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

TL;DR

This paper critiques prior DFT-based claims about flat bands in copper-doped lead phosphate apatite, showing that the flat band is an artifact of the functional used and that the material is likely an insulator, not a superconductor.

Contribution

The authors demonstrate that the flat band observed in previous DFT studies is an artifact of the functional choice and advocate for using hybrid functionals for accurate predictions.

Findings

Flat band is an artifact of the semilocal DFT functional.

Using hybrid functionals reveals the material is an insulator.

Future studies should employ advanced functionals for accurate results.

Abstract

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.