First Principles Study of Structures and Electronic Properties of Pb_(10-x)Cu_x(PO₄)₆O

Recently, the experimental realization of potential room-temperature ambient-pressure superconductivity was reported for Cu-substituted lead apatite, Pb_(10-x)Cu_x(PO₄)₆O (x~0.9-1.0), so-called LK-99 material. However, the superconductivity in this material is in question and some relevant questions remain unresolved such as how the arrangements of substituted Cu on Pb sites in the LK-99 structure would minimize system's energy and might affect its electronic structure. In this work, we address these questions to some extent by enumerating possible configurations of Cu in Pb_(10-x)Cu_x(PO₄)₆O at 10% Cu substitution and performing density functional theory with Hubbard U correction (DFT+U) calculations of structural and electronic properties of selected configurations. We find that for (1x1x2) supercell, the most energetically favorable substitution sites are the nearest Pb(1) and Pb(2). The partially filled electronic state calculated at the Brillouin zone center is spatially localized around the Cu atom. For the low-energy configuration of single Cu substitution, we find that one electronic band is very flat with a narrow bandwidth of ~0.06 eV. The bands degeneracy at Γ and A high-symmetry points that is observed for a higher-energy configuration with one Cu substitution, disappears when two Cu atoms form a local dimer in a distorted LK-99 structure.