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