Importance of effective Coulomb interactions for $T_c$ in cuprates

Abstract

Cuprate superconductors exhibit the highest observed superconducting $T_c$ at atmospheric pressure. However, the magnitude of $T_c$ varies significantly between different cuprates. At present, it is unclear what properties of the crystal structure affect $T_c$ most strongly, yet such an understanding must underpin any efforts toward high-$T_c$ materials design. To address this issue, we perform a large scale systematic study, employing a combination of data collection, state-of-the-art numerical methods, and statistical analysis. We identify about 40 different cuprate compounds, and we compile detailed data about their $T_c$'s and crystal structures from literature and the available databases. Using a fully automated procedure, for each compound we compute the DFT bandstructure and downfold it to two of the most commonly studied low-energy lattice models, namely the single-band Hubbard and the three-band Emery models. The downfolding is based on the approach of MLWFs and cRPA. Finally, we apply a thorough and unbiased statistical analysis to investigate the correlations between the experimentally measured $T_c$'s and the computed parameters of our theoretical models. Our data indicates that more sophisticated models might be needed to describe all cuprates on the same footing. Nevertheless, we find that $T_c$ scales well with simple functions of model parameters. We confirm a previously observed trend that $t'$ in the single-band model correlates with the experimental $T_c$, and we find that $T_c$ appears to vanish below a finite value of $t'$, in agreement with recent ground-state calculations for the Hubbard model. However, we find that the coupling strength also plays a role: throughout our entire dataset, $T_c$ correlates the most with the Coulomb coupling on the $p$-orbitals in the 3-band model, highlighting the importance of the oxygen sites in the copper-oxide planes.