Correlation between the boson peak frequency and transverse Ioffe-Regel limit in four-dimensional structural glasses

TL;DR

The paper investigates whether the commonly observed coincidence between the boson peak frequency $\omega_{\rm BP}$ and the transverse Ioffe-Regel limit $\omega_{\rm IR,T}$ in 2D/3D glasses holds in higher dimensions. Using four-dimensional structural glasses with IPL and spring-like potentials, the authors compute the vibrational density of states and the transverse attenuation to extract $\omega_{\rm BP}$ and $\omega_{\rm IR,T}$. Their central finding is that $\omega_{\rm IR,T}$ exceeds $\omega_{\rm BP}$ in 4D, and the two frequencies are not simply proportional, with an effective scale factor $A$ around 2–3 depending on the model. This demonstrates a dimension-dependent breakdown of the boson peak–Ioffe-Regel coincidence and calls for revised theoretical frameworks that account for spatial dimensionality.

Abstract

The emergence of excess vibrational modes over the Debye prediction, typically manifested as the well-known boson peak in the plot of vibrational density of states scaled by the Debye prediction, has become a hallmark of various amorphous solids. The origin of the boson peak has been attracting considerable attention but is still under debate. A popular view is that the position of the boson peak coincides well with that of the Ioffe-Regel limit for transverse modes in both two- and three-dimensional glasses, which is primarily derived from simulation studies of model structural glasses. However, it remains unknown whether the proposed coincidence could be generalized to higher spatial dimensions, and addressing this could contribute to the advancement of relevant phenomenological theories. Here, we find that the transverse Ioffe-Regel limit frequency is higher than and not proportional to the boson peak frequency in our studied four-dimensional glasses. Our findings therefore suggest that the proposed coincidence between the boson peak frequency and the transverse Ioffe-Regel limit depends on spatial dimensions, which was not anticipated previously.

Figures (5)

• Figure 1: (a) Illustration of velocity correlation functions $C(k,t)$ at wavevectors $k=0.334$ and $k=0.579$ in 4D glasses. (b) Time dependence of the envelope $E(k,t)$ determined by the peaks in the absolute value of $C(k,t)$ shown in (a). Data in (a) and (b) are obtained at $\rho=0.8$ in 4D IPL-12 glasses.
• Figure 2: Reduced VDOS $D(\omega)/\omega$ in (a) and transverse sound attenuation coefficient $\Gamma_{\rm T} (\omega)$ in (b) at $\rho=1$ in 2D IPL-12 glasses with $N$ ranging from 20000 to 50000. Reduced VDOS $D(\omega)/\omega^2$ in (c) and transverse sound attenuation coefficient $\Gamma_{\rm T} (\omega)$ in (d) at $\rho=1$ in 3D IPL-12 glasses with $N$ ranging from 48000 to 192000. The lines passing through data points of $\Gamma_{\rm T} (\omega)$ in (b) and (d) are obtained from polynomial fits.
• Figure 3: Reduced VDOS $D(\omega)/\omega^3$ in (a) and (c) and transverse sound attenuation coefficient $\Gamma_{\rm T} (\omega)$ in (b) and (d) in 4D IPL-10 glasses. Data in (a) and (b) are obtained at $\rho=0.8$, and (c) and (d) are at $\rho=1.5$. The lines passing through data points of $\Gamma_{\rm T} (\omega)$ in (b) and (d) are obtained from polynomial fits.
• Figure 4: Reduced VDOS $D(\omega)/\omega^3$ in (a) and (c) and transverse sound attenuation coefficient $\Gamma_{\rm T} (\omega)$ in (b) and (d) in 4D glasses with spring-like potentials. Data in (a) and (b) are calculated at $\rho=2$ in HARM glasses, and (c) and (d) are at $\rho=1.5$ in HERTZ glasses. The lines passing through data points of $\Gamma_{\rm T} (\omega)$ in (b) and (d) are obtained from polynomial fits.
• Figure 5: Correlation between the boson peak frequency $\omega_{\rm BP}$ and the transverse Ioffe-Regel limit frequency $\omega_{\rm IR,T}$. Some 2D and 3D data shown here are from Ref. bp_shintani_NM2008. The values of $\omega_{\rm BP}$ and $\omega_{\rm IR,T}$ for each 4D system shown here are listed in Table. \ref{['table']}