Unifying description of the vibrational anomalies of amorphous materials

The vibrational density of states of solids controls their thermal and transport properties. Amorphous materials' vibrational modes differ from crystals' for the following reasons: (i) there is an excess of modes over Debye's prediction or Boson peak; (ii) there exist quasi-localized low-frequency vibrational modes; and (iii) low-frequency phonons attenuate via Rayleigh scattering. It is unclear if any connection exists between these vibrational features, as they occur in different frequency regimes.

Via extensive simulations of LJ-like computer glasses, we relate amorphous materials' vibrational anomalies. We validate fluctuation elasticity theory in its extended version that assumes the elastic heterogeneities have a finite correlation length, linking Boson peak and sound attenuation, and demonstrate that the elastic heterogeneities are the soft quasi-localized vibrational modes.

The emerging picture is that the Rayleigh's original model, an elastic continuum punctuated by localized defects, describes amorphous materials' vibrational anomalies by identifying defects as quasi-localized vibrational modes.