Substrate and cation engineering for optimizing superconductivity in infinite-layer nickelates

In a recent experiment [Nature 642, 58 (2025)], a new record for the superconducting critical temperature $T_c$ among infinite-layer nickelates has been reported in doped SmNiO$_2$. Here, we use the cutting-edge dynamical vertex approximation (D$\Gamma$A), and qualitatively as well as quantitatively reproduce the $T_c$ vs. doping dome for this compound. Encouraged by this, we go further and identify a path towards realizing even higher $T_c$'s by changing the cation along the line Nd$\rightarrow$Sm$\rightarrow$Y$\rightarrow$Lu with matching substrates. The successively smaller cation radius allows for smaller lattice constants of the substrate. This in turn increases the in-plane hopping and thus eventually $T_c$.