Transverse and longitudinal vibrations in amorphous silicon

TL;DR

This study decomposes harmonic vibrations in amorphous silicon into transverse and longitudinal components across all frequencies, revealing a frequency-dependent transition that explains features in vibrational diffusivity.

Contribution

It introduces a method to decompose vibrational eigenmodes into transverse and longitudinal parts without a well-defined wave vector in amorphous silicon.

Findings

Vibrations are mostly transverse below 7 THz and above 15 THz.

Between 7 and 15 THz, vibrations are predominantly longitudinal.

The transition at 7 THz correlates with a peak in vibrational diffusivity.

Abstract

We show that harmonic vibrations in amorphous silicon can be decomposed to transverse and longitudinal components in all frequency range even in the absence of the well defined wave vector ${\bf q}$. For this purpose we define the transverse component of the eigenvector with given $\omega$ as a component, which does not change the volumes of Voronoi cells around atoms. The longitudinal component is the remaining orthogonal component. We have found the longitudinal and transverse components of the vibrational density of states for numerical model of amorphous silicon. The vibrations are mostly transverse below 7 THz and above 15 THz. In the frequency interval in between the vibrations have a longitudinal nature. Just this sudden transformation of vibrations at 7 THz from almost transverse to almost longitudinal ones explains the prominent peak in the diffusivity of the amorphous silicon just above 7 THz.