Disorder-induced vibrational anomalies from crystalline to amorphous solids

TL;DR

This study investigates the origin of the boson peak in vibrational density of states across crystalline to amorphous solids, revealing it is linked to uncorrelated shear modulus fluctuations, distinct from van-Hove singularities.

Contribution

It demonstrates that boson peaks and van-Hove singularities are separate phenomena, with the former related to uncorrelated shear modulus fluctuations and the latter to correlated fluctuations, across different disorder levels.

Findings

Boson peak is associated with uncorrelated shear modulus fluctuations.

Van-Hove singularities shift and broaden with increasing disorder.

Boson peak and van-Hove singularities are well separated in disordered systems.

Abstract

The origin of boson peak -- an excess of density of states over Debye's model in glassy solids -- is still under intense debate, among which some theories and experiments suggest that boson peak is related to van-Hove singularity. Here we show that boson peak and van-Hove singularity are well separated identities, by measuring the vibrational density of states of a two-dimensional granular system, where packings are tuned gradually from a crystalline, to polycrystals, and to an amorphous material. We observe a coexistence of well separated boson peak and van-Hove singularities in polycrystals, in which the van-Hove singularities gradually shift to higher frequency values while broadening their shapes and eventually disappear completely when the structural disorder $\eta$ becomes sufficiently high. By analyzing firstly the strongly disordered system ($\eta=1$) and the disordered granular crystals ($\eta=0$), and then systems of intermediate disorder with $\eta$ in between, we find that boson peak is associated with spatially uncorrelated random flucutations of shear modulus $\delta G/\langle G \rangle$ whereas the smearing of van-Hove singularities is associated with spatially correlated fluctuations of shear modulus $\delta G/\langle G \rangle$.