Suppression of d-wave superconductivity in the checkerboard Hubbard   model
  Using a dynamical cluster quantum Monte Carlo approximation we investigate the d-wave superconducting transition temperature $T_c$ in the doped 2D repulsive Hubbard model with a weak inhomogeneity. The inhomogeneity is introduced in the hoppings $\tp$ and $t$ in the form of a checkerboard pattern where $t$ is the hopping within a $2\times2$ plaquette and $\tp$ is the hopping between the plaquettes. We find inhomogeneity suppresses $T_c$. The characteristic spin excitation energy and the strength of d-wave pairing interaction decrease with decreasing $T_c$ suggesting a strong correlation between these quantities. 
D. G. S. P. Doluweera, A. Macridin, T. A. Maier, M. Jarrell, Th.   Pruschke