At optimal doping, different cuprate compounds can exhibit vastly different critical temperatures for superconductivity ($T_c$), ranging from about 20 to about 135 K. The precise properties of the lattice that determine the magnitude of the $T_c$ are currently unknown. In this paper, we investigate the dependence of the optimal doping $T_c$ on the parameters of the Emery ($d\text{−}p$) model for the ${\mathrm{CuO}}_2$ planes in the cuprates. We show that the best scaling is obtained not with the parameters of the model written in the real ($d/p$-orbital) space but rather written in the space of effective Wannier orbitals. In this basis, one obtains a model of three sublattices coupled through all possible four-point interactions. We identify multiple predictor variables that fit the experimental $T_c$ to about $\pm 4–5\mathrm{K}$ and that remarkably depend on the leading attractive coupling constants in the transformed Hamiltonian.

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• Superconducting phase transition
• Charge-transfer insulators
• Cuprates
• High-temperature superconductors
• Strongly correlated systems
• Thin films
• Density functional theory
• Lattice models in condensed matter
• Materials modeling
• Methods in superconductivity