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Surface nucleation of superconductivity in 3-dimensions. (English) Zbl 0972.35152
The authors study the surface nucleation of superconductivity and estimate the value of the upper critical field \(H_{C_3}\) for superconductors occupying an arbitrary smooth domain in \(\mathbb{R}^3\). It is proved that \(H_{C_3}\simeq K/\beta_0\), the ratio of the Ginzburg-Landau parameter \(K\) and the first eigenvalue \(\beta_0\) for the Schrödinger operator with unit magnetic field on the half plane. When the applied magnetic field is spatially homogeneous and close to \(H_{C_3}\), a superconducting layer nucleates on a portion of the surface at which the applied field is tangential to the surface. Nucleation under nonhomogeneous applied fields is also discussed.

MSC:
35Q55 NLS equations (nonlinear Schrödinger equations)
82D55 Statistical mechanical studies of superconductors
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