Thermal conductivity of solids from lattice dynamics

Heat transport is a fundamental process underlying both natural phenomena and technological advancements.In semiconductors and insulators, where heat is primarily carried by lattice vibrations, the lattice thermal conductivity ( L ) plays a crucial role in governing thermal transport.Lattice dynamics provides a robust theoretical framework for calculating L , with different approaches tailored to the structural and morphological characteristics of materials.Solids can be broadly classified into crystals, glasses, and partially disordered solids, with a continuous crossover between these categories (see Figure 1).In crystalline semiconductors and insulators, heat is primarily carried by phonons.The phonongas model (PGM), introduced by Peierls in 1929, reliably predicts L in simple crystals, ranging from 1000 W/mK for boron arsenide to 0.9 W/mK for silver chloride at 300 K.In glasses, strong atomic disorder breaks down the phonon definition, making the PGM unsuitable for computing glassy L .To address this, Allen and Feldman [1] proposed the AF model in 1993, which describes the glassy heat transport in harmonic glasses through Zener-like tunneling between quasi-degenerate vibrational eigenstates.However, exceptions to these models exist.In certain complex crystals with glass-like heat conduction, such as Tl 3 VSe 4 [2], severe phonon scattering reduces the phonon mean free path below the minimum interatomic spacing, significantly limiting phonon propagation.As a result, L of Tl 3 VSe 4 computed using the PGM substantially underestimates experimental results [2].Moreover, the transition from crystals to glasses is nonsharp, with partially disordered materials [3] occupying an intermediate regime where heat transport cannot be accurately described by either the PGM or the AF model.In 2019, Simoncelli et al. [4] introduced the Wigner transport equation (WTE) to describe heat conduction in solids, incorporating both intraband propagation ( P ) and interband coherence ( C ) via Zener-like tunneling.This framework unifies particle-like phonon propagation (dominant in crystals) and wavelike phonon coherence (dominant in glasses), and the overall L is the summation of P and C .Later, Isaeva et al. [5] developed the Quasi-harmonic Green-Kubo theory (QHGK), which is