Magnetic Field Dependence of T C and Temperature Dependence of H C 2 in Layered Superconductors with Open Normal State Fermi Surface

A theoretical framework for treating the effects of magnetic fieldH on the pairing theory of superconductivity is considered, where the field is taken in an arbitrary direction with respect to crystal axes. This is applicable to closed, as well as open normal state Fermi surface (FS), including simple layered metals. The orbital effects of the magnetic field are treated semiclassically while retaining the full anisotropic paramagnetic contribution. Explicit calculations are presented in the limits |H| → |H c2(T)|,T ∼ 0 andT →T c(|H|), |H| ∼ 0. Effects of weak nonmagnetic impurity scattering, without vertex corrections, have also been taken into account in a phenomenological way. The final results for the case of open FS and layered materials are found to differ considerably from those of the closed FS. For example, an important parameter,h(T=0)=|Hc2(0)|/[-Tδ|H c2 T|δT]T{s0} for the case of a FS open ink z-direction with thek z-bandwidth, 4t 3, very small compared to the Fermi energy,E F, is close to 0.5906, compared to 0.7273 for the closed FS, in the clean limit. Analytical results are given for the magnetic field dependence ofT c and the temperature dependence of H c2 for a model of layered superconductors with widely open FS. For a set of band structure parameters for YBa2Cu3O7 used elsewhere, we find reasonable values for the upper critical fieldH c2(0), the slope (dH c2/dT)T c0, anisotropic coherence lengths ζi(T=0),i=x, y, z, and (dT c/d|H|)|H| → 0.