Microscopic mechanism of unusual lattice thermal transport in TlInTe₂: Roles of anharmonic renormalization and wave-like tunneling of phonons

TlInTe₂ represents a class of chain-like crystalline semiconductors (InTe, TlSe, TlGaTe₂) that exhibit ultralow lattice thermal conductivity (κ_l).  Here, we investigate the microscopic mechanism of the ultralow-κ_l in TlInTe₂ using an advanced theory of lattice heat transport that considers contributions arising from the particle-like propagation as well as wave-like tunneling of phonons. While we evaluate the former term using the Peierls-Boltzmann transport equation, the latter quantity has been determined by calculating the off-diagonal (OD) components in the heat-flux operator using density functional theory. At each temperature, T, we anharmonically renormalize the phonon frequencies using the self-consistent phonon theory including quartic anharmonicity and utilize them to calculate κ_l. With the combined inclusion of the particle-like and OD contributions, and additional grain boundary scatterings, our calculations successfully reproduce available experimental results. Our analysis shows that the presence of the large quartic anharmonicity (a) strongly hardens the rattling phonon branches, (b) diminishes the three-phonon scattering processes at finite T, and (c) recovers the correct T-dependence of κ_l that deviates from T^-1 behavior found in weakly anharmonic solids.