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

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.

7 pages, 5 figures

References in corpus (11)

• Jamming at Zero Temperature and Zero Applied Stress: the Epitome of Disorder
• Irreversible reorganization in a supercooled liquid originates from localised soft modes
• Suppression of tunneling two-level systems in ultrastable glasses of indomethacin
• Universality of the nonphononic vibrational spectrum across different classes of computer glasses
• Nonlinear modes disentangle glassy and Goldstone modes in structural glasses
• Low-frequency vibrational spectrum of mean-field disordered systems
• Universal low-frequency vibrational modes in silica glasses
• Low-frequency excess vibrational modes in two-dimensional glasses
• Universal Density of Low Frequency States in Amorphous Solids at Finite Temperatures
• Universal non-Debye low-frequency vibrations in sheared amorphous solids
• Random quench predicts universal properties of amorphous solids

Cited by in corpus (7)

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• Properties of stable ensembles of Euclidean random matrices
• Enhanced Vibrational Stability in Glass Droplets
• Two-level systems and harmonic excitations in a mean-field anharmonic quantum glass
• Computational Methods toward Ultrastable Glasses