Recently, Lee et al. claimed the experimental observation of room-temperature ambient-pressure superconductivity in a Cu-doped lead apatite $\left[{\mathrm{Pb}}_{10-x}{\mathrm{Cu}}_x{\left(\mathrm{P}{\mathrm{O}}_4\right)}_6\mathrm{O}\right]$ [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 ${\mathrm{Pb}}_{10}{\left(\mathrm{P}{\mathrm{O}}_4\right)}_6\mathrm{O}$ 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 ${\mathrm{Pb}}_9\mathrm{Cu}{\left(\mathrm{P}{\mathrm{O}}_4\right)}_6\mathrm{O}$, 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.

• Received 31 August 2023
• Revised 3 November 2023
• Accepted 11 December 2023

DOI:https://doi.org/10.1103/PhysRevB.108.224114