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Abstract

Heat transport is an important phenomenon in many branches of physics and adjacent fields, be it astrophysics and earth sciences, where thermodynamic properties of planets are studied, or materials science investgating technologically relevant compounds. In dielectric solids, the most important contribution to heat transport comes from the transfer of vibrational energy of atoms – heat – mediated by the interatomic bonding. The simplest model to describe this bonding is the harmonic approximation, i. e., the description of atom bonds as perfect springs. However, the harmonic approximation is incapable of describing thermal conductivity in periodic systems: A perfectly harmonic, defect-free crystal would approach vanishing thermal resistance in the bulk limit. Finite thermal conductivity in realistic systems is a consequence of deviations from the harmonic description of atom bonds: Anharmonicity. Depending on the strength of anharmonic contributions to the interatomic bonding, these can be captured as a small correction to the harmonic approximation in the framework of perturbation theory, or require a non-perturbative description once they become too strong.
In this work, we describe how a non-perturbative heat transport formalism for solids emerges in the framework of ab initio simulations coupled with linear response theory. The resulting ab initio Green Kubo method allows for studying heat transport in solids of arbitrary anharmonic strength, and is particularly suited to describe “strongly anharmonic” systems where per- turbative approaches become unreliable. In order to discern harmonic from anharmonic materials in a systematic way, we introduce an “anharmonicity measure” which quantifies the anharmonic contribution to the interatomic forces under thermodynamic conditions. Using this anharmonicity measure, we investigate typical dynamical effects occurring in strongly anharmonic compounds and investigate the limits of perturbative approaches for the study of thermal transport. We show that this measure negatively correlates with bulk thermal conductivities in simple solids, supporting the intuitive notion that more harmonic materials are better heat conductors and vice versa. Based on these findings, we identify anharmonic compounds as candidates for thermal transport simulations in the search for novel thermal insulators. In this way, we identify several new thermal insulators of potential technological relevance as thermal barriers or thermoelectric materials which we suggest for experimental study.