Impact of sulfur doping on copper-substituted lead apatite

Room-temperature superconductivity represents a significant scientific milestone, with the initial report [S. Lee et al., arXiv:2307.12008; arXiv:2307.12037] of LK-99, a copper-substituted lead apatite ${\mathrm{Pb}}_{10\ensuremath{-}x}{\mathrm{Cu}}_{x}{({\mathrm{PO}}_{4})}_{6}\mathrm{O}$, offering a potential breakthrough. However, other researchers have encountered numerous challenges in replicating the original experimental results. In recent studies, Wang et al. [arXiv:2401.00999 and arXiv:2403.11126] successfully observed signs of a possible superconducting phase, such as smaller resistance and stronger diamagnetism, upon doping S into the samples. This indicates that the introduction of S is of significant importance for achieving an appropriate structure. To further investigate the role of S, we have considered ${\mathrm{Pb}}_{10\ensuremath{-}x}{\mathrm{Cu}}_{x}{({\mathrm{PO}}_{4})}_{6}\mathrm{S}$, systematically discussing its thermodynamic stability as well as the influence of S on the distribution, concentration, and electronic properties of Cu. In this paper, we provide valuable insights into the synthesis of potential apatite-based room-temperature superconductors and the role of S in facilitating Cu doping.