Inpurity-induced states in inhomogeneous superconductivity in high-T _c cuprates

Quasiparticle states around a nonmagnetic impurity in inhomogeneous superconducting states observed in high-T_c cuprates are studied using a two-dimensional t-J type model. The spatial dependences of the superconducting order parameters are determined within the Bogoliubov-de Gennes theory based on the Gutzwiller approximation. We show that a peak structure is found in the local density of states around the impurity in the large gap regions of the inhomogeneous superconducting states, which has not been experimentally observed yet. Our results suggest that a competing order is realized in the large gap regions in high-T_c cuprates.