Anharmonicity, vibrational instability and Boson peak in glasses

TL;DR

This paper demonstrates that vibrational instability caused by weakly interacting modes, limited by anharmonicity, leads to the Boson peak in glasses and results in a universal vibrational density of states dependent on the Boson peak frequency.

Contribution

It introduces a universal model linking vibrational instability, anharmonicity, and the Boson peak, explaining the DOS reconstruction in glasses.

Findings

Vibrational instability creates the Boson peak in glasses.

The reconstructed DOS is universal and independent of anharmonicity.

DOS exhibits a ffff dependence at low frequencies.

Abstract

We show that a {\em vibrational instability} of the spectrum of weakly interacting quasi-local harmonic modes creates the maximum in the inelastic scattering intensity in glasses, the Boson peak. The instability, limited by anharmonicity, causes a complete reconstruction of the vibrational density of states (DOS) below some frequency $\omega_c$, proportional to the strength of interaction. The DOS of the new {\em harmonic modes} is independent of the actual value of the anharmonicity. It is a universal function of frequency depending on a single parameter -- the Boson peak frequency, $\omega_b$ which is a function of interaction strength. The excess of the DOS over the Debye value is $\propto\omega^4$ at low frequencies and linear in $\omega$ in the interval $\omega_b \ll \omega \ll \omega_c$. Our results are in an excellent agreement with recent experimental studies.