Anharmonicity, vibrational instability and Boson peak in glasses

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 $ω_c$, 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, $ω_b$ which is a function of interaction strength. The excess of the DOS over the Debye value is $\proptoω^4$ at low frequencies and linear in $ω$ in the interval $ω_b \ll ω\ll ω_c$. Our results are in an excellent agreement with recent experimental studies.