Nonperturbative Simulation of Anharmonic Rattler Dynamics in Type-I Clathrates with Vibrational Dynamical Mean-Field Theory

Abstract: We use vibrational dynamical mean-field theory (VDMFT) to study the vibrational structure of type-I clathrate solids, specifically X$8$Ga${16}$Ge$_{30}$, where X=Ba,Sr. These materials are cage-like chemical structures hosting loosely bound guest atoms, resulting in strong anharmonicity, short phonon lifetimes, and ultra-low thermal conductivities. Presenting the methodological developments necessary for this first application to three-dimensional, atomistic materials, we validate our approach through comparison to molecular dynamics simulations and show that VDMFT is extremely accurate at a fraction of the cost. Through the use of nonperturbative methods, we find that anharmonicity is dominated by four-phonon and higher-order scattering processes, and it causes rattler modes to shift up in frequency by 50% (10 cm$^{-1}$) and to have lifetimes of less than 1 ps; this behavior is not captured by traditional perturbation theory. Furthermore, we analyze the phonon self-energy and find that anharmonicity mixes guest rattling modes and cage acoustic modes, significantly changing the character of the harmonic phonons.