Universal relationship of boson peak with Debye level and Debye-Waller factor in disordered materials

Abstract

Due to the topological disorder, glass displays an anomalous vibrational density of states beyond the Debye model, i.e., formation of boson peaks, which is fundamental for understanding many glassy physical properties. However, the understanding of the boson peak remains notoriously complex and is a topic of hot debate. Here we report a universal quantitative relation between boson peak intensity and the Debye level of transverse phonons in different glasses, confirming the intrinsic link between boson peaks and transverse phonons. Moreover, an equation is derived for the boson peak intensity and Debye-Waller factor, indicating that boson peaks are fundamentally determined by the Debye-Waller factor. These findings could clarify some controversial issues and reveal a common basis for high-frequency boson peak dynamics $(\ensuremath{\sim}{10}^{12}\phantom{\rule{0.28em}{0ex}}\mathrm{Hz})$, short-time $\ensuremath{\beta}$ processes $({10}^{3}\ensuremath{\sim}{10}^{6}\phantom{\rule{0.28em}{0ex}}\mathrm{Hz})$, and long-time $\ensuremath{\alpha}$ processes $({10}^{\ensuremath{-}4}\ensuremath{\sim}{10}^{3}\phantom{\rule{0.28em}{0ex}}\mathrm{Hz})$ in disordered materials.