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The physical properties of high-$T_c$ superconductors are affected by spatialinhomogeneities introduced by impurities. In addition, superconductivity andelectronic nematicity seem intertwined in these materials. To address thesequestions, we apply inhomogeneous cluster dynamical mean field theory to thestudy of superconductivity in the Hubbard model, in the presence of a repeatedimpurity, at zero temperature. We find that the superconducting phase isshifted slightly away from half-filling due to the presence of the impurity.This can be explained by a competition with the Mott insulating phase whichthen persists at finite doping. In addition, the impurity triggers theappearance of spontaneous nematicity. The nematic order parameter follows adome shape as a function of doping, similar to that of the superconductingorder parameter, and increases with impurity potential.

Spontaneous nematicity triggered by impurities in a Hubbard model for the cuprates