Influence of four-phonon scattering and wavelike phonon tunneling effects on the thermal transport properties of TlBiSe2

${\mathrm{TlBiSe}}_{2}$ is considered a potential thermoelectric material due to its ultralow lattice thermal conductivity ${\ensuremath{\kappa}}_{\mathrm{L}}$ and excellent electrical properties. However, previous studies on the thermal properties of ${\mathrm{TlBiSe}}_{2}$ only considered the effects of three-phonon scattering, which resulted in significant differences between theoretical and experimental values. In this material, four-phonon scattering processes mainly reduce the thermal transport of acoustic phonons, resulting in an approximate 28% reduction in particlelike thermal conductivity ${\ensuremath{\kappa}}_{\mathrm{p}}$ at 300 K. The high-frequency optical branches are dense and the phonon lifetime is short, making it easy to generate wavelike phonon tunneling. After considering wavelike thermal conductivity ${\ensuremath{\kappa}}_{\mathrm{c}}$, ${\ensuremath{\kappa}}_{\mathrm{L}}$ along the in-plane direction is in good agreement with the experimental values. A nonstandard ${\ensuremath{\kappa}}_{\mathrm{L}}\ensuremath{\propto}{\mathrm{T}}^{\ensuremath{-}0.36}$ dependence is revealed in the cross-plane direction. At high temperatures, ${\ensuremath{\kappa}}_{\mathrm{c}}$ in the cross-plane direction is greater than ${\ensuremath{\kappa}}_{\mathrm{p}}$ and ${\ensuremath{\kappa}}_{\mathrm{c}}$ dominates the thermal transport with 61% of ${\ensuremath{\kappa}}_{L}$ at 700 K. In addition to the frequency difference of the phonon pairs, the interbranch phonon group velocity also has an important effect on ${\ensuremath{\kappa}}_{\mathrm{c}}$. Our work improves the calculational accuracy of thermal conductivity for ${\mathrm{TlBiSe}}_{2}$ and broadens the field for application of ternary-layered thallium-based semiconductors.