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The most recent discovery, the Cu-doped lead apatite LK-99, is a proposedroom-temperature superconductor operating under ambient pressure. However, thisdiscovery has brought a slew of conflicting results from different scientificgroups. While some observed the absence of electrical resistance, others couldnot confirm any signs of superconductivity in LK-99. Here, we investigate thestructural and electronic properties of LK-99 and its antecedent compoundsthrough quantum mechanics (QM) and QM-based molecular dynamics (QM-MD)simulations. Our study elucidates the insulating nature of base compounds,Pb$_{10}$(PO$_4$)$_6$O and Pb$_{10}$(PO$_4$)$_6$(OH)$_2$, spotlighting theirlarge band gaps. Notably, Cu doping in LK-99 disrupts its symmetry, yielding adistorted ground-state crystal structure with a triclinic P1 symmetry andCuO$_4$ square coordination. Such alterations predispose LK-99 to exhibitsemiconducting behaviors, characterized by a flat band above the Fermi energy,arising from Cu-3d and O-2p orbitals. In addition, the S doping sustains thetriclinic P1 symmetry but leads to a significantly reduced band gap, with aband emerging primarily from Cu-3d and S-3p orbitals. These findings areimportant in understanding LK-99's structural and electronic properties andprovide a strategic compass for the development of high-T$_C$ superconductors.

Deciphering the Enigma of Cu-Doped Lead Apatite (LK-99): Structural  Insights, Electronic Properties, and Implications for Ambient-Pressure  Superconductivity