On the Relation Between the Boson Peak and the Vibrational Phases in Glasses

The boson peak is a vibrational feature commonly found in glassy and disordered systems described as the deviation from the scaling of the Debye model ($g(E)\propto E^2$). Despite much interest, the microscopic nature of the vibrations is only anecdotally discussed. Here we report how the boson peak appears in conjunction with a crossover from localized to extended but non-wave-like and coincide with a maximum in phase coherence and spatial periodicity. Our analyses provide new insights into the microscopic origin of the boson peak across a wide range of glasses.