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

TL;DR

This paper models how non-magnetic and magnetic impurities like Zn and Ni affect quasiparticle scattering in high-temperature cuprate superconductors, matching experimental STM data.

Contribution

It introduces an effective Anderson model capturing impurity scattering effects with specific localized electron distributions for Zn and Ni in cuprates.

Findings

Ni impurities produce two resonant states above Fermi level.

Zn impurities create a sharp resonant peak below Fermi level.

Results agree with STM observations in Bi2212 with Zn or Ni impurities.

Abstract

To describe the scattering of superconducting quasiparticles from non-magnetic (Zn) or magnetic (Ni) impurities in optimally doped high T$_c$ cuprates, we propose an effective Anderson model Hamiltonian of a localized electron hybridizing with $d_{x^2-y^2}$-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 $d_{x^2-y^2}$ symmetric form of the wave function. 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 resonant state above the Fermi level mainly induced by the potential scattering. In both cases, there are no Kondo screening effects. The local density of states and their spatial distribution at the dominant resonant energy around the substituted impurities are calculated for both cases, and they are in good agreement with the experimental results of scanning tunneling microscopy in Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ with Zn or Ni impurities, respectively.