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

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.