Geometric origin of excess low-frequency vibrational modes in amorphous solids

TL;DR

This paper explains the excess low-frequency vibrational modes in amorphous solids as a consequence of their geometric structure, linking vibrational properties to the inherent geometry of weakly connected systems.

Contribution

It reveals the geometric origin of excess vibrational modes in glasses and predicts a new length scale affecting vibrational behavior at small scales.

Findings

Density of states remains constant with frequency.

A low-frequency cutoff appears and increases with compression.

Vibrations below a certain length scale differ from elastic continuum predictions.

Abstract

Glasses have a large excess of low-frequency vibrational modes in comparison with crystalline solids. We show that such a feature is a necessary consequence of the geometry generic to weakly connected solids. In particular, we analyze the density of states of a recently simulated system, comprised of weakly compressed spheres at zero temperature. We account for the observed a) constancy of the density of modes with frequency, b) appearance of a low-frequency cutoff, and c) power-law increase of this cutoff with compression. We predict a length scale below which vibrations are very different from those of a continuous elastic body.