Jamming Criticality of Near-Crystals

TL;DR

This paper investigates the critical jamming behavior of nearly crystalline packings, revealing universal scaling laws for force and vibrational properties, with some non-universal features in localized modes.

Contribution

It demonstrates that minimal polydispersity packings exhibit universal critical behavior consistent with mean-field theory, extending understanding from amorphous to near-crystalline systems.

Findings

Force and gap distributions follow power-law tails.

Vibrational density of states is flat at jamming.

Most normal modes are delocalized with inverse participation ratio scaling.

Abstract

We report on the critical properties of minimaly-polydisperse crystals, hexagonal in 2d and face-centered cubic in 3 dimensions, at the isostatic jamming point. The force and gap distributions display power-law tails for small values. The vibrational density of states (VDOS) is flat. The scaling behavior of forces of extended floppy modes and the VDOS are universal and in agreement with an infinite-dimensional mean-field theory and maximally amorphous packings down to 2 dimensions. The distributions of gaps and forces of localized floppy modes of near-crystals appear non-universal. A small fraction of normal modes exhibit partial localization at low frequency. The majority of normal modes is delocalized exhibiting a characteristic inverse participation ratio scaling with frequency. The packing fraction and order at jamming decay linearly and quadratically respectively with polydispersity down to the maximally amorphous state.