Recently, above-room-temperature superconductivity was reported in the Cu-doped lead apatite ${\mathrm{Pb}}_{10-x}{\mathrm{Cu}}_x{\left({\mathrm{PO}}_4\right)}_6\mathrm{O}$, dubbed LK-99. By relaxing the structure with Cu substitution, we derive a four-band low-energy model with two 3/4 filled bands of predominantly $\mathrm{Cu}\text{−}{d}_{xz,yz}$ character and two filled $\mathrm{O}\text{−}{p}_{x,y}$ bands. This model is further downfolded to a two-band $\mathrm{Cu}\text{−}{d}_{xz/yz}$ model. Using ab initio derived interaction parameters, we perform dynamical mean-field theory calculations to determine the correlated electronic structure in the normal state. These calculations yield a Mott insulator at $x=1$ and a strongly correlated non-Fermi-liquid metal upon doping. The very large interaction versus bandwidth ratio $U/W\approx 30-50$ and the local moment paramagnetic behavior in the relevant filling regime are hard to reconcile with diamagnetism and high-temperature superconductivity. Our calculations suggest that this behavior comes from a component with a different stoichiometry.

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• Meissner effect
• Superconducting gap
• Superconducting phase transition
• High-temperature superconductors
• Mott insulators
• Strongly correlated systems
• DC susceptibility measurements
• Density functional calculations
• Dynamical mean field theory
• Electron-correlation calculations
• Hubbard model
• Random phase approximation