Unified first-principles theory of thermal properties of insulators

Abstract

The conventional first-principles theory for the thermal and thermodynamic properties of insulators is based on the perturbative treatment of the anharmonicity of crystal bonds. While this theory has been a successful predictive tool for strongly-bonded solids such as diamond and silicon, here we show that it fails dramatically for strongly anharmonic (weakly-bonded) materials, and that the conventional quasi-particle picture breaks down at relatively low temperatures. To address this failure, we present a unified first-principles theory of the thermodynamic and thermal properties of insulators that captures multiple thermal properties within the same framework across the full range of anharmonicity from strongly-bonded to weakly-bonded insulators. This theory features a new phonon renormalization approach derived from many-body physics that creates well-defined quasi-particles even at relatively high temperatures, and it accurately captures the effects of strongly anharmonic bonds on phonons and thermal transport. Using a prototypical strongly anharmonic material -sodium chloride (NaCl) as an example, we demonstrate that our new first-principles framework simultaneously captures the apparently contradictory experimental observations of large thermal expansion and low thermal conductivity of NaCl on the one hand, and anomalously weak temperature dependence of phonon modes on the other, while the conventional theory fails in all three cases. We demonstrate that four-phonon scattering due to higher-order anharmonicity significantly lowers the thermal conductivity of NaCl and is required for a proper comparison to experiment. Furthermore, we show that our renormalization framework, along with four-phonon scattering, also successfully predicts the measured phonon frequencies and thermal properties of a weakly anharmonic material -diamond, indicating universal applicability for thermal properties of insulators. Our work gives new insights into the physics of heat flow in solids, and presents a computationally efficient and rigorous framework that captures the thermal and thermodynamic properties of both weakly and strongly-bonded insulators simultaneously. *

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