Local resonator stimulated polarization transition in metamaterials and the formation of topological interface states

Developing the acoustic-elastic analogy of a topological insulator has attracted extensive research attention in recent years. Designs developed in the literature strongly rely on reforming the host structure of a system to achieve topology transition. In this article, an innovative topological metamaterial is presented. Unlike topological phononic crystals, the proposed topological metamaterial has a uniform host structure without any phononic crystal features. The band inversion and polarization transition are achieved by manipulating the design of local resonators. It has been proven that by changing the coupling spring constant of local resonators, the mode topologies at the bound states associated with the band gaps can be converted. Three polarization transition points have been found from the bound evolution analysis, and all of them possess the capability of stimulating topological interface states in the corresponding band gaps. The Zak phase calculations have further ascertained the prediction about the topological interface states. The band structure and transmittance spectrum of a supercell lattice of the proposed topological metamaterial have been examined. The topological interface states, as well as the energy localization effects, have been successfully observed in all the three band gaps. The proposed metamaterial brings the convenience of creating topological interface states by carefully manipulating the local resonators only. The methodology presented in this work is thus of practical significance in transforming existing structures into topological systems without revising them.