Generation of Thermodynamically Favorable Crystal Structures of Pb_{10-x}Cu_x(PO4)6O using Atom Combinatorics Approach

Superconductivity, a fascinating quantum state of matter, at room temperature and ambient pressure can find many promising next-generation technological applications such as quantum sensing and quantum computing devices. The ability to enhance the superconducting transition temperature (Tc) by several state-of-the-art design techniques, including the structural modification in materials, has been a long sought-after goal in solid-state physics and materials science. Very 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. Nonetheless, important questions remain unresolved, particularly, understanding 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. We address these relevant questions 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.