https://arxiv.org/abs/2308.08458
Comment on "Origin of correlated isolated flat bands in copper-substituted lead phosphate apatite"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.arxiv.orghttps://arxiv.org/abs/2308.08454
Different phase leads to different transport behavior in Pb$_9$Cu(PO$_4$)$_6$O compoundsThe recent claimed room-temperature superconductivity in Cu-doped lead apatite at ambient pressure are under highly debate. To identify its physical origin, we studied the crystal structures, energy band structures, lattice dynamics 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. Our results show that the Pb$_{10}$(PO$_4$)$_6$O compound is an indirect band gap semiconductor, where Cu doping at the 4$f$ site of Pb leads to a semiconducting to half-metallic transition. Two half-filled flat bands spanning the Fermi energy levels are present in the 4$f$-phase of LK-99, which are mainly formed by 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 the bottom of the conduction band and at the top of the valence band, making the material a bipolar magnetic semiconductor. Our results are basically consistent with the recent experimental transport properties of LK-99 posted on arXiv:2308.05778.arxiv.orghttps://arxiv.org/abs/2308.07941
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 have room-temperature ambient-pressure superconductivity. Here we utilize density functional theory (DFT) total energy and harmonic phonon calculations to investigate the thermodynamic and dynamic stability of two lead phosphate apatites in their pure and Cu-substituted structures. Though Pb$_{10}$(PO$_4$)$_6$O and Pb$_{10}$(PO$_4$)$_6$(OH)$_2$ are found to be thermodynamically stable (i.e., on the T=0K ground state convex hull), their Cu-substituted counterparts are above the convex hull. Harmonic phonon calculations reveal dynamic instabilities in all four of these structures. Oxygen vacancy formation energies demonstrate that the addition of Cu dopant substituting for Pb increases the likelihood of the formation of oxygen vacancies 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 two Pb(1) atoms and the anion oxygen is removed. We also propose several reaction pathways for Pb$_9$Cu(PO$_4$)$_6$O and Pb$_8$Cu$_2$(PO$_4$)$_6$, and found that both of these two structures are likely to be synthesized under a 1:1 ratio of reactants Pb$_2$SO$_5$ and Cu$_3$P. Our work provides a thorough foundation for the thermodynamic and dynamic stabilities of LK-99 related compounds and we propose several possible novel synthesis reaction pathways and a new predicted structure for future studies.arxiv.org
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