Effects of four-phonon interaction and vacancy defects on the thermal conductivity of the low-temperature phase of SnSe

Tin selenide ($\mathrm{Sn}\mathrm{Se}$) has recently been widely studied due to its ultralow lattice thermal conductivity and excellent thermoelectric properties. However, the thermal conductivity of the low-temperature phase of $\mathrm{Sn}\mathrm{Se}$ is usually overestimated with consideration of only three-phonon scattering processes and the effect of the four-phonon interaction has not been investigated. Meanwhile, it is still unclear how the widely distributed intrinsic vacancy defects, ${V}_{\mathrm{Sn}}$ and ${V}_{\mathrm{Se}}$, affect the lattice thermal conductivity. In this work, using the accurate first-principles-based deep-neural-network potential combined with the phonon Boltzmann transport equation and molecular-dynamics simulations, the lattice thermal conductivity of the low-temperature phase of $\mathrm{Sn}\mathrm{Se}$ is calculated with high-order phonon-scattering processes being considered, and the results match well with the experimental values. In addition, the effect of intrinsic vacancy defects on the thermal conductivity is also investigated using nonequilibrium molecular-dynamics simulations. The results show that the $\mathrm{Se}$ vacancy has a more significant effect on the reduction of the thermal conductivity than the $\mathrm{Sn}$ vacancy, due to the enhanced phonon anharmonicity attributed to the more significant vibration of the weakly bonded $\mathrm{Sn}$ atom, as well as the appreciable inhibition of the low-frequency-phonon propagation speed. The weakening of interactions for the transition of $\mathrm{Sn}$ atoms around vacancies from bonding with $\mathrm{Se}$ atoms to bonding with $\mathrm{Sn}$ atoms is the reason for the decline of the phonon group velocity. This study deepens our understanding of phonon thermal transport in the low-temperature phase of $\mathrm{Sn}\mathrm{Se}$ and provides a good example of using the deep-neural-network potential to explore the effects of the four-phonon interaction and intrinsic point defects on the thermal conductivity of solids.