Unified theory of thermal transport in crystals and disordered solids

The phonon Boltzmann equation formulated by Peierls [1] describes the heat conduction in perfectly ordered solids in terms of interacting phonon wave-packets. Several methods have been recently developed to solve this equation in a numerically exact way, allowing to determine the thermal conductivity of crystals [2,3]

In the presence of disorder, it is possible to reach a point where the phonon wave-packets do not propagate far enough to sample the periodicity of the solid, rendering impossible to attribute them a wave vector or a group velocity. This regime is often described by a harmonic theory introduced by Allen and Feldman [4].

We generalize the Peierls and Allen-Feldman approaches with a unified master equation, which enables reliable first-principles predictions of the thermal conductivity of any insulator, ranging from complex crystals to anharmonic glasses. We showcase this approach with an application to a thermoelectric material that displays ultra-low glass-like thermal conductivity and rattling phonon modes.

[1] R. Peierls, Ann. Phys. 395, 1055 (1929).
[2] A. Cepellotti and N. Marzari, Phys. Rev. X 6, 041013 (2016).
[3] G. Fugallo, M. Lazzeri, L. Paulatto, and F. Mauri, Phys. Rev. B 88, 045430 (2013).
[4] P. B. Allen and J. L. Feldman, Phys. Rev. B 48, 12581 (1993).