  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.
