We present results of investigations on the correlated nature of electronic states crossing the Fermi level in ${\mathrm{Pb}}_9\mathrm{Cu}{\left({\mathrm{PO}}_4\right)}_6\mathrm{O}$ (also referred to as LK-99) obtained within the $\mathrm{DFT}+\mathrm{DMFT}$ approach. We found that the band structure in the vicinity of the Fermi level is formed by extremely narrow $\mathrm{Cu}d$ states and $p$ states of extra O weakly hybridized with each other. Coulomb correlations between $\mathrm{Cu}d$ electrons open the band gap between Cu $d_{xz}/d_{yz}$ and the extra-O $p$ states that form the top of the valence band. Our conclusion is that the extra-oxygen $p$ states play a significant role in the electronic properties and LK-99 cannot be mapped onto a two-band Hubbard model. We also conclude that doping with electrons will turn the stoichiometric ${\mathrm{Pb}}_9\mathrm{Cu}{\left({\mathrm{PO}}_4\right)}_6\mathrm{O}$ into a metal, whereas the result of doping with holes is less certain.

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• Band gap
• Superconductivity
• DFT+DMFT
• Density functional theory
• Quantum Monte Carlo
• Wannier function methods