Unifying description of the vibrational anomalies of amorphous materials

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 ${\omega }_{\mathrm{bp}}$, 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.

Supplemenatry Material included

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Cited by in corpus (6)

• Microscopic analysis of sound attenuation in low-temperature amorphous solids reveals quantitative importance of non-affine effects
• Disordered crystals reveal soft quasilocalized glassy excitations
• A unified quantifier of mechanical disorder in solids
• Vibrational phenomena in glasses at low temperatures captured by field theory of disordered harmonic oscillators
• Quasi-localized vibrational modes, Boson peak and sound attenuation in model mass-spring networks
• Transport and relaxation of current-generated nonequilibrium phonons from nonlocal electronic measurements