Harmonic Vibrational Excitations in Disordered Solids and the "Boson Peak"

TL;DR

This study models disordered solids using coupled harmonic oscillators with fluctuating force constants, revealing a low-frequency peak in the vibrational density of states analogous to the boson peak in glasses, linked to system instability.

Contribution

It introduces a simplified oscillator model with spatially fluctuating force constants and demonstrates the emergence of a boson-peak-like feature near instability, supported by numerical and analytical methods.

Findings

Density of states matches between numerical and CPA methods.

Low-frequency peak appears near the instability threshold.

Peak is associated with extended, not localized, vibrational states.

Abstract

We consider a system of coupled classical harmonic oscillators with spatially fluctuating nearest-neighbor force constants on a simple cubic lattice. The model is solved both by numerically diagonalizing the Hamiltonian and by applying the single-bond coherent potential approximation. The results for the density of states $g(\omega)$ are in excellent agreement with each other. As the degree of disorder is increased the system becomes unstable due to the presence of negative force constants. If the system is near the borderline of stability a low-frequency peak appears in the reduced density of states $g(\omega)/\omega^2$ as a precursor of the instability. We argue that this peak is the analogon of the "boson peak", observed in structural glasses. By means of the level distance statistics we show that the peak is not associated with localized states.