Ab initio investigation of thermal transport in insulators: Unveiling the roles of phonon renormalization and higher-order anharmonicity
Description
The occurrence of thermal transport phenomena is widespread in nature and plays a pivotal role in the functionality of diverse electronic and thermo-electric energy-conversion devices. The traditional first-principles theory governing the thermal and thermodynamic properties of insulators relies on the perturbative treatment of interatomic potential and ad hoc displacement of atoms within supercells. However, the limitations of these approaches for highly anharmonic and weakly bonded materials, along with discrepancies arising from not considering explicit finite temperature effects, highlight the necessity for a well-defined quasiparticle approach to the lattice vibrations. To address these limitations, we present a comprehensive numerical framework in this study, designed to compute the thermal and thermodynamic properties of crystalline semiconductors and insulators. The self-consistent phonon renormalization method we have devised reveals phonons as quasiparticles, diverging from their conventional characterization as bare normal modes of lattice vibration. The extension of renormalization effects to third- and fourth-order interatomic force constants (IFCs) is also implemented and demonstrated. For the comprehensive physical insights, we employed an iterative solution of the Peierls-Boltzmann transport equation (PBTE) to determine thermal conductivity and carry out Helmholtz free energy calculations, treating anharmonic effects up to the fourth order. We utilize our numerical framework to showcase its applicability through an investigation of phonon dispersion, phonon linewidth, anharmonic phonon scattering rates, and temperature-dependent lattice thermal conductivity in both highly anharmonic materials (NaCl and AgI) and weakly anharmonic materials (cBN and 3C-SiC). Our study reveals that neglecting higher-order phonon scattering processes, particularly four-phonon interactions, is not viable for materials with strong anharmonicity in their interatomic potential. Meanwhile, renormalization demonstrates a negligible impact on materials characterized by weak anharmonicity. We also investigate the effects of fourth-order anharmonicity on the Helmholtz free energy and pressure-dependent thermal conductivity of the NaCl crystal. The theoretical and computational framework developed in this work will help to understand the physical insight of phonons and phonon-driven thermal and thermodynamic properties of materials and offer valuable guidance for the strategic development of efficient thermal management techniques.