Low-Frequency Excess Vibrational Modes in Two-Dimensional Glasses (vol 127, 248001, 2021)

Glasses possess more low-frequency vibrational modes than predicted by Debye theory. These excess modes arc 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 omega as omega(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 D-exc(omega) similar to omega(2) up to around the boson peak, regardless of the glass stability. The stability dependence of the overall scale of D-exc(omega) 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 a omega(3).