Pairing theory for strongly correlated d -wave superconductors

Motivated by recent proposals of correlation induced insensitivity of d-wave superconductors to impurities, we develop a simple pairing theory for these systems for up to a moderate strength of disorder. Our description implements the key ideas of Anderson, originally proposed for disordered s-wave superconductors, but in addition takes care of the inherent strong electronic repulsion in these compounds, as well as disorder induced inhomogeneities. We first obtain the self-consistent one-particle states, which capture the effects of disorder exactly, and strong correlations using Gutzwiller approximation. These "normal states," representing the interplay of strong correlations and disorder, when coupled through pairing attractions following the path of Bardeen-Cooper-Schrieffer (BCS), produce results nearly identical to those from a more sophisticated inhomogeneous Hartree-Fock-Bogoliubov analysis that takes care of strong electronic repulsions.