Boson peak as a phenomenon participated by the vast majority of particles

Abstract

The origin of the excess vibrational density of states (DOS) beyond Debye's theory in amorphous solids (often referred to as the Boson peak) has been attributed to the presence of quasi-localized vibrational modes in recent years. However, by dispersing the total DOS onto each degree of freedom (DOF), the results of this report provide evidence that \(99.9\%\) of DOFs, and hence almost all particles, contribute to the Boson peak (BP). These results challenge the prevailing opinion that BP is contributed by a minority of particles and highlight its long-neglected global and collective origin.

Figures (1)

• Figure 1: a, The reduced total DOS obtained by $g(\omega)/\omega = -\mathrm{Im}[\mathrm{Tr}[G(\omega)]]$. The gray area indicates the position of BP around $\omega = 0.15$. b, The reduced local DOS on $8192$ DOFs obtained by $g_i(\omega)/\omega = -\mathrm{Im}[G_{ii}(\omega)]$. Colors are used to distinguish the $8192$ DOFs, and the gray area shows the position of BP. The inset shows an enlarged view of the near-zero region. All curves have been normalized by the global maximum value. c, Statistics of the coefficients of the second derivative $\partial^2 (-\mathrm{Im}[G_{ii}(\omega)])/ \partial \omega ^2$ in the low-frequency region. A positive coefficient indicates that the reduced local DOS has an upward trend and contributes to BP. $8184/8192$ of the second derivative coefficients are positive. The inset shows that $116/4096$ particles (in gray) have DOFs with reduced local DOS higher than $0.1$. All units are normalized according to the hidden energy unit in the Hessian matrix.