Disordered s-, d-, and p-wave superconductors: Exact results in infinite dimensions

The coherent potential approximation (CPA) has recently been applied to dis ordered s-wave, p-wave and d-wave superconductors. Here we show that for sy stems with hypercubic lattices and generalized local s-wave, d-wave, extend ed s-wave or p-wave superconductivity the exact average Green function is e qual to the CPA Green function in the limit where the number of dimensions goes to infinity. As in the case of normal systems, the d-->infinity limit is regularized by demanding that the second moment of the quasiparticle den sity of states be finite. Surprisingly, this condition leads to the scaling s t(ij) = t*/root d and Delta(ij) = Delta*/root d for the hopping integral and the nonlocal pairing potential, respectively, but does not require scal ing of the effective electron-electron interaction constant, U-ij even if i and j refer to different sites.