Extremely Strong Dependence of Superconductivity on Disorder in ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$

A key signature of unconventional or non- $s$-wave superconductivity is a strong suppression of $T_c$ by nonmagnetic as well as by magnetic impurities. We report measurements of chemical composition and of transport properties in the same single crystals of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ which show that nonmagnetic impurities destroy superconductivity when the residual resistivity exceeds $1\mu \Omega \mathrm{cm}$, i.e., when the carrier mean free path falls below the superconducting coherence length. This behavior strongly supports models of non- $s$-wave (e.g., $p$- or $d$-wave) pairing in this layered perovskite oxide.