High-frequency vibrational density of states of a disordered solid

TL;DR

This paper studies the high-frequency vibrational density of states in disordered solids, revealing that disorder causes localized excitations and an exponential decay in the density of states, similar to Lifshitz tails in electronic systems.

Contribution

It introduces a theoretical framework using instanton solutions to describe high-frequency vibrational states in disordered elastic media, highlighting the role of disorder-induced localization.

Findings

Exponential decay of vibrational density of states at high frequencies.

Localization of vibrational excitations due to disorder fluctuations.

Density of states governed by the statistics of a fluctuating-elasticity landscape.

Abstract

We investigate the high-frequency behavior of the density of vibrational states in three-dimensional elasticity theory with spatially fluctuating elastic moduli. At frequencies well above the mobility edge, instanton solutions yield an exponentially decaying density of states. The instanton solutions describe excitations, which become localized due to the disorder-induced fluctuations, which lower the sound velocity in a finite region compared to its average value. The exponentially decaying density of states (known in electronic systems as the Lifshitz tail) is governed by the statistics of a fluctuating-elasticity landscape, capable of trapping the vibrational excitations.