Electronic structure and vibrational stability of copper-substituted lead apatite LK-99

Two recent preprints [Lee et al., arXiv:2307.12008 and Lee et al., arXiv:2307.12037] have received attention because they claim experimental evidence that a Cu-substituted apatite material (dubbed LK-99) exhibits superconductivity at room temperature and pressure. If this proves to be true, LK-99 will be a holy grail of superconductors. In this work, we use density functional theory $+$ $U$ calculations to elucidate some key features of the electronic structure of LK-99. We find two different phases of this material: (i) a hexagonal lattice featuring metallic half-filled and spin-split bands, nesting of the Fermi surface, and a remarkably large electron-phonon coupling that is vibrationally unstable and (ii) a triclinic lattice, with the Cu and surrounding O distorted. This lattice is vibrationally stable, and its bands correspond to an insulator. In a crystal, the Cu atoms should oscillate between equivalent triclinic positions, with an average close to the hexagonal positions. We discuss the electronic structure expected from these fluctuations and whether it is compatible with superconductivity.