Magnetic field-dependence of Tc and temperature-dependence of Hc2 in layered superconductors with open normal state Fermi surface

Abstract

A theoretical framework for treating the effects of magnetic field H 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 and T → 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) ≡ |H_c2(0)|/[—Tδ|H_c2(T)|/δT]T_eo for the case of a FS open in k_z-direction with the k_z bandwidth, 4t₃, 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 of T_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 YBa₂Cu₃0₇, used elsewhere, we find reasonable values for the upper critical field H_c2,(0), the slope (dH_c2/dT)T_co, anisotropic coherence lengths ξ_i(T = 0), i = x, y,z, and(dT_c/d|H|)_|H|→o.