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

TL;DR

This study identifies simple predictors for the critical temperature in cuprate superconductors by analyzing the role of interactions between effective Wannier orbitals in the $d-p$ 3-band model, revealing key parameters that correlate with $T_c$.

Contribution

It demonstrates that the optimal doping $T_c$ correlates better with parameters in the Wannier orbital basis rather than the real orbital basis, highlighting the importance of effective orbital interactions.

Findings

Predictor variables fit $T_c$ within ±4-5 K.

Effective Wannier orbital parameters better correlate with $T_c$.

Interactions between sublattices influence superconducting properties.

Abstract

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 $\pm4-5$ K and that remarkably depend on the leading attractive coupling constants in the transformed Hamiltonian.