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The pursuit of room-temperature ambient-pressure superconductivity in novelmaterials has sparked interest, with recent reports suggesting such propertiesin Cu-substituted lead apatite, known as LK-99. However, these claims lackcomprehensive experimental and theoretical support. In this study, we addressthis gap by conducting ab initio calculations to explore the impact of varyingdoping concentrations (x = 0, 1, 2) on the stability and electronic propertiesof five compounds in the LK-99 family. Our investigations confirm the isolatedflat bands that intersect the Fermi level in LK-99 (Pb9Cu(PO4)6O:Cu<Pb(1)>). Incontrast, the other four parent compounds exhibit insulating behavior with wideband gaps. X-ray diffraction spectra based on the DFT simulations at 0K confirmthe presence of Cu substitution on Pb(1) sites in the originally synthesizedLK-99 sample, while an extra peak suggests potential alternative likePb8Cu2(PO4)6 phases due to compositional variations in the original LK-99samples. Furthermore, the LK-99 structure undergoes substantial latticeconstriction, resulting in a significant 5.5% reduction in volume and 6.8% inarea of two mutually inverted triangles formed by Pb(2) atoms. Meanwhile,energy calculations reveal a marginal energy preference for substituting Cu onPb(2) sites over Pb(1) sites, with a difference of approximately 0.010 eV peratom (roughly 0.9645 k/mol). Intriguingly, at pressures exceeding 73 GPa,stability shifts towards LK-99 containing Cu substitutions on Pb(1) sites.Despite exhibiting higher electronic conductivity than parent compounds,Pb9Cu(PO4)6O:Cu<Pb(1)> falls short of the conductivity levels observed inmetals or advanced oxide conductors with the simulation based on the Boltzmanntransport theory.

Ab initio Investigations on the Electronic Properties and Stability of  Cu-Substituted Lead Apatite (LK-99) family with different doping  concentrations (x=0, 1, 2)