Tight-binding model for torsional and compressional waves in high-quality coupled-resonator phononic metamaterials

A tight-binding theoretical model which describes the vibration properties of a new type of mechanical metamaterial, the coupled-resonator phononic metamaterial (CRPM), is developed. This metamaterial, composed of mechanical resonators coupled through finite phononic crystals, exhibits spectral properties analogue to those of crystalline atomic systems. The CRPMs obey a quantum tight-binding model when a normal mode frequency of the resonators lies within a bandgap of the finite phononic crystals. Analytical expressions for the dispersion relation and group velocity are obtained. The results suggest that almost any material described by the tight-binding model, of solid-state physics, can be emulated with CRPMs.