Resonance state localized around nonmagnetic impurity with unitarity scattering in two-dimensional d-wave superconductor

Effects of nonmagnetic impurities with unitarity scattering in two-dimensional d-wave superconductors are investigated by the numerical diagonalization of finite-size systems of up to 35 x 35 sites. It is shown that a localized state with almost zero excitation energy is formed around an impurity site if it is isolated. However, its localized state is extended in real space along the direction of the node of the d-wave gap, so that the localized states of adjacent impurities easily interfere with each other forming a kind of impurity band, i.e., resonance states around the zero energy. It is also pointed out that there exists a strong association between the resonance density of states due to impurity scattering in the unitarity limit and the so-called zero-bias anomaly of tunneling conductance.