VARIATIONAL CALCULATIONS OF SHEATH-STATE NUCLEATION IN ISOTROPIC TYPE-II SUPERCONDUCTORS

It has long been known that superconductivity can initially nucleate i n a thin sheath at the surface of a sample which is of finite extent i n some direction. A small number of exact results are known for this c ritical field H-c3(T) at which such nucleation occurs in very simple g eometries. We show here that a simple variational calculation can yiel d results indistinguishable from those given by exact calculations and also be easily applied to more complicated geometries where exact sol utions do not exist. Wr demonstrate that when the applied external fie ld is oblique to the surface of a semi-infinite slab a variational est imate 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 an gles, 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 n ucleation in a spherical superconductor. (C) 1998 Elsevier science B.V .