Microscopic mechanism of unusual lattice thermal transport in TlInTe$_2$
We investigate the microscopic mechanism of ultralow lattice thermal conductivity ($\kappa_l$) of TlInTe$_2$ and its weak temperature dependence using a unified theory of lattice heat transport that considers contributions arising from the particle-like propagation as well as wave-like tunneling of phonons. While we use the Peierls-Boltzmann transport equation (PBTE) to calculate the particle-like contributions ($\kappa_l$(PBTE)), we explicitly calculate the off-diagonal (OD) components of the heat-flux operator within a first-principles density functional theory framework to determine the contributions ($\kappa_l$(OD)) arising from the wave-like tunneling of phonons. At each temperature, T, we anharmonically renormalize the phonon frequencies using the self-consistent phonon theory including quartic anharmonicity, and utilize them to calculate $\kappa_l$(PBTE) and $\kappa_l$(OD). With the combined inclusion of $\kappa_l$(PBTE), $\kappa_l$(OD), and additional grain-boundary scatterings, our calculations successfully reproduce the experimental results. Our analysis shows that large quartic anharmonicity of TlInTe$_2$ (a) strongly hardens the low-energy phonon branches, (b) diminishes the three-phonon scattering processes at finite T, and (c) recovers the weaker than T$^{-1}$ decay of the measured $\kappa_l$.