Interplay of quantum magnetic and potential scattering around Zn or Ni impurity ions in superconducting cuprates

To describe the scattering of superconducting quasiparticles from nonmagnetic (Zn) or magnetic (Ni) impurities in optimally doped high Tc cuprates, we propose an effective Anderson model Hamiltonian of a localized electron hybridizing with dx2−y2-wave BCS type superconducting quasiparticles with an attractive scalar potential at the impurity site. Due to the strong local antiferromagnetic couplings between the original Cu ions and their nearest neighbors, the localized electron in the Ni-doped materials is assumed to be on the impurity sites, while in the Zn-doped materials the localized electron is distributed over the four nearest neighbor sites of the impurities with a dominant dx2−y2 symmetric form of the wave function. Since both scatterings from the localized electron and the scalar potential are relevant, localized resonant states due to their interplay are formed below the maximal superconducting gap. With Ni impurities, two resonant states are formed above the Fermi level in the local density of states at the impurity site, while for Zn impurities a sharp resonant peak below the Fermi level dominates in the local density of states at the Zn site, accompanied by a small and broad reso-