Density of States below the First Sound Mode in 3D Glasses

TL;DR

This study investigates the low-frequency vibrational density of states in 3D glasses, revealing that the previously assumed universal $\, extomega^4$ scaling law only holds in an intermediate regime and breaks down at very low frequencies.

Contribution

It provides the first direct numerical evidence that the $ extomega^4$ law does not extend to the lowest frequencies in 3D glasses, challenging prior assumptions.

Findings

$D( extomega)$ scales with $ extomega^{eta}$ where $eta<4$ at very low frequencies

The $ extomega^4$ law is valid only in a limited intermediate-frequency regime

The breakdown of the $ extomega^4$ law is independent of glass models or stabilities examined

Abstract

Glasses feature universally low-frequency excess vibrational modes beyond Debye prediction, which could help rationalize, e.g., the glasses' unusual temperature dependence of thermal properties compared to crystalline solids. The way the density of states of these low-frequency excess modes $D(\omega)$ depends on the frequency $\omega$ has been debated for decades. Recent simulation studies of 3D glasses suggest that $D(\omega)$ scales universally with $\omega^4$ in a low-frequency regime below the first sound mode. However, no simulation study has ever probed as low frequencies as possible to test directly whether this quartic law could work all the way to extremely low frequencies. Here, we calculated $D(\omega)$ below the first sound mode in 3D glasses over a wide range of frequencies. We find $D(\omega)$ scales with $\omega^{\beta}$ with ${\beta}<4.0$ at very low frequencies examined, while the $\omega^4$ law works only in a limited intermediate-frequency regime in some glasses. Moreover, our further analysis suggests our observation does not depend on glass models or glass stabilities examined. The $\omega^4$ law of $D(\omega)$ below the first sound mode is dominant in current simulation studies of 3D glasses, and our direct observation of the breakdown of the quartic law at very low frequencies thus leaves an open but important question that may attract more future numerical and theoretical studies.