Unifying description of the vibrational anomalies of amorphous materials

TL;DR

This paper presents a unified description of vibrational anomalies in amorphous materials, linking the boson peak and phonon damping through correlated elasticity theory and modeling amorphous solids as elastic media with localized heterogeneities.

Contribution

It introduces a unified framework connecting vibrational anomalies to elastic heterogeneities, resolving previous theoretical conflicts.

Findings

Boson peak and phonon attenuation are related via correlated fluctuating elasticity theory.

Amorphous materials can be modeled as homogeneous elastic media with localized elastic heterogeneities.

The approach reconciles theories attributing anomalies to elastic disorder and localized defects.

Abstract

The vibrational density of states $D(\omega)$ of solids controls their thermal and transport properties. In crystals, the low-frequency modes are extended phonons distributed in frequency according to Debye's law, $D(\omega) \propto \omega^2$. In amorphous solids, phonons are damped, and at low frequency $D(\omega)$ comprises extended modes in excess over Debye's prediction, leading to the so-called boson peak in $D(\omega)/\omega^2$ at $\omega_{\rm bp}$, and quasi-localized (QLMs) ones. Here we show that boson peak and phonon attenuation in the Rayleigh scattering regime are related, as suggested by correlated fluctuating elasticity theory (corr-FET), and that amorphous materials can be described as homogeneous isotropic elastic media punctuated by QLMs acting as elastic heterogeneities. Our numerical results resolve the conflict between theoretical approaches attributing amorphous solids' vibrational anomalies to elastic disorder and localized defects.