Thermal transport in solids beyond the Ioffe-Regel limit

Recently it has been shown that the two established heat conduction mechanisms—namely the propagation of atomic vibrational waves in anharmonic crystals elucidated by the phonon Boltzmann transport equation [R. Peierls, Ann. Phys. 395, 1055 (1929)], and the couplings between atomic vibrational modes in harmonic glasses rationalized by Allen and Feldman’s equation [P. B. Allen and J. L. Feldman, Phys. Rev. Lett. 62, 645 (1989)]—naturally emerge as limiting cases of a unified theory, derived from the Wigner formulation of quantum mechanics and describing on an equal footing solids ranging from crystals to glasses [M. Simoncelli, N. Marzari, and F. Mauri, Nat. Phys. 15, 809 (2019)]. Here, we combine this unified theoretical framework with first-principles calculations to investigate what happens when atomic vibrational waves reach the Ioffe-Regel limit (i.e. their mean free paths become comparable or shorter than the interatomic spacing), showing that they can still contribute to heat transport due to their wave-like capability to interfere and tunnel. We showcase these findings in various silica polymorphs with different degree of disorder, and in materials with ultralow thermal conductivity employed for thermal barrier coatings or thermoelectrics.