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

## TL;DR

This paper presents an analytical model for phonon spectra in host-guest crystals, incorporating anharmonic damping, to understand vibrational properties and thermal behavior, including the boson peak and its relation to soft optical modes.

## Contribution

The model uniquely accounts for anharmonic damping and analytically describes avoided crossing phonon modes in host-guest lattices, linking vibrational features to thermal properties.

## Key findings

- Identification of a boson peak linked to anharmonicity-smeared van Hove singularity.
- Demonstration of a linear correlation between boson peak frequency and soft optical mode energy.
- Enhanced boson peak with increased host-guest coupling and decreased optical mode energy.

## Abstract

We develop an analytical model to describe the phonon dispersion relations of host-guest lattices with heavy guest atoms (rattlers). Crucially, the model also accounts for phonon damping arising from anharmonicity. The spectrum of low energy states contains acoustic-like and (soft) optical-like modes, which display the typical avoided crossing, and which can be derived analytically by considering the dynamical coupling between host lattice and guest rattlers. Inclusion of viscous anharmonic damping in the model allows us, for the first time, to compute the vibrational density of states (VDOS) and the specific heat, unveiling the presence of a boson peak (BP) linked to an anharmonicity-smeared van Hove singularity. Upon increasing the coupling strength between the host and the guest dynamics, and by decreasing the energy of the soft optical modes, the BP anomaly becomes stronger and it moves towards lower frequencies. Moreover, we find a robust linear correlation between the BP frequency and the energy of the soft optical-like modes. This framework provides a useful model for tuning the thermal properties of host-guest lattices by controlling the VDOS, which is crucial for optimizing thermal conductivity and hence the energy conversion efficiency in these materials.