Electronic structure of the putative room-temperature superconductor Pb9Cu(PO4)6O

A recent paper [Lee et al., J. Kor. Cryst. Growth Cryst. Technol. 33, 61 (2023)] provides some experimental indications that ${\mathrm{Pb}}_{10\ensuremath{-}x}{\mathrm{Cu}}_{x}{({\mathrm{PO}}_{4})}_{6}\mathrm{O}$ with $x\ensuremath{\approx}1$, coined LK-99, might be a room-temperature superconductor at ambient pressure. Our density-functional theory (DFT) calculations show lattice parameters and a volume contraction with $x$, very similar to experiment. The DFT electronic structure shows ${\mathrm{Cu}}^{2+}$ in a $3{d}^{9}$ configuration with two flat Cu bands crossing the Fermi energy. This puts ${\mathrm{Pb}}_{9}\mathrm{Cu}{({\mathrm{PO}}_{4})}_{6}\mathrm{O}$ in an ultracorrelated regime and suggests that, without doping, it is a Mott or charge-transfer insulator. If doped, such an electronic structure might support flat-band superconductivity or a correlation-enhanced electron-phonon mechanism, whereas a diamagnet without superconductivity appears to be rather at odds with our results.