Non-magnetic impurity scattering in a $d_{x^2 - y^2}$ superconductor near a van Hove point: Zn versus Ni in the cuprates

TL;DR

This paper studies how non-magnetic impurities like Zn and Ni affect a $d_{x^2 - y^2}$ superconductor near a van Hove point, revealing impurity resonances and their impact on residual density of states and critical temperature suppression.

Contribution

It demonstrates that impurity scattering resonances occur at intermediate potentials near a van Hove singularity and explains experimental differences in Zn and Ni doped cuprates.

Findings

Resonant scattering occurs at intermediate impurity potentials.

Residual density of states depends strongly on carrier concentration.

Quantitative agreement with experiments on Zn and Ni doping achieved.

Abstract

We consider the effect of non-magnetic impurities in a $d_{x^2 - y^2}$ superconductor with $\ef$ close to a van Hove singularity. It is shown that the non-trivial density of states (DOS) allows for resonant scattering already at intermediate potential strengths $|u| \approx 1-2$eV. The residual DOS at $\ef$, and the \tc suppression rate are found to strongly depend on the carrier concentration. Quantitative agreement with experiments on Zn and Ni doped cuprates is obtained by adjusting a single parameter, $u$.