Phonons are quantized atomic vibrations of a material, and they play a central role in phenomena ranging from heat generation and transport to superconductivity. Unique phonon-phonon interactions, or anharmonic vibrational structure, have been identified in cage-like chemical structures called clathrates. In these materials, acoustic modes of the clathrate cages interact with optical, “rattling” modes of guest atoms loosely bound in those cages, leading to strong anharmonicity. We calculate the anharmonic vibrational structure of model clathrate systems using vibrational dynamical mean-field theory (VDMFT), which treats the local anharmonicity exactly. At its heart, VDMFT requires calculating the dynamics of a single unit cell that is coupled to a self-consistently defined bath of harmonic oscillators. We demonstrate that VDMFT accurately captures phonon frequency shifts and lifetimes for various degrees of cage-guest anharmonicity. Furthermore, we see that in certain systems, anharmonicity between the clathrate cage and rattling modes is so strong that the modes hybridize and the traditional phonon picture breaks down. We use the anharmonic phonon Green’s function obtained using VDMFT to compute thermal conductivities, accurately accounting for this hybridization, which is often neglected but is crucial for correctly describing the hallmark ultralow thermal conductivity in clathrates.
