Low-Frequency Excess Vibrational Modes in Two-Dimensional Glasses

Abstract

Glasses possess more low-frequency vibrational modes than predicted by Debye theory. These excess modes are crucial for the understanding of 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 ω as ω 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 Dexc(ω) ∼ ω 2 up to around the boson peak, regardless of the glass stability. The stability dependence of the overall scale of Dexc(ω) 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 ω 3 .

The ω3 scaling of the vibrational density of states in quasi-2D nanoconfined solids

“…Using extensive molecular dynamic simulations, we have been able to confirm this prediction proving that our simple theoretical framework is not only able to explain the ω 3 scaling but it also provides a good quantitative estimate of its frequency window. Finally, we stress that the nature of this scaling is not linked to the appearance of additional low-energy quasi-localized modes typical of amorphous systems as in 54 but it results from the geometric effects of confinement on the phase space of acoustic phonons.…”

“…Such a cubic power law has also been recently reported in ref. 54 for a 2D model glass system. Despite the tempting similarities, our setup is different with respect to that of ref.…”

“…Despite the tempting similarities, our setup is different with respect to that of ref. 54 in various aspects. First, our is a quasi-2D system, rather than a small 2D system, with excitations also in the vertical z direction.…”

“…All in all, the nature of the scaling discussed in this manuscript appears to be profoundly different with respect to the one reported in ref. 54 .…”

Glassy Behavior Depends on Dimension

“…This distinction is especially pronounced at low temperatures because of the different vibrational spectra that glasses and crystalline solids support. In detailed numerical simulations, Lijin Wang, Elijah Flenner, and their colleagues at Colorado State University now determine that the scaling law describing low-frequency vibrational modes in glasses is different in 2D than in 3D and also in 2D glasses of different sizes [1]. The finding shows that, contrary to common assumptions about glasses, behaviors may not be extrapolated across dimensions.…”