Boson peak in amorphous systems: role of phonon mediated coupling of nano-clusters

TL;DR

This paper models amorphous solids as coupled nanoscale clusters to analyze vibrational states, revealing a Gaussian distribution in the bulk and an Airy function at low frequencies, aligning well with experimental data.

Contribution

It introduces a novel cluster-based Hamiltonian approach to describe vibrational properties in amorphous materials, connecting microscopic structure to the boson peak.

Findings

Vibrational density of states is Gaussian in the bulk.

Low-frequency states follow an Airy function distribution.

Model predictions agree with experimental data for glasses.

Abstract

Based on a description of an amorphous solid as a collection of coupled nanosize molecular clusters referred as basic blocks, we analyse the statistical properties of its Hamiltonian. The information is then used to derive the ensemble averaged density of the vibrational states (non-phonon) which turns out to be a Gaussian in the bulk of the spectrum and an Airy function in the low frequency regime. A comparison with experimental data for five glasses confirms validity of our theoretical predictions.