Type-I clathrate solids have attracted significant interest because of their ultralow thermal conductivities and subsequent promise for thermoelectric applications, yet the mechanisms underlying these properties are not well understood. Here, we extend the framework of vibrational dynamical mean-field theory (VDMFT) to calculate temperature-dependent thermal transport properties of solids using a many-body Green's function approach. When applied to a coarse-grained description of $X_8{\mathrm{Ga}}_{16}{\mathrm{Ge}}_{30}$, where $X=\mathrm{Ba},\mathrm{Sr}$, we find that nonresonant scattering between cage acoustic modes and rattling modes leads to a reduction of acoustic phonon lifetimes and thus thermal conductivities. Moreover, we find that the moderate temperature dependence of conductivities above 300 K, which is consistent with experimental measurements, cannot be reproduced by textbook perturbation theory calculations, which predict a $T^{-1}$ dependence. Therefore, we suggest that nonperturbative anharmonic effects, including four- and higher-phonon scattering processes, are responsible for the ultralow thermal conductivities of type-I clathrates.

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• Anharmonic lattice dynamics
• Lattice thermal conductivity
• Phonons
• Clathrates
• Thermoelectrics
• Boltzmann theory
• Dynamical mean field theory
• Green's function methods