Nonlinear phonon dispersion in disordered solids and non-Debye vibrational spectra

TL;DR

This study investigates how nonlinear phonon dispersion and non-phononic vibrations contribute to non-Debye vibrational spectra, especially the boson peak, in disordered solids through simulations and analysis.

Contribution

It reveals that nonlinear phonon dispersion arises from a disorder-induced lengthscale and quantifies its role alongside non-phononic vibrations in the boson peak.

Findings

Nonlinear phonon dispersion is linked to a disorder-induced lengthscale.

Both phonon softening and non-phononic modes significantly contribute to the boson peak.

The relative importance of these contributions depends on the disorder strength.

Abstract

All solids, whether crystalline or disordered, support elastic wave propagation with a linear dispersion relation in the long-wavelength limit. These waves, corresponding to low-frequency phonons, feature a vibrational density of states that follows Debye's classical model. Deviations from Debye's predictions with increasing frequency can emerge from phonon dispersion nonlinearity and from non-phononic vibrational modes, which exist in non-crystalline solids due to structural disorder. Both nonlinear phonon dispersion in disordered solids and its relative contribution to non-Debye anomalies, most notably manifested by the controversial boson peak, remain poorly understood. Here we show that nonlinear phonon dispersion in a broad range of disordered solids, including elastic networks and various glasses, emerge from a mesoscopic, disorder-induced lengthscale, which also controls wave attenuation. We subsequently use analysis and large-scale computer simulations to quantitatively determine the relative contributions of nonlinear phonon softening and non-phononic vibrations to the onset of non-Debye anomalies and to the boson peak. We show that the relative magnitude of the two contributions strongly depends on the strength of disorder of the solid, e.g., controlled by the thermal history upon glass formation, and that for realistic laboratory glasses both pieces of physics significantly contribute to the boson peak. These findings constitute basic progress in understanding disordered solids.