Optimizing superconductivity: from cuprates via nickelates to palladates

Motivated by cuprate and nickelate superconductors, we perform a comprehensive study of the superconducting instability in the single-band Hubbard model. We calculate the spectrum and superconducting transition temperature $T_{\mathrm{c}}$ as a function of filling and Coulomb interaction for a range of hopping parameters, using the dynamical vertex approximation. We find the sweet spot for high $T_{\mathrm{c}}$ to be at intermediate coupling, moderate Fermi surface warping, and low hole doping. Combining these results with first principles calculations, neither nickelates nor cuprates are close to this optimum within the single-band description. Instead, we identify some palladates, notably RbSr${}_2$PdO${}_3$ and $A_2^{\mathrm{\prime }}$PdO${}_2$Cl${}_2$ ($A^{\mathrm{\prime }}$=Ba${}_{0.5}$La${}_{0.5}$), to be virtually optimal, while others, such as NdPdO${}_2$, are too weakly correlated.