Low-frequency excess vibrational modes in two-dimensional glasses

TL;DR

This study investigates low-frequency vibrational modes in two-dimensional glasses, revealing a universal  power law up to the boson peak and a  power law in small systems below the first sound mode, with implications for understanding glass properties.

Contribution

The paper provides extensive numerical evidence that excess vibrational modes in 2D glasses follow a  power law up to the boson peak, differing from previous  predictions.

Findings

Excess modes follow a  power law up to the boson peak.

In small systems, excess modes below the first sound mode scale as .

The stability dependence of excess modes correlates with sound attenuation.

Abstract

Glasses possess more low-frequency vibrational modes than predicted by Debye theory. These excess modes are crucial for the understanding the low temperature thermal and mechanical properties of glasses, which differ from those of crystalline solids. Recent simulational studies suggest that the density of the excess modes scales with their frequency $\omega$ as $\omega^4$ in two and higher dimensions. Here, we present extensive numerical studies of two-dimensional model glass formers over a large range of glass stabilities. We find that the density of the excess modes follows $D_\text{exc}(\omega)\sim \omega^2 $ up to around the boson peak, regardless of the glass stability. The stability dependence of the overall scale of $D_\text{exc}(\omega)$ correlates with the stability dependence of low-frequency sound attenuation. However, we also find that in small systems, where the first sound mode is pushed to higher frequencies, at frequencies below the first sound mode there are excess modes with a system size independent density of states that scales as $\omega^3$.