Oxygen hole content,charge-transfer gap,covalency, and cuprate superconductivity

Experiments have shown that the families of cuprate superconductors that have the largest transition temperature at optimal doping also have the largest oxygen hole content at that doping D. Rybicki et al., Nat. Commun. 7, 1–6 (2016)]. They have also shown that a large charge-transfer gap W. Ruan et al., Sci. Bull. (Beijing) 61, 1826–1832 (2016)], a quantity accessible in the normal state, is detrimental to superconductivity. We solve the three-band Hubbard model with cellular dynamical mean-field theory and show that both of these observations follow from the model. Cuprates play a special role among doped charge-transfer insulators of transition metal oxides because copper has the largest covalent bonding with oxygen. Experiments L. Wang et al., arXiv Preprint] (2020). https://arxiv.org/abs/2011.05029 (Accessed 10 November 2020)] also suggest that superexchange is at the origin of superconductivity in cuprates. Our results reveal the consistency of these experiments with the above two experimental findings. Indeed, we show that covalency and a charge-transfer gap lead to an effective short-range superexchange interaction between copper spins that ultimately explains pairing and superconductivity in the three-band Hubbard model of cuprates.

Although several classes of high-temperature superconductors have been discovered, including pnictides, sulfur hydrides, and rare earth hydrides, cuprate high-temperature superconductors are still particularly interesting from a fundamental point of view because of the strong quantum effects expected from their doped charge-transfer insulator nature and single-band spin-one-half Fermi surface (1, 2).Among the most enduring mysteries of cuprate superconductivity is the experimental discovery, early on, that the hole content on oxygen plays a crucial role (2–5). Oxygen hole content (2np) is particularly relevant since NMR (5, 6) suggests a correlation between optimal Tc and 2np on the CuO2 planes: A higher oxygen hole content at the optimal doping of a given family of cuprates leads to a higher critical temperature. This is summarized in figure 2 of ref. 6. The charge-transfer gap also seems to play a central role for the value of Tc, as suggested by scanning tunneling spectroscopy (7) and by theory (8). Many studies have shown that doped holes primarily occupy oxygen orbitals (3, 9–11). This long unexplained role of oxygen hole content and charge-transfer gap on the strength of superconductivity in cuprates is addressed in this paper.The vast theoretical literature on the one-band Hubbard model in the strong-correlation limit shows that many of the qualitative experimental features of cuprate superconductors (12, 13) can be understood (14), but obviously not the above experimental facts regarding oxygen hole content. Furthermore, variational calculations (15) and various Monte Carlo approaches (16, 17) suggest that d-wave superconductivity in the one-band Hubbard model may not be the ground state, at least in certain parameter ranges (18, 19).It is thus important to investigate more realistic models, such as the three-band Emery-VSA (Varma–Schmitt-Rink–Abrahams) model that accounts for copper–oxygen hybridization of the single band that crosses the Fermi surface (20, 21). A variety of theoretical methods (8, 22–27) revealed many similarities with the one-band Hubbard model, but also differences related to the role of oxygen (28, 29).Investigating the causes for the variation of the transition temperature Tc for various cuprates is a key scientific goal of the quantum materials roadmap (30).^* We find and explain the above correlations found in NMR and in scanning tunnelling spectroscopy; highlight the importance of the difference between electron affinity of oxygen and ionization energy of copper (21, 31); and, finally, document how oxygen hole content, charge-transfer gap, and covalency conspire to create an effective superexchange interaction between copper spins that is ultimately responsible for superconductivity.We do not address questions related to intraunit-cell order (32, 33).