Inhomogeneity and d-wave superconductivity in the Hubbard model

Whether or not inhomogeneity plays a significant role in determining the superconducting properties of the cuprate high-Tc superconductors remains an open issue, in spite of extensive theoretical and experimental focus. To this end, we study d-wave superconductivity in the checkerboard Hubbard model on a square lattice. We employ the Cellular Dynamical Mean Field theory method with an exact diagonalization solver at zero temperature. The d-wave order parameter is computed for various inhomogeneity levels over the entire doping range of interest. We find a monotonic decrease in the maximum amplitude of the superconducting order parameter with inhomogeneity. However, the order parameter increases with inhomogeneity in a small doping interval lying in the extreme overdoped regime. For any doping, an inhomogeneity-induced change in the height of the lowest energy peak in the antiferromagnetic spin susceptibility correlates with the change in amplitude of the order parameter.