Spatial structure of quasi-localized vibrations in nearly jammed amorphous solids

TL;DR

This study investigates the spatial structure of quasi-localized vibrational modes in nearly jammed amorphous solids, revealing their core and far-field components, and relates their properties to the Boson peak and vibrational spectrum.

Contribution

It uncovers the detailed spatial structure of quasi-localized modes near jamming and links their divergence to anomalous modes causing the Boson peak.

Findings

Core size diverges as p^{-1/4}

Core volume diverges as p^{-1/2}

Density of modes scales as ω^4/p^2

Abstract

The low-temperature properties of amorphous solids are widely believed to be controlled by low-frequency quasi-localized modes. What governs their spatial structure and density is however debated. We study these questions numerically in very large systems as the jamming transition is approached and the pressure p vanishes. We find that these modes consist of an unstable core in which particles undergo the buckling motions and decrease the energy, and a stable far-field component which increases the energy and prevents the buckling of the core. The size of the core diverges as $p^{-1/4}$ and its characteristic volume as $p^{-1/2}$ These features are precisely those of the anomalous modes known to cause the Boson peak in the vibrational spectrum of weakly-coordinated materials. From this correspondence we deduce that the density of quasi-localized modes must go as $g_{\mathrm{loc}}(\omega) \sim \omega^4/p^2$ , in agreement with previous observations. Our analysis thus unravels the nature of quasi-localized modes in a class of amorphous materials.