# Low-energy optical phonons induce glassy-like vibrational and thermal anomalies in ordered crystals

## TL;DR

This paper presents a theory explaining glassy-like vibrational and thermal anomalies in perfectly ordered crystals as caused by low-energy optical phonons, challenging the notion that such anomalies only occur in disordered materials.

## Contribution

The study introduces a model showing that low-energy optical phonons in ordered crystals can produce glass-like vibrational and thermal anomalies without disorder.

## Key findings

- Boson peak in VDOS can be caused by low-energy optical phonons.
- Optical phonons contribute to low-temperature heat capacity deviations from Debye law.
- Ordered crystals can exhibit glass-like thermal behavior due to optical phonons.

## Abstract

It is widely accepted that structural glasses and disordered crystals exhibit anomalies in the their thermal, mechanical and acoustic properties as manifestations of the breakdown of the long-wavelength approximation in a disordered dissipative environment. However, the same type of glassy-like anomalies (i.e. boson peak in the vibrational density of states (VDOS) above the Debye level, peak in the normalized specific heat at $T\simeq10 K$ etc) have been recently observed also in perfectly ordered crystals, including thermoelectric compounds. Here we present a theory that predicts these surprising effects in perfectly ordered crystals as a result of low-lying (soft) optical phonons. In particular, it is seen that a strong boson peak anomaly (low-energy excess of modes) in the VDOS can be due almost entirely to the presence of low-energy optical phonons, provided that their energy is comparable to that of the acoustic modes at the Brillouin zone boundary. The boson peak is predicted also to occur in the heat capacity at low $T$. In presence of strong damping (which might be due to anharmonicities in the ordered crystals), these optical phonons contribute to the low-$T$ deviation from Debye's $T^{3}$ law, producing a linear-in-$T$ behavior which is typical of glasses, even though no assumptions of disorder whatsoever are made in the model. These findings are relevant for understanding and tuning thermal transport properties of thermoelectric compounds, and possibly for the enhancement of electron-phonon superconductivity.