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In this comment on "Origin of correlated isolated flat bands incopper-substituted lead phosphate apatite" (arXiv:2307.16892[cond-mat.supr-con]), we discuss the flat half-occupied two-band manifold thatappears in $\mathrm{Pb}_9\mathrm{Cu}(\mathrm{PO}_4)_6(\mathrm{OH})_2$ whenusing a semilocal DFT functional. We argue that the flat band is an artifact ofthe functional's overestimation of the energy of the oxygen p states in thevalence band. When using the HSE hybrid functional, the energy of the oxygen pstates is reduced, and the copper-derived manifold splits into one fullyoccupied and one empty band. While these results do not rule out thepossibility of superconductivity in doped LK-99, they do predict thatstoichiometric $\mathrm{Pb}_9\mathrm{Cu}(\mathrm{PO}_4)_6(\mathrm{OH})_2$ is aninsulator, not a superconductor. Furthermore, we have shown that futurefirst-principles studies of these materials should employ hybrid functionals orother advanced methods to ensure that the oxygen-derived valence-band energiesare correctly described.

Comment on "Origin of correlated isolated flat bands in copper-substituted lead phosphate apatite"