Machine learning for predicting ultralow thermal conductivity and high ZT in complex thermoelectric materials

Efficient and precise calculations of thermal transport properties and figure of merit, alongside a deep comprehension of thermal transport mechanisms, are essential for the practical utilization of advanced thermoelectric materials. In this study, we explore the microscopic processes governing thermal transport in the distinguished crystalline material Tl$_9$SbTe$_6$ by integrating a unified thermal transport theory with machine learning-assisted self-consistent phonon calculations. Leveraging machine learning potentials, we expedite the analysis of phonon energy shifts, higher-order scattering mechanisms, and thermal conductivity arising from various contributing factors like population and coherence channels. Our finding unveils an exceptionally low thermal conductivity of 0.31 W m$^{-1}$ K$^{-1}$ at room temperature, a result that closely correlates with experimental observations. Notably, we observe that the off-diagonal terms of heat flux operators play a significant role in shaping the overall lattice thermal conductivity of Tl$_9$SbTe$_6$, where the ultralow thermal conductivity resembles that of glass due to limited group velocities. Furthermore, we achieve a maximum $ZT$ value of 3.17 in the $c$-axis orientation for \textit{p}-type Tl$_9$SbTe$_6$ at 600 K, and an optimal $ZT$ value of 2.26 in the $a$-axis and $b$-axis direction for \textit{n}-type Tl$_9$SbTe$_6$ at 500 K. The crystalline Tl$_9$SbTe$_6$ not only showcases remarkable thermal insulation but also demonstrates impressive electrical properties owing to the dual-degeneracy phenomenon within its valence band. These results not only elucidate the underlying reasons for the exceptional thermoelectric performance of Tl$_9$SbTe$_6$ but also suggest potential avenues for further experimental exploration.