Atomistic origin of low thermal conductivity in quaternary chalcogenides Cu(Cd, Zn)₂InTe₄

Crystalline semiconductors with intrinsically low lattice thermal conductivity $mathcal{K}$ are vital for device applications such as barrier coatings and thermoelectrics. Quaternary chalcogenide semiconductors such as CuCd₂InTe₄ and CuZn₂InTe₄ are experimentally shown to exhibit low mathcal{K}, yet its microscopic origin remains poorly understood. Here, we analyse their thermal transport mechanisms using a unified first-principles framework that captures both the Peierls particle-like propagation, $mathcal{K}_P$ and coherence wave-like tunneling, $mathcal{K}_C$ mechanisms of phonon transport. We show that extended antibonding states below the Fermi level lead to enhanced phonon anharmonicity and strong scattering of heat-carrying phonon modes, suppressing mathcal{K} in these chalcogenides. We show that mathcal{K}_P dominates the total thermal conductivity, while mathcal{K}_C remains negligible even under strong anharmonicity of the phonon modes. The heavier Cd ions in CuCd₂InTe₄ induce greater acoustic-optical phonon overlap and scattering compared to CuZn₂InTe₄, further lowering thermal conductivity of the former. Additionally, grain boundary scattering in realistic samples contributes to further suppression of thermal transport. Our findings establish the atomistic origins of low mathcal{K} in quaternary chalcogenides and offer guiding principles for designing low-thermal-conductivity semiconductors.