Coherent Potential Approximation for `d - wave' Superconductivity in Disordered Systems

A Coherent Potential Approximation is developed for s-wave and d-wave superconductivity in disordered systems. We show that the CPA formalism reproduces the standard pair-breaking formula, the self-consistent Born Approximation and the self-consistent T-matrix approximation in the appropriate limits. We implement the theory and compute T_c for s-wave and d-wave pairing using an attractive nearest neighbor Hubbard model featuring both binary alloy disorder and a uniform distribution of scattering site potentials. We determine the density of states and examine its consequences for low temperature heat capacity. We find that our results are in qualitative agreement with measurements on Zn doped YBCO superconductors.