Microscopic origin of Boson peak in two-dimensional scalar spring network

We proposed a non-analytic model to explain the microscopic origin of the anomalous vibrational density of states (DOS), the Boson peak (BP), in amorphous solids based on the scalar dynamical matrix of a network with springs and nodes. We argue that disorder can be classified into two factors: fluctuation of spring strength and fluctuation of coordination numbers (the number of springs connected to a node). The results suggest that BP originates from fluctuation of coordination numbers, while the fluctuation of spring strength only contributes to the effect of damping and has very limited effect on low frequency DOS. This work converts complexity into simplicity and provides a direct answer to the puzzle of the microscopic origin of BP in amorphous solids.