Simple predictors of Tc in superconducting cuprates and the role of interactions between effective Wannier orbitals in the d-p three-band model

At optimal doping, different cuprate compounds can exhibit vastly different critical temperatures for superconductivity (Tc), ranging from about 20 to about 135 K. The precise properties of the lattice that determine the magnitude of the Tc are currently unknown. In this paper, we investigate the dependence of the optimal doping Tc on the parameters of the Emery (d-p) model for the CuO2 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 Tc to about ±4-5K and that remarkably depend on the leading attractive coupling constants in the transformed Hamiltonian.