The transverse nature of the Boson peak: A rigidity theory approach

The transversal nature of the Boson peak in crystals and glasses is investigated by using a model inspired from rigidity theory of glasses. By tuning the rigidity of the network using second-neighbor interactions, we show that the transversal van Hove singularity – associated with the Boson peak – arises when the transverse dispersion branch touches for the first time the boundary of the first Brillouin zone, leading to an anomaly in the low frequency region. The frequency of the singularity is determined by the rigidity of the network. For the disordered version of the model, the singularity arises when the transversal dispersion branch touches the limit of a pseudo-Brillouin zone, suggesting that the Boson peak in glasses has a similar origin. Increasing rigidity shifts the position of the Boson peak towards high frequencies while its intensity decreases. This provides an important clue to understand pressure effects on the Boson peak in glasses and crystals.