Disorder-induced vibrational anomalies from crystalline to amorphous solids

The origin of the boson peak—an excess of the density of states over Debye's model in glassy solids—is still under intense debate, among which some theories and experiments suggest that the boson peak is related to a van-Hove singularity. Here we show that the boson peak and the van-Hove singularity are well separated entities by measuring the vibrational density of states of a two-dimensional granular system, where the packings are tuned gradually from a crystalline to polycrystalline structure and toward an amorphous material. We observe the coexistence of the boson peak and the van-Hove singularities being well separated in the polycrystals. The van-Hove singularities gradually shift to higher-frequency values while broadening their shape. They disappear completely when the structural disorder becomes sufficiently high. By analyzing the system at different degrees of disorder, we find that the boson peak is associated with spatially uncorrelated random flucutations of the shear modulus, whereas the smearing of the van-Hove singularities is associated with spatially correlated fluctuations of the shear modulus.