Surface Nucleation of Superconductivity in 3-Dimensions

In this paper we study the surface nucleation of superconductivity and estimate the value of the upper critical field HC3 for superconductors occupying arbitrary bounded smooth domains in 3. We show that HC3 κ/β0, the ratio of the Ginzburg–Landau parameter κ and the first eigenvalue β0 of the Schrödinger operator with unit magnetic field on the half plane. When the applied magnetic field is spacially homogeneous and close to HC3, a superconducting layer nucleates on a portion of the surface at which the applied field is tangential to the surface. Nucleation under non-homogeneous applied fields is also discussed