A coherent-potential approximation CPA 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.

• Received 21 December 1998

DOI:https://doi.org/10.1103/PhysRevB.60.7523