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We develop an analytical model to describe the phonon dispersion relations ofhost-guest lattices with heavy guest atoms (rattlers). Crucially, the modelalso accounts for phonon damping arising from anharmonicity. The spectrum oflow energy states contains acoustic-like and (soft) optical-like modes, whichdisplay the typical avoided crossing, and which can be derived analytically byconsidering the dynamical coupling between host lattice and guest rattlers.Inclusion of viscous anharmonic damping in the model allows us, for the firsttime, to compute the vibrational density of states (VDOS) and the specificheat, unveiling the presence of a boson peak (BP) linked to ananharmonicity-smeared van Hove singularity. Upon increasing the couplingstrength between the host and the guest dynamics, and by decreasing the energyof the soft optical modes, the BP anomaly becomes stronger and it moves towardslower frequencies. Moreover, we find a robust linear correlation between the BPfrequency and the energy of the soft optical-like modes. This frameworkprovides a useful model for tuning the thermal properties of host-guestlattices by controlling the VDOS, which is crucial for optimizing thermalconductivity and hence the energy conversion efficiency in these materials.

Theory of the phonon spectrum in host-guest crystalline solids with avoided crossing