Critical temperature of an anisotropic superconductor containing both nonmagnetic and magnetic impurities

Abstract

The combined effect of both nonmagnetic and magnetic impurities on the superconducting transition temperature is studied theoretically within the BCS model. An expression for the critical temperature as a function of potential and spin-flip scattering rates is derived for a two-dimensional superconductor with arbitrary in-plane anisotropy of the superconducting order parameter, ranging from isotropic $s$ wave to $d$ wave (or any pairing state with nonzero angular momentum) and including anisotropic $s$ wave and mixed $(d+s)$ wave as particular cases. This expression generalizes the well-known Abrikosov-Gor'kov formula for the critical temperature of impure superconductors. The effect of defects and impurities in high-temperature superconductors is discussed.