Tunable band gap in distorted square lattice’s phonon spectrum

The multi-body system’s elasticity and vibrational behavior is an old topic. The conventional method to study this issue is to transform a multi-body system to an abstracted network model consisting of nodes connected by central-force springs. In recent years, abnormal mechanical responses, including negative Poisson ratio, vanishing shear modulus, non-trivial topological characteristics, are discovered in such network systems making this topic be with lasting charms. In this paper, we investigate the vibrational modes of a series of distorted square lattice networks. The distorted degree for this network is only characterized by one parameter, the twisting angle θ. By studying their phonon spectrums, we find a band gap between the two lowest modes of the distorted square lattice. The gap width is linearly correlated to θ, and the gap will be closed when θ reaches a specific value. Our results may find applications in device protection and energy harvesting