Localization, disorder and boson peak in an amorphous solid

TL;DR

This study uses classical density functional theory to show that a specific level of mass localization in amorphous solids is crucial for the emergence of the boson peak, linking disorder and vibrational properties.

Contribution

It identifies a critical localization length in amorphous solids necessary for the boson peak, providing a theoretical framework connecting disorder and vibrational anomalies.

Findings

Boson peak requires an intermediate degree of mass localization.

A limiting localization length $ ext{l}_0$ exists below which the boson peak cannot occur.

More delocalized states do not exhibit the boson peak.

Abstract

We demonstrate using the classical density functional theory (DFT) model that an intermediate degree of mass localization in the amorphous state is essential for producing the boson peak. The localization length $\ell$ is identified from the width of the gaussian density profile in terms of which the inhomogeneous density n(x) of the solid is expressed in DFT. At a fixed average density, there exists a limiting value $\ell_0$ of $\ell$ signifying a minimum mass localization in the amorphous state. For more delocalized states ($\ell>\ell_0$) occurrence of boson peak is unfeasible.