Pressure-induced one-dimensional oxygen ion diffusion channel in lead apatite

Recently, Lee et al. claimed the experimental observation of room-temperature ambient-pressure superconductivity in a Cu-doped lead apatite $[{\mathrm{Pb}}_{10\ensuremath{-}x}{\mathrm{Cu}}_{x}{(\mathrm{P}{\mathrm{O}}_{4})}_{6}\mathrm{O}]$ [S. Lee et al., arXiv:2307.12008 and arXiv:2307.12037]. The study revealed the Cu doping induces a chemical pressure, resulting in a structural contraction of one-dimensional Cu-O-Cu atomic column. This unique structure promotes a one-dimensional electronic conduction channel along the $c$ axis mediated by the O atoms, which may be related to superconductivity. These O atoms occupy 1/4 of the equivalent positions along the $c$ axis and exhibit a low diffusion activation energy of 0.8 eV, indicating the possibility of diffusion between these equivalent positions. Here, using a machine-learning based deep potential, we predict the pressure-induced fast diffusion of 1/4-occupied O atoms along the one-dimensional channel in ${\mathrm{Pb}}_{10}{(\mathrm{P}{\mathrm{O}}_{4})}_{6}\mathrm{O}$ at 500 K, while the frameworks of Pb triangles and $\mathrm{P}{\mathrm{O}}_{4}$ tetrahedra remain stable. The calculation results also indicate Cu doping can provide appropriate effective chemical pressure, indicating the one-dimensional ion diffusion channel may appear in ${\mathrm{Pb}}_{9}\mathrm{Cu}{(\mathrm{P}{\mathrm{O}}_{4})}_{6}\mathrm{O}$, even at ambient pressure. Our finding shows that the one-dimensional ion diffusion channel may be an important factor to affect the fabrication and electrical measurement of doped lead apatite.