Comparative Assessment of Thermal Transport Theories: Dual-Channel Mechanism Dictates Heat Transport in Ultralow-$\kappa$ Materials

Abstract

Anomalous heat transport in strongly anharmonic crystalline solids poses both a fundamental challenge to the theoretical understanding and an opportunity for thermoelectric and thermal barrier coating applications. Although Green-Kubo theory reproduces experimental thermal conductivity ($\kappa$) at high temperatures, it lacks microscopic insight and neglects the Bose-Einstein statistics of lattice vibrations. On the other hand, the conventional Boltzmann transport equation (BTE) framework, based on a phonon-gas picture, fails due to strong anharmonicity-induced overdamped phonons. Herein, the thermal transport properties in TlAgSe, a metal chalcogenide, and Cs$_2$PbI$_2$C$_2$, an all-inorganic layered Ruddlesden-Popper perovskite, are investigated by explicitly accounting for temperature-dependent lattice dynamics through machine learning interatomic potentials and employing the Wigner transport equation (WTE) framework. Crucially, heat conduction is governed not only by higher-order phonon scattering-dominated populations'transport channel described within the BTE, but also by a coherences'channel in the WTE framework arising from wave-like interbranch coherence between eigenstates. Incorporating four-phonon scattering, WTE predicts average room-temperature $\kappa$ values of 0.31 Wm$^{-1}$K$^{-1}$ (TlAgSe) and 0.38 Wm$^{-1}$K$^{-1}$ (Cs$_2$PbI$_2$C$_2$), in excellent agreement with experiments. Phonon scattering-rate analysis reveals strong coherences'contributions and prevalent overdamped phonon modes, demonstrating the breakdown of the conventional BTE framework based on the phonon quasiparticle picture with only first-order anharmonic perturbation. This computational approach provides a unified description of heat transport in ultralow-$\kappa$ materials, offering a basis for the rational design of phononic and thermoelectric devices.