Disordered crystals reveal soft quasilocalized glassy excitations

TL;DR

This study demonstrates that disordered crystals, like glasses, exhibit a universal $ ext{ω}^4$ distribution of low-energy quasilocalized excitations, extending the universality beyond amorphous materials and revealing new insights into disordered solids.

Contribution

It shows that the universal quartic law applies to disordered crystals with finite long-range order, and explores the relationship between disorder level and quasilocalized excitations.

Findings

Universal $ ext{ω}^4$ distribution in disordered crystals.

Disordered crystals host more quasilocalized excitations than expected.

Stability bounds on excitations hold in disordered crystals.

Abstract

Structural glasses formed by quenching a melt are known to host a population of low-energy quasilocalized (nonphononic) excitations whose frequencies $\omega$ follow a universal $\sim\!\omega^4$ distribution as $\omega\!\to\!0$, independently of the glass formation history, the interparticle interaction potential or spatial dimension. Here, we show that the universal quartic law of nonphononic excitations also holds in disordered crystals featuring finite long-range order, which is absent in their glassy counterparts. We thus establish that the degree of universality of the quartic law extends beyond structural glasses quenched from a melt. We further find that disordered crystals, whose level of disorder can be continuously controlled, host many more quasilocalized excitations than expected based on their degree of mechanical disorder -- quantified by the relative fluctuations of the shear modulus -- as compared to structural glasses featuring a similar degree of mechanical disorder. Finally, we show that the stability bound on nonlinear quasilocalized excitations -- previously established in structural glasses -- also holds in disordered crystals. Our results are related to glass-like anomalies experimentally observed in disordered crystals. More broadly, they constitute an important step towards tracing the essential ingredients necessary for the emergence of universal nonphononic excitations in disordered solids.