Simple predictors of T_c in superconducting cuprates and the role of interactions between effective Wannier orbitals in the d-p 3-band model

At optimal doping, different cuprate compounds can exhibit vastly different critical temperatures for superconductivity (T_c), ranging from about 20 K 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-p) model for the 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 4-point interactions. We identify multiple predictor variables that fit the experimental T_c to about ±4-5 K and that remarkably depend on the leading attractive coupling constants in the transformed Hamiltonian.