Sound modes in composite incommensurate crystals

TL;DR

This paper introduces a phenomenological model for composite incommensurate crystals, revealing distinct high and low frequency sound modes and explaining experimental spectra features.

Contribution

The paper presents a simple model capturing the eigenmodes of composite incommensurate crystals, including a crossover between propagating and over-damped modes.

Findings

High frequency: two longitudinal sound modes with standard attenuation

Low frequency: one propagating sound mode and an over-damped phase mode

Model reproduces key features of experimental spectra

Abstract

We propose a simple phenomenological model describing composite crystals, constructed from two parallel sets of periodic inter-penetrating chains. In the harmonic approximation and neglecting thermal fluctuations we find the eigenmodes of the system. It is shown that at high frequencies there are two longitudinal sound modes with standard attenuation, while in the low frequency region there is one propagating sound mode and an over-damped phase mode. The crossover between these two regions is analyzed numerically and the dynamical structure factor is calculated. It is shown that the qualitative features of the experimentally observed spectra can be consistently described by our model.