Advances in lattice thermal transport in crystals and glasses

Thermal conductivity is a fundamental property for describing the non-equilibrium phenomenon of thermal transport. In solid insulators, whether disordered or crystalline, heat is primarily carried by lattice vibrations, emphasizing the need to accurately understand and compute the lattice thermal conductivity. This computation remains a central challenge in condensed matter physics, and lattice dynamical approaches have long been favored for this purpose. Despite being limited to (quasi-) harmonic dynamics, these methods can address key challenges in Molecular Dynamics, such as incorporating nuclear quantum effects and avoiding the sampling problems. Historically, separate lattice dynamical approaches were applied to glasses and crystals, creating a division in the field. However, recent advances, such as the development of unified frameworks like the Quasi-Harmonic Green-Kubo theory, have revolutionized the study of lattice thermal conductivity. This theory, derived by solving the Green-Kubo expression in the quasi-harmonic regime, provides a common theoretical framework for modeling heat transport across both ordered and disordered systems. Nevertheless, simplifying assumptions and computational scaling issues have limited its broad application. This thesis addresses these challenges through two main advancements. First, the theory is extended beyond the single-mode relaxation time approximation, enabling the accurate modeling of the low-temperature thermal conductivity of crystals. Second, the computational limitations, particularly relevant for glasses, are mitigated by combining hydrodynamic insights with efficient algorithms to achieve the bulk limit. This investigation of the bulk limit not only provides a quantitative correction but also reveals new insights into the behavior of glasses, highlighting the critical role of anharmonicity. While the inclusion of anharmonicity hardly brings significant changes to the thermal conductivity of typical glass samples containing only a few thousand atoms, the harmonic model typically exhibits a singular behavior in the bulk limit, which is then regularized by anharmonic effects. The ability to compute lattice thermal conductivity in large disordered systems is essential for designing materials with impactful applications. The theoretical and numerical tools developed here have been applied to spatially correlated silicon-germanium alloys, studied from first principles. These results suggest that correlated disorder may significantly enhance thermoelectric efficiency compared to standard SiGe alloys, highlighting the potential of these materials for thermoelectric applications.