Variational calculations of sheath-state nucleation in isotropic type II superconductors

It has long been known that superconductivity can initially nucleate in a thin sheath at the surface of a sample which is of finite extent in some direction. A small number of exact results are known for this critical field H-c3(T) at which such nucleation occurs in very simple geometries. We show here that a simple variational calculation can yield results indistinguishable from those given by exact calculations and also be easily applied to more complicated geometries where exact solutions do not exist. Wr demonstrate that when the applied external field is oblique to the surface of a semi-infinite slab a variational estimate can reproduce the results of perturbation theory when the field makes a small angle with the surface, and will yield exactly the usual bulk critical field H-c2(T) for normal incidence. For intermediate angles, our calculations yield a smooth interpolation between these two results and we offer some interpretation of these results. Finally we apply our variational calculation to the more complicated problem of nucleation in a spherical superconductor. (C) 1998 Elsevier science B.V.