Pairing of renormalized eigenstates of disordered superconductors with strong correlations

Strongly correlated d-wave superconductors show amazing robustness to impurities up to moderate strengths within Hartree-Fock-Bogoliubov (HFB) calculations [1]. Motivated by this finding, we investigate the interplay of interactions and disorder in these systems using a simple pairing mechanism, similar to what leads to Anderson's theorem for s-wave superconductors. We first solve for the effective one-particle eigenstates in the presence of disorder, including the inherently strong electronic repulsions at the Hartree-Fock channels using Gutzwiller renormalization. These `normal-states' are then paired up keeping track of disorder induced inhomogeneities. Our results, matching with those in the literature [1], show that the inhomogeneities in the normal-states is qualitatively different from the eigenstates of noninteracting disordered Hamiltonian. The pairing, however, reflects strong insensitivity to inhomogeneities. Our results shed light on why d-wave superconductivity is robust to disorder in HFB formalism, compared to conventional Abrikosov Gorkov mechanism.\\ (1) D. Chakraborty and A. Ghosal, New J. Phys. 16, 103018 (2014)