Antibonding or Nonbonding Interaction-Driven Phonon Modes Softening and Wave-like Interband Thermal Conduction in Layered In₄Te₃ under the Framework of Wigner Transport Formalism

In 4 Te 3, a p -type analogue of n -type In 4 Se 3, exhibits anomalous thermal conductivity (κ L ). The value of κ L is intrinsically very low, 0.7 W m –1 K –1 at 300 K, and it is weakly temperature ( T )-dependent, which deviates from the conventional κ L ∝ T –1 variation. Thus, In 4 Te 3 finds its application as a thermoelectric material in the midtemperature range. Here, employing a completely ab initio-based DFT framework, three-phonon scattering process, and Wigner transport equation, we found that In 4 Te 3 exhibits strong anharmonicity in the acoustic region as well as the low energy optical region. The mean free path already reached the “ Ioffe-Regel limit ” in space even at a low T which is consistent with low κ L . The anharmonicity arises due to the antibonding and nonbonding overlap of In4 valence electrons with its neighbors. Such a weak bond formation capability of In4 has very low interatomic force constants, which results in overall low elastic properties, viz. sound velocity (1947.24 m s –1 ), Debye temperature (184 K), Young’s modulus (51.56 GPa), etc., indicating considerable amount of lattice softening. Interestingly, those softened Einstein-like modes at ∼0.72 THz form overlapped phonon bands and promote their wave-like tunneling. Even at low T (50 K), the line-widths of the individual modes are still larger than their interband spacing, which lowers their particle-like propagation but enhances wave-like tunneling, eventually leading to the dual particle-wave behavior of the heat carrying phonons. At high T, the intrinsic phonon–phonon interaction dominates and the calculated three-phonon scattering time lies between the “ Wigner ” and “ Ioffe-Regel limits ” in time which manifests nonstandard wave-like thermal conductivity in the system.