Materials with ultralow lattice thermal conductivity (LTC) are of fundamental and technological importance for thermal management and thermoelectric energy conversion, yet identifying crystalline solids that intrinsically suppress heat transport remains challenging. Here, we present a comprehensive first-principles investigation of lattice thermal transport in the tetragonal chalcogenides ${\text{Tl}}_2{\text{CdSnTe}}_4$, ${\text{Tl}}_2{\text{CdGeTe}}_4$, and ${\text{Tl}}_2{\text{HgSnSe}}_4$. By integrating temperature-dependent effective potential theory, anharmonic phonon renormalization, four-phonon scattering, and the multichannel transport formalism, we predict exceptionally low in-plane LTC values of 0.32, 0.30, and $0.29\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$ at 300 K, placing these materials among the lowest reported for bulk inorganic crystals. The ultralow thermal transport originates from pronounced rattling dynamics of Tl atoms, which induce localization of low-frequency vibrational modes and strongly suppress heat-carrying acoustic phonons. Beyond conventional particlelike transport, coherent contributions become increasingly important at elevated temperatures, leading to a weak temperature dependence of LTC. We further show that tensile strain enhances anharmonicity and reduces LTC, while mass perturbation via isovalent substitution yields additional suppression through enhanced phonon scattering, reaching $0.16\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$ under 1% strain. These results establish Tl-based chalcogenides as a promising class of intrinsically ultralow-LTC materials and highlight the effectiveness of combining heavy-atom rattling, strain, and compositional tuning for phonon engineering in these materials.

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• Lattice dynamics
• Lattice thermal conductivity
• Boltzmann theory
• Density functional calculations