Dual-band topological states in actively convertible metamaterials with parallel platforms

Abstract

Topological propagation in elastic wave metamaterials is widely investigated due to the superior transmission performance but most studies are focused on a single frequency range. This work proposes the elastic wave metamaterial composed of parallel platforms with active control, which illustrates topological interface states in two separate frequency ranges. In order to show basic features, band gap properties and localized modes in the rectilinear structure are considered at first. Then, the honeycomb system is investigated to present dynamic behaviors with two Dirac cones which belong to two frequency regions. The topological phase transition is identified by the eigenstates and topological invariants, respectively. Based on the k·p perturbation method, the effective Hamiltonian of two Dirac degeneracies is derived. Due to different stiffness of two platforms within a unit cell, two nontrivial degeneracies will be destroyed. Two band gaps support the interface states with topological protection and robust characteristic between lattices with different valley Hall phases. In addition, the topological transmission can be flexibly tuned by the active control system, which is supported by experiments. This work wishes to provide new designs of mechanical metamaterial with multiple functions.