More explicitly, we focus on the second term of the first digamma function argument in Eq. (1) and start by substituting $\alpha =\hslash /2\tau k_B{T}_{\mathrm{c}0}$ to rewrite as $$\frac{\alpha T_{\mathrm{c}0}}{2\pi T_{\mathrm{c}}}=\frac{\hslash }{4\pi k_B{T}_{\mathrm{c}}\tau }.$$Further substituting the Drude expression for scattering time $1/\tau =({\omega }_{pl}^2/4\pi ){\rho }_0$ into the same term, we get $$\frac{{\rho }_0^G}{T_{\mathrm{c}}}\frac{\hslash {\omega }_{pl}^2}{4\pi k_{B}4\pi },$$where ${\rho }_0^G$ denotes the resistivity in Gaussian CGS units (dimensions of time). For comparison to our experimental measurements, we convert into SI units by $${\rho }_0^G={\rho }_0^{I}4\pi {ϵ}_0,$$where ${\rho }_0^I$ is the resistivity in SI units (dimensions of Ohm meters). Combining the previous two expressions and taking the assumption ${\rho }_0\to \mathrm{\Delta }{\rho }_0$ as discussed in the text, we obtain a simplified digamma argument term $C\mathrm{\Delta }{\rho }_0^I/T_{\mathrm{c}}$, where $$C=\frac{{ϵ}_0\hslash }{4\pi k_B}{\omega }_{pl}^2$$in SI units, with dimensions of Kelvin per resistivity. All resistivities reported within the text are ${\rho }^I$.

From optical measurements of ${\mathrm{Nd}}_{0.8}{\mathrm{Sr}}_{0.2}{\mathrm{NiO}}_2$ films on ${\mathrm{SrTiO}}_3$, Cervasio et al. [61] reported a room-temperature plasma frequency of $\sim 5500{\mathrm{cm}}^{-1}(\hslash {\omega }_{pl}\sim 0.68\mathrm{eV})$, which would correspond to $C\sim 57\mathrm{K}/\mathrm{m}\mathrm{\Omega }·\mathrm{cm}$ in our formulation. Encouragingly, this falls within the same order of magnitude as our fits to S1, though we note several challenges for more precise comparison, which include accounting for sample-to-sample variation with the reported transport data, temperature dependence, and low sensitivity of the fit dependence on $C$.

In an ideal unconventional superconductor with only point defects, the critical mean free path ${\lambda }^{\mathrm{crit}}$ for the appearance of superconductivity provides an estimate of the superconducting coherence length $\xi$. Notwithstanding the concerns about sample-to-sample variation of $\mathrm{\Delta }{\rho }_0$ for a given radiation dose [Fig. 2], one reasonable hypothesis would be to consider the lowest $\mathrm{\Delta }{\rho }_0$ values [Fig. 3] as the closest to the intrinsic values that would result from purely point defect scattering. It is then possible to estimate ${\lambda }^{\mathrm{crit}}$ from $\mathrm{\Delta }{\rho }_0^{\mathrm{crit}}\cong 60\mathrm{\mu \Omega }·\mathrm{cm}$ in sample S1. In a sweeping approximation, we use the 2D expression $\lambda \cong (1/\rho )(hd/(e^2{k}_F))$, where $d$ is the interlayer spacing and $k_F$ the Fermi wave vector, taking $k_F\sim 0.45{\AA }^{-1}$ from recent photoemission experiments [65, 66], considering only the large quasi-two-dimensional Fermi surface and neglecting the electron pockets near the zone corners. The resulting estimate of ${\lambda }^{\mathrm{crit}}\cong \xi \cong 33\AA$ is, therefore, only a rough one, but yields a value for $\xi$ in reasonable agreement with estimates from other measurements [2, 67].