FERMI-SURFACE HARMONICS IN THE THEORY OF THE UPPER CRITICAL-FIELD

We derive general equations for the angular and temperature (T) dependence of the upper critical field B(c2) for anisotropic systems extending the standard theory of Werthamer, Helfand, and Hohenberg (WHH) by circumventing those approximations and simplifications that are appropriate only in the weak anisotropic case. They axe applicable to materials with a highly anisotropic Fermi surface and/or a Fermi surface consisting of several disjoint pieces also, and a possible anisotropy of the coupling mechanism is taken into account by means of Fermi-surface harmonics (FSH). Several limiting cases are discussed. Especially, for B(c2) --> 0 the T(c) equations of P. B. Allen are recovered, and for isotropic systems with a Fermi surface consisting of several disjoint pieces, multiple-band generalizations of the WHH equations result. Furthermore, the relevance of the FSH is demonstrated by means of two simple examples allowing for explicit results.