Microscopic Hamiltonian for Zn or Ni substituted high temperature cuprate superconductors

TL;DR

This paper derives an effective low-energy Hamiltonian for Zn and Ni substituted high-T_c cuprates, revealing how impurity potentials and hopping influence superconductivity and electronic spectra.

Contribution

It introduces a microscopic Hamiltonian accounting for impurity effects, explaining the different impacts of Zn and Ni on high-T_c superconductors.

Findings

Zn has a strong, attractive scattering potential.

Ni's scattering potential is weaker due to hybridization.

Impurity effects influence superconducting transition temperature and spectra.

Abstract

We have derived the effective low energy Hamiltonian for Zn or Ni substituted high-T_c cuprates from microscopic three-band models consisting of the most relevant Cu or impurity 3d and O 2p orbitals. We find that both scattering potential and hopping integral induced by impurities have a finite range but decay very fast with distance from the impurity. The Zn scattering potential is very strong and attractive for electrons. The Ni scattering potential is much weaker than the Zn case, resulting from the hybridization between Ni ions and O holes. This profound difference is due to neither the electric charge nor d-level location, but rather because of the interplay between the valence state of the impurity and the strong correlation background. It gives a natural account for the unusual effect of Ni and Zn on the reduction of superconducting transition temperature. The interlayer hopping of electrons is highly anisotropic and nonlocal, determined by the in-plane electronic structure. This leads to a quantum interference of states from different sites and affects strongly the scanning tunneling spectrum perpendicular to CuO_2 planes.