Phonons in supercooled liquids: a possible explanation for the Boson Peak

TL;DR

This paper proposes that the Boson peak in glasses results from a phase transition in the energy landscape, transitioning from phonon-supporting minima to saddle-dominated states, supported by numerical and theoretical analysis.

Contribution

It demonstrates a phase transition in the energy landscape of glasses explaining the Boson peak, supported by numerical spectra and Euclidean Random Matrix Theory.

Findings

Boson peak frequency decreases approaching the transition

Peak height diverges at the critical point

Numerical results align with theoretical predictions

Abstract

Glasses are amorphous solids, in the sense that they display elastic behaviour. In crystals, elasticity is associated with phonons, quantized sound-wave excitations. Phonon-like excitations exist also in glasses at very high frequencies (THz), and they remarkably persist into the supercooled liquid. A universal feature of these amorphous systems is the Boson peak: the vibrational density of states $g(\omega)$ has an excess over the Debye (squared frequency) law, seen as a peak in $g(\omega)/\omega^2$. We claim that this peak is the signature of a phase transition in the space of the stationary points of the energy, from a minima-dominated phase (with phonons) at low energy to a saddle-point dominated phase (without phonons). Here, by studying the spectra of inherent structures (local minima of the potential energy), we show that this is the case in a realistic glass model: the Boson peak moves to lower frequencies on approaching the phonon-saddle transition and its height diverges at the critical point. The numerical results agree with Euclidean Random Matrix Theory predictions on the existence of a sharp phase transition between an amorphous elastic phase and a phonon-free one.