First-principles study on the electronic structure of Pb10−xCux(PO4)6O (x = 0, 1).

• Our work represents the first theoretical study aiming to build the connection between the claimed superconducting properties of LK-99 and its unique flat-band electronic structures. • Our work suggests that the bandwidth of the low-energy flat bands of LK-99 are much smaller than those of other correlated d -band superconductors. • Our work shows that a minimal two-band low-energy effective model should be used for describing the physics of LK-99. • Our work elucidates the effects of electronic correlations and doping on the flat-band electronic structures. • Our calculated results suggest that synthesizing a sample with doped Cu atoms substituted at the Pb1 sites is most likely necessary for obtaining superconductivity, but would be challenging due to its thermodynamic unfavorability. Recently, Lee et al. claimed the experimental discovery of room-temperature ambient-pressure superconductivity in a Cu-doped lead-apatite (LK-99) (arXiv:2307.12008, arXiv:2307.12037). Remarkably, the claimed superconductivity can persist up to 400 K at ambient pressure. Despite the experimental implication, the electronic structure of LK-99 has not yet been studied. Here, we investigate the electronic structures of LK-99 and its parent compound using first-principles calculations, aiming to elucidate the doping effects of Cu. Our results reveal that the parent compound Pb 10 (PO 4) 6 O is an insulator, while Cu doping induces an insulator-metal transition and thus volume contraction. The band structures of LK-99 around the Fermi level are featured by a half-filled flat band and a fully-occupied flat band. These two very flat bands arise from both the 2p orbitals of 1/4-occupied O atoms and the hybridization of the 3d orbitals of Cu with the 2p orbitals of its nearest-neighboring O atoms. Interestingly, we observe four van Hove singularities on these two flat bands. Furthermore, we show that the flat band structures can be tuned by including electronic correlation effects or by doping different elements. We find that among the considered doping elements (Ni, Cu, Zn, Ag, and Au), both Ni and Zn doping result in the gap opening, whereas Au exhibits doping effects more similar to Cu than Ag. Our work establishes a foundation for future studies to investigate the role of unique electronic structures of LK-99 in its claimed superconducting properties. [ABSTRACT FROM AUTHOR]