Controllable suppression of the unconventional superconductivity in bulk and thin-film Sr$_2$RuO$_4$ via high-energy electron irradiation

In bulk Sr$_2$ RuO$_4$, the strong sensitivity of the superconducting transition temperature 𝑇c to nonmagnetic impurities provides robust evidence for a superconducting order parameter that changes sign around the Fermi surface. In superconducting epitaxial thin-film Sr$_2$ RuO$_4$, the relationship between 𝑇c and the residual resistivity 𝜌0, which in bulk samples is taken to be a proxy for the low-temperature elastic scattering rate, is far less clear. Using high-energy electron irradiation to controllably introduce point disorder into bulk single-crystal and thin-film Sr$_2$ RuO$_4$, we show that 𝑇c is suppressed in both systems at nearly identical rates. This suggests that part of 𝜌0 in films comes from defects that do not contribute to superconducting pairbreaking and establishes a quantitative link between the superconductivity of bulk and thin-film samples.