  The physical properties of high-$T_c$ superconductors are affected by spatial
inhomogeneities introduced by impurities. In addition, superconductivity and
electronic nematicity seem intertwined in these materials. To address these
questions, we apply inhomogeneous cluster dynamical mean field theory to the
study of superconductivity in the Hubbard model, in the presence of a repeated
impurity, at zero temperature. We find that the superconducting phase is
shifted slightly away from half-filling due to the presence of the impurity.
This can be explained by a competition with the Mott insulating phase which
then persists at finite doping. In addition, the impurity triggers the
appearance of spontaneous nematicity. The nematic order parameter follows a
dome shape as a function of doping, similar to that of the superconducting
order parameter, and increases with impurity potential.
