A flat-band perspective on the boson peak in amorphous solids

Abstract

The boson peak is a characteristic anomaly of amorphous solids broadly defined as a low-energy excess in the density of states and heat capacity compared to the textbook predictions of Debye theory. The origin of this anomaly has long been the subject of ongoing debate and remains a topic of active controversy. We propose that the boson peak may have a defining dynamical feature: the accumulation of vibrational spectral weight within a narrow frequency window that is only weakly dependent on wavevector. In this perspective, the boson peak reflects a flat or weakly dispersive band in the dynamical structure factor rather than a propagating excitation. We revisit both experimental and simulation data from the literature through this lens and conduct further simulations in 2D and 3D amorphous systems. Taken together, these analyses provide compelling converging evidence for this interpretation and sharply constrain the space of viable theoretical descriptions of the boson peak.

Figures (17)

• Figure 1: (a) Schematic representation of the boson peak as conventionally identified from a peak in the reduced vibrational density of states. (b) Schematic dynamic structure factor illustrating the viewpoint that the boson peak is associated with a flat band in $S(q,\omega)$, a perspective that provides constraints on theoretical descriptions of its physical origin.
• Figure 2: Transverse dynamic structure factor $S_T(q,\omega)$ of simulated 3DIPL glasses. (a) 1D representation along constant $q$ cuts; (b) 2D color map. Vertical red and orange lines indicate the BP frequency as obtained from the reduced density of states. Blue dotted and green dashed lines correspond respectively to the contribution of the flat dispersionless mode and the transverse acoustic phonons for $q=2.427$. Figure adapted with permission from Ref. tanakaPRR.
• Figure 3: Transverse dynamic structure factor for silica glass (a) and a high-connectivity harmonic spheres (HSH) model (b). The black solid curve is the linear dispersion of the acoustic phonon. The horizontal cyan solid line indicates the BP frequency. Figures adapted from Ref. mizuno2025bosonpeakcovalentnetwork with permission from the authors.
• Figure 4: The transverse dynamic structure factor $S_T(q,\omega)$ for different wave vectors and its two-dimensional contour plot for the 3D-KA binary mixture (a)-(b); the 3D-attractive system with $x_c = 1.5$(c)-(d); the 3D-attractive system with $x_c = 1.8$(e)-(f); the 2D-attractive system with $x_c = 1.5$(g)-(h); the 2D-attractive system with $x_c = 1.8$(i)-(j); the $\mathrm{Cu_{50}Zr_{50}}$ model (k)-(l). Dashed lines correspond to the linear dispersion relation $\omega = vq$. The vertical bands identify the BP frequency extracted independently from the vibrational density of states.
• Figure 5: (a) An image of the experimental system in Ref. PhysRevB.98.174207 showing the random packing of bi-disperse photoelastic disks. (b) The transverse correlation function as a function of the frequency $\omega$ for different values of the wavevector $k$. Solid lines are the fits combining the DHO phononic contribution \ref{['DHOfit']} and the non-phononic one \ref{['nph']}. The two contributions are shown independently with dotted and dashed lines. The vertical grey bar indicates the BP frequency. (c) The reduced density of states showing the emergence of a BP anomaly around $\omega_{\text{BP}}\approx 0.5$ (vertical grey bar). Data are taken with permission of the authors in Ref. PhysRevB.98.174207.