Enumerating low-frequency nonphononic vibrations in computer glasses

TL;DR

This paper introduces a new method to accurately identify and analyze nonphononic vibrational modes in computer glasses, revealing their universal spectral tail and overcoming previous hybridization challenges.

Contribution

The authors develop a simple scheme to enumerate nonphononic modes in computer glasses, clarifying their additive contribution and universal spectral behavior.

Findings

Nonphononic modes contribute additively to the vibrational spectrum.

The nonphononic spectrum exhibits a universal ω^4 tail.

The method overcomes hybridization effects in spectral analysis.

Abstract

In addition to Goldstone phonons that generically emerge in the low-frequency vibrational spectrum of any solid, crystalline or glassy, structural glasses also feature other low-frequency vibrational modes. The nature and statistical properties of these modes -- often termed `excess modes' -- have been the subject of decades-long investigation. Studying them, even using well-controlled computer glasses, has proven challenging due to strong spatial hybridization effects between phononic and nonphononic excitations, which hinder quantitative analyses of the nonphononic contribution ${\cal D}_{\rm G}(\omega)$ to the total spectrum ${\cal D}(\omega)$, per frequency $\omega$. Here, using recent advances indicating that ${\cal D}_{\rm G}(\omega)\!=\!{\cal D}(\omega)-{\cal D}_{\rm D}(\omega)$, where ${\cal D}_{\rm D}(\omega)$ is Debye's spectrum of phonons, we present a simple and straightforward scheme to enumerate nonphononic modes in computer glasses. Our analysis establishes that nonphononic modes in computer glasses indeed make an additive contribution to the total spectrum, including in the presence of strong hybridizations. Moreover, it cleanly reveals the universal ${\cal D}_{\rm G}(\omega)\!\sim\!\omega^4$ tail of the nonphononic spectrum, and opens the way for related analyses of experimental spectra of glasses.