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The recent report of superconductivity in the Cu-doped PbPO compoundstimulates the extensive researches on its physical properties. Herein, thedetailed atomic and electronic structures of this compound are investigated,which are the necessary information to explain the physical properties,including possible superconductivity. By the first-principles electronicstructure calculations, we find that the partial replacement of Pb at $4f$ siteby Cu atom, instead of Pb at $6h$ site, plays a crucial role in dominating theelectronic state at Fermi energy. The $3d$ electronic orbitals of Cu atomemerge near the Fermi energy and exhibit strong spin-polarization, resulting inthe local moment around the doped Cu atom. Particularly, the ground state ofPb$_{10-x}$Cu$_x$(PO$_4$)$_6$O (x = 1) is determined to be a semiconductingphase, in good agreement with the experimental measurements.

Structural, electronic, magnetic properties of Cu-doped lead-apatite Pb$_{10-x}$Cu$_x$(PO$_4$)$_6$O