关键词: density of states, vibrational modes, sound attenuation, two-dimensional glasses

Abstract: One hallmark of glasses is the existence of excess vibrational modes at low frequencies $\omega$ beyond Debye's prediction. Numerous studies suggest that understanding low-frequency excess vibrations could help gain insight into the anomalous mechanical and thermodynamic properties of glasses. However, there is still intensive debate as to the frequency dependence of the population of low-frequency excess vibrations. In particular, excess modes could hybridize with phonon-like modes and the density of hybridized excess modes has been reported to follow $D_{\rm exc}(\omega) \sim \omega^{2}$ in 2D glasses with an inverse power law potential. Yet, the universality of the quadratic scaling remains unknown, since recent work suggested that interaction potentials could influence the scaling of the vibrational spectrum. Here, we extend the universality of the quadratic scaling for hybridized excess modes in 2D to glasses with potentials ranging from the purely repulsive soft-core interaction to the hard-core one with both repulsion and attraction as well as to glasses with significant differences in density or interparticle repulsion. Moreover, we observe that the number of hybridized excess modes exhibits a decrease in glasses with higher density or steeper interparticle repulsion, which is accompanied by a suppression of the strength of the sound attenuation. Our results indicate that the density bears some resemblance to the repulsive steepness of the interaction in influencing low-frequency properties.

Key words: density of states, vibrational modes, sound attenuation, two-dimensional glasses