Disordered Solids Without Well-Defined Transverse Phonons: The Nature of Hard Sphere Glasses

TL;DR

This study investigates the vibrational properties of hard sphere glasses near the jamming transition, revealing that only longitudinal phonons remain well-defined in certain regimes and highlighting differences in elastic properties across transitions.

Contribution

It provides new insights into the nature of vibrational excitations in hard sphere glasses near jamming, especially regarding the absence of transverse phonons at zero temperature.

Findings

Transverse Ioffe-Regel frequency vanishes at jamming transition.

Longitudinal Ioffe-Regel frequency remains finite at zero temperature.

Glasses between glass and jamming-like transitions support only longitudinal phonons.

Abstract

We probe the Ioffe-Regel limits of glasses with repulsions near the zero-temperature jamming transition by measuring the dynamical structure factors. At zero temperature, the transverse Ioffe-Regel frequency vanishes at the jamming transition with a diverging length, but the longitudinal one does not, which excludes the existence of a diverging length associated with the longitudinal excitations. At low temperatures, the transverse and longitudinal Ioffe-Regel frequencies approach zero at the jamming-like transition and glass transition, respectively. As a consequence, glasses between the glass transition and jamming-like transition, which are hard sphere glasses in the low temperature limit, can only carry well-defined longitudinal phonons and have an opposite pressure dependence of the ratio of the shear modulus to the bulk modulus from glasses beyond the jamming-like transition.