Unusual lattice thermal conductivity in the simple crystalline compounds TlXTe2(X=Ga,In)

It is generally believed that the lattice thermal conductivity in crystalline solids is mainly carried by phonons, whereas diffusons are regarded as the most important vibrational entity in amorphous solids. Contrary to this belief, here we show that the behavior of lattice thermal conductivity (LTC) of simple crystalline $\mathrm{Tl}X\mathrm{T}{\mathrm{e}}_{2}(X=\mathrm{Ga},\mathrm{In})$ compounds cannot be characterized either by phonons or diffusons alone. The calculated LTC based on first-principles density functional theory and the semiclassical Boltzmann transport equation (BTE) is only half of the experimental value. We show that the relatively weak bonding between Tl atoms and rigid $X\mathrm{T}{\mathrm{e}}_{2}$ chains gives rise to strong vibrational anharmonicity, which suppresses the mean free path of a large portion of phonon modes to even below the Ioffe-Regel limit and thus invalidates the precondition of the semiclassical BTE. We further show that the ultralow LTC of $\mathrm{Tl}X\mathrm{T}{\mathrm{e}}_{2}(X=\mathrm{Ga},\mathrm{In})$ can be rationalized by using the two-channel transport model. This finding would enhance the understanding of the underlying heat transport behavior in such materials.