Thermal conductivity of glasses above the plateau: first-principles theory and applications

Abstract: Predicting the thermal conductivity of glasses from first principles has hitherto been a prohibitively complex problem. In fact, past works have highlighted challenges in achieving computational convergence with respect to length and/or time scales using either the established Allen-Feldman or Green-Kubo formulations, endorsing the concept that atomistic models containing thousands of atoms -- thus beyond the capabilities of first-principles calculations -- are needed to describe the thermal conductivity of glasses. In addition, these established formulations either neglect anharmonicity (Allen-Feldman) or miss the Bose-Einstein statistics of atomic vibrations (Green Kubo), thus leaving open the question on the relevance of these effects. Here, we present a first-principles formulation to address the thermal conductivity of glasses above the plateau, which can account comprehensively for the effects of structural disorder, anharmonicity, and quantum Bose-Einstein statistics. The protocol combines the Wigner formulation of thermal transport with convergence-acceleration techniques, and is validated in vitreous silica using both first-principles calculations and a quantum-accurate machine-learned interatomic potential. We show that models of vitreous silica containing less than 200 atoms can already reproduce the thermal conductivity in the macroscopic limit and that anharmonicity negligibly affects heat transport in vitreous silica. We discuss the microscopic quantities that determine the trend of the conductivity at high temperature, highlighting the agreement of the calculations with experiments in the temperature range above the plateau where radiative effects remain negligible (50<T <450 K).