Microscopic thermal transport mechanisms in Tl₃VSe₄: lattice phonons or localized oscillators?

Recently, crystalline Tl₃VSe₄ was experimentally reported to exhibit an ultralow lattice thermal conductivity (κ_l) of 0.3±0.05 W/mK at 300 K [Science 360, 1455 (2018)]. Understanding of the underlying thermal transport mechanism has been deemed nontrivial, which requires a complex scenario that involves two channels: lattice phonons and localized oscillators. However, the observed Raman spectra, specific heat, and temperature dependence of κ_l only reveal features characteristic of phonons in an ordered crystalline compound. To resolve this conundrum, we investigate the heat transfer in Tl₃VSe₄ by combining a first-principles density-functional theory based framework of anharmonic lattice dynamics with the Peierls-Boltzmann transport equation for phonons. Specifically, we include contributions of the three- and four-phonon scattering processes to the phonon lifetimes as well as the temperature-dependent anharmonic renormalization of phonon energies. We reveal the dominant thermal transport mechanism by explicitly evaluating both diagonal (particle-like propagation) and off-diagonal (wave-like tunneling) terms of the heat current operator.