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

Different phase leads to different transport behavior in Pb$_9$Cu(PO$_4$)$_6$O compoundsThe recent claimed room-temperature superconductivity in Cu-doped leadapatite at ambient pressure are under highly debate. To identify its physicalorigin, we studied the crystal structures, energy band structures, latticedynamics and magnetic properties of the parent Pb$_{10}$(PO$_4$)$_6$O compound,in which two different phases of the LK-99 compound are analyzed in detail. Ourresults show that the Pb$_{10}$(PO$_4$)$_6$O compound is an indirect band gapsemiconductor, where Cu doping at the 4$f$ site of Pb leads to a semiconductingto half-metallic transition. Two half-filled flat bands spanning the Fermienergy levels are present in the 4$f$-phase of LK-99, which are mainly formedby hybridization of the $d_{x^2-y^2}$ and $d_{zy}$ orbitals of Cu with the 2$p$orbitals of O. In addition, 6$h$-phase of LK-99 always has spin polarity at thebottom of the conduction band and at the top of the valence band, making thematerial a bipolar magnetic semiconductor. Our results are basically consistentwith the recent experimental transport properties of LK-99 posted onarXiv:2308.05778.arxiv.org

Phase Stability of Lead Phosphate Apatite Pb$_{10-x}$Cu$_{x}$(PO$_{4}$)$_{6}$O, Pb$_{10-x}$Cu$_{x}$(PO$_{4}$)$_{6}$(OH)$_{2}$, and Pb$_{8}$Cu$_{2}$(PO$_{4}$)$_{6}$Recently, Cu-substituted lead apatite LK-99 was reported to haveroom-temperature ambient-pressure superconductivity. Here we utilize densityfunctional theory (DFT) total energy and harmonic phonon calculations toinvestigate the thermodynamic and dynamic stability of two lead phosphateapatites in their pure and Cu-substituted structures. ThoughPb$_{10}$(PO$_4$)$_6$O and Pb$_{10}$(PO$_4$)$_6$(OH)$_2$ are found to bethermodynamically stable (i.e., on the T=0K ground state convex hull), theirCu-substituted counterparts are above the convex hull. Harmonic phononcalculations reveal dynamic instabilities in all four of these structures.Oxygen vacancy formation energies demonstrate that the addition of Cu dopantsubstituting for Pb increases the likelihood of the formation of oxygenvacancies on the anion site. We propose a new possible phase in this system,Pb$_8$Cu$_2$(PO$_4$)$_6$, where two monovalent Cu atoms are substituted for twoPb(1) atoms and the anion oxygen is removed. We also propose several reactionpathways for Pb$_9$Cu(PO$_4$)$_6$O and Pb$_8$Cu$_2$(PO$_4$)$_6$, and found thatboth of these two structures are likely to be synthesized under a 1:1 ratio ofreactants Pb$_2$SO$_5$ and Cu$_3$P. Our work provides a thorough foundation forthe thermodynamic and dynamic stabilities of LK-99 related compounds and wepropose several possible novel synthesis reaction pathways and a new predictedstructure for future studies.arxiv.org


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