Scaling of the Non-Phononic Spectrum of Two-Dimensional Glasses

TL;DR

This study investigates how the low-frequency vibrational modes in two-dimensional glasses scale with system size, revealing a transition from plane-wave-like to quasi-localized modes and a universal power-law behavior.

Contribution

It demonstrates a size-dependent transition in vibrational mode characteristics and identifies a universal power-law scaling of the density of states in large 2D glasses.

Findings

Modes are plane-wave-like in small systems (<100 particles).

Modes become quasi-localized in larger systems (>100 particles).

Density of states follows a universal power-law with exponent 3.5 in large systems.

Abstract

Low-frequency vibrational harmonic modes of glasses are frequently used to understand their universal low-temperature properties. One well studied feature is the excess low-frequency density of states over the Debye model prediction. Here we examine the system size dependence of the density of states for two-dimensional glasses. For systems of fewer than 100 particles, the density of states scales with the system size as if all the modes were plane-wave-like. However, for systems greater than 100 particles we find a different system-size scaling of the cumulative density of states below the first transverse sound mode frequency, which can be derived from the assumption that these modes are quasi-localized. Moreover, for systems greater than 100 particles, we find that the cumulative density of states scales with frequency as a power law with the exponent that leads to the exponent $\beta=3.5$ for the density of states independent of system size.