Renormalization of non-magnetic impurity potential by strong electron correlation is investigated in detail. We adopt the t-t-t-J model and consider mainly a delta-function impurity potential. The variational Monte Carlo method shows that impurity potential scattering matrix elements between Gutzwiller-projected quasi-particle excited states are as strongly renormalized as the hopping terms. Such renormalization is also seen by the Bogoliubov-de Gennes equation with an impurity, where the strong correlation is treated by a Gutzwiller mean-field theory with local Gutzwiller factors and local chemical potentials. Namely, the delta-function potential is effectively weakened and broadened. We emphasize the importance of including the local chemical potential, which is paid little attention to in the literature, by physical consideration of the doping dependence of a local hole density. We also investigate effect of smooth impurity potential variation; the strong correlation yields anticorrelation between the gap energy and the coherence peak height simultaneously with large gap distribution, which is consistent with the experiments.
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