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Recently, Lee et al. reported the experimental discovery of room-temperatureambient-pressure superconductivity in a Cu-doped lead-apatite (LK-99)(arXiv:2307.12008, arXiv:2307.12037). Remarkably, the superconductivitypersists up to 400 K at ambient pressure. Despite strong experimental evidence,the electronic structure of LK-99 has not yet been studied. Here, weinvestigate the electronic structures of LK-99 and its parent compound usingfirst-principles calculations, aiming to elucidate the doping effects of Cu.Our results reveal that the parent compound Pb$_{10}$(PO$_4$)$_6$O is aninsulator, while Cu doping induces an insulator-metal transition and thusvolume contraction. The band structures of LK-99 around the Fermi level arefeatured by a half-filled flat band and a fully-occupied flat band. These twoflat bands arise from both the $2p$ orbitals of $1/4$-occupied O atoms and thehybridization of the $3d$ orbitals of Cu with the $2p$ orbitals of itsnearest-neighboring O atoms. Interestingly, we observe four van Hovesingularities on these two flat bands. Furthermore, we show that the flat bandstructures can be tuned by including electronic correlation effects or bydoping 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 workprovides a foundation for future studies on the role of unique electronicstructures of LK-99 in superconductivity.

First-principles study on the electronic structure of Pb$_{10-x}$Cu$_x$(PO$_4$)$_6$O ($x$=0, 1)