Recent STM measurements have observed many inhomogeneous patterns of the local density of states on the surface of high-T_c cuprates. As a first step to study such disordered strong correlated systems, we use the BdG equation for the t-t-t-J model with an impurity. The impurity is taken into account by a local potential or local variation of the hopping/exchange terms. Strong correlation is treated by a Gutzwiller mean-field theory with local Gutzwiller factors and local chemical potentials. It turned out that the potential impurity scattering is greatly suppressed, while the local variation of hoppings/exchanges is enhanced.
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