Novel elastic instability of amorphous solids in finite spatial dimensions

TL;DR

This paper introduces a new type of elastic instability in amorphous solids that explains the observed gapless vibrational density of states and suggests glasses are marginally stable due to this novel instability.

Contribution

The study proposes and analyzes a new instability mechanism in amorphous solids, extending previous work and demonstrating its relevance to real glasses in finite dimensions.

Findings

Real glasses can be marginally stable due to the new instability.

The proposed instability explains the quartic vibrational density of states.

Analysis of disorder examples supports the theory.

Abstract

Recently, progress has been made in the understanding of anomalous vibrational excitations in amorphous solids. In the lowest-frequency region, the vibrational spectrum follows a non-Debye quartic law, which persists up to zero frequency without any frequency gap. This gapless vibrational density of states (vDOS) suggests that glasses are on the verge of instability. This feature of marginal stability is now highlighted as a key concept in the theories of glasses. In particular, the elasticity theory based on marginal stability predicts the gapless vDOS. However, this theory yields a quadratic law and \textit{not} the quartic law. To address this inconsistency, we presented a new type of instability, which is different from the conventional one, and proposed that amorphous solids are marginally stable considering the new instability in the preceding study~[M. Shimada, H. Mizuno, and A. Ikeda, Soft Matter, {\bf 16}, 7279, 2020]. In this study, we further extend and detail the results for these instabilities. By analyzing various examples of disorder, we demonstrate that real glasses in finite spatial dimensions can be marginally stable by the proposed novel instability.