Upper critical field ofs- andd-wave superconductors with anisotropic effective mass

Abstract

We have derived strong-coupling equations for the upper critical field ${\mathit{B}}_{\mathit{c}2}$(T) of a spin-fluctuation-mediated d-wave superconductor. Two possible choices for the d-wave gap function are examined. Even for an isotropic Fermi surface they lead to different reduced fields ${\mathit{b}}_{\mathit{c}2}$ when the magnetic field is applied in the z direction or in the xy plane. They also cause a temperature-dependent ${\mathit{B}}_{\mathit{c}2}$ anisotropy. We include in the analysis the full angular dependence of the upper critical field near ${\mathit{T}}_{\mathit{c}}$ and compare it with the angular dependence caused by an s-wave superconductor with different masses (m) in the xy plane and (M) in the z direction. As the ratio of the d wave to constant part of the magnetic susceptibility g is reduced below 1, the upper critical field is strongly suppressed as is the critical temperature, compared with g=1, which corresponds to the conventional electron-phonon case. Strong-coupling effects are also considered explicitly.