Unified theory of vibrational spectra in amorphous materials

TL;DR

This paper presents a unified theoretical framework for understanding the vibrational density of states in amorphous materials, accurately matching experimental data and providing insights into phonon behavior and material properties.

Contribution

It introduces an effective field theory approach that accounts for disorder via momentum diffusion, unifying the description of VDOS in amorphous solids with minimal fitting parameters.

Findings

Accurately describes VDOS of silica glass and amorphous Si.

Phonon speeds and linewidths match experimental values.

Enables reverse-engineering of phonon dispersion from VDOS.

Abstract

The phonon spectra of solids, described through the measurable vibrational density of states (VDOS), provide a wealth of information about the underlying atomic structure and bonding, and they determine fundamental macroscopic properties such as specific heat, thermal conductivity and superconductivity. In amorphous solids, structural disorder generates a number of poorly understood phenomena that are absent in crystals. Starting from an effective field theory description which accounts for disorder in terms of momentum diffusion, we provide a unified theoretical description of the VDOS of amorphous materials. The theory provides an excellent description of the simulated/experimental VDOS of two quite different materials (silica glass and amorphous Si) with very few non-trivial fitting parameters. In particular, the phonons speeds and diffusive linewidths obtained from the fits are fully consistent with the tabulated values from experiments. This semi-analytical approach solves the long-standing problem of describing and explaining the features of the VDOS and Raman spectra of amorphous solids in relation with the underlying acoustic dispersion relations and acoustic attenuation. Furthermore, it can be used in a reverse-engineered way to estimate phonon dispersion relations, acoustic attenuation and dynamic structure factors from a simple fitting of the VDOS with the presented model.