Resonant coupling and the non-phononic flat band in amorphous solids

Recent experiments and simulations provide compelling evidence for the emergence of a non-phononic flat band in the dynamical structure factor of two- and three-dimensional amorphous solids. This feature has been suggested to be connected to the excess in the reduced vibrational density of states of glasses, commonly known as the boson peak, and displays several apparently universal characteristics. First, it is nearly dispersionless, with an energy close to the boson-peak frequency. Second, its intensity is negligible below a critical wave vector of the order of the first diffraction peak. Third, its reduced intensity exhibits a strong correlation with the static structure factor. Here, we revisit the resonant-coupling model, a single-mode harmonic realization of the soft-potential scenario in which acoustic phonons interact with single frequency quasi-localized vibrations. We show that, under minimal phenomenological assumptions, this framework naturally reproduces the main features of the observed flat band and clarifies its connection to the boson peak.