Nonmagnetic Impurity Scattering in a $d_{x^2-y^2}$ Superconductor near a Van Hove Point: Zn versus Ni in the Cuprates

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