Anomalous phonon dispersion near yielding in athermal crystals

TL;DR

This paper investigates vibrational properties of sheared athermal crystals near yielding, revealing a transition from linear to quadratic dispersion and a divergence in vibrational density of states due to multimode softening.

Contribution

It uncovers the role of directionally extended multimode softening in yielding, providing analytical derivations of the associated scaling laws.

Findings

Yielding involves a cross-shaped soft region in wave number space.

The dispersion relation changes from ω∼k to ω∼k^2 near yielding.

Vibrational density of states transitions from Debye to non-Debye scaling.

Abstract

Vibrational properties of ordered athermal solids near yielding remain poorly understood. We show that yielding in a sheared crystal is governed not by a single localized instability but by directionally extended multimode softening that forms a cross-shaped low-frequency region in wave number space. Near yielding, the acoustic dispersion $\omega\sim k$ is replaced by $\omega\sim k^2$ along the soft direction, and the vibrational density of states crosses over from Debye to non-Debye scaling, with a diverging length scale. We analytically derive these scaling laws.