We apply the Coherent Potential Approximation (CPA) to an extended Hubbard model to describe disordered superconductors with d-wave pairing. We discuss the pair-breaking effect caused by non-magneticdisorder in presence of Van Hove Singularity.
The coherent potential approximation (CPA) has recently been applied to disordered s-wave, p-wave and d-wave superconductors. Here we show that for systems with hypercubic lattices and generalized local s-wave, d-wave, extended s-wave or p-wave superconductivity the exact average Green function is equal to the CPA Green function in the limit where the number of dimensions goes to infinity. As in the case of normal systems, the $\stackrel{\ensuremath{\rightarrow}}{d}\ensuremath{\infty}$ limit is regularized by demanding that the second moment of the quasiparticle density of states be finite. Surprisingly, this condition leads to the scalings tij=t∗/d and ${\ensuremath{\Delta}}_{\mathrm{ij}}={\ensuremath{\Delta}}^{*}/\sqrt{d}$ for the hopping integral and the nonlocal pairing potential, respectively, but does not require scaling of the effective electron-electron interaction constant, Uij even if i and j refer to different sites.
We devise a computational approach to the Hubbard model that captures the strong coupling dynamics arising when the Fermi level is at a Van Hove singularity in the density of states. We rely on an approximate degeneracy among the many-body states accounting for the main instabilities of the system (antiferromagnetism, d-wave superconductivity). The Fermi line turns out to be deformed in a manner consistent with the pinning of the Fermi level to the Van Hove singularity. For a doping rate $\ensuremath{\delta}\ensuremath{\sim}0.2,$ the ground state is characterized by d-wave symmetry, quasiparticles gapped only at the saddle points of the band, and a large peak at zero momentum in the d-wave pairing correlations.
Many theoretical approaches find d-wave superconductivity in the prototypical one-band Hubbard model for high-temperature superconductors. At strong coupling ($U\ensuremath{\ge}W$, where U is the on-site repulsion and W=8t the bandwidth) pairing is controlled by the exchange energy J=4t2/U. One may then surmise, ignoring retardation effects, that near-neighbor Coulomb repulsion V will destroy superconductivity when it becomes larger than J, a condition that is easily satisfied in cuprates, for example. Using cellular dynamical mean-field theory with an exact diagonalization solver for the extended Hubbard model, we show that pairing at strong coupling is preserved, even when $V\ensuremath{\gg}J$, as long as $V\ensuremath{\lesssim}U/2$. While at weak coupling V always reduces the spin fluctuations and hence d-wave pairing, at strong coupling, in the underdoped regime, the increase of $J=4{t}^{2}/(U\ensuremath{-}V)$ caused by V increases binding at low frequency while the pair-breaking effect of V is pushed to high frequency. These two effects compensate in the underdoped regime, in the presence of a pseudogap. While the pseudogap competes with superconductivity, the proximity to the Mott transition that leads to the pseudogap, and retardation effects, protect d-wave superconductivity from V.