spectral asymptotics of the Neumann Laplacian with magnetic field, we give precise estimates on the critical field, \(H_{C_3}\), describing the appearance of superconductivity in superconductors of type II. Furthermore, we prove that the local and global definitions of this field coincide. Near \(H_{C_3}\) only a small part, near the boundary points where the curvature is maximal, of the sample carries superconductivity. We give precise estimates on the size of this zone and decay estimates in both the normal (to the boundary) and parallel variables.