Tunable frequency response of topologically protected interface modes for membrane-type metamaterials via voltage control

Abstract

The analogy of quantum spin Hall effect in phononic fields has received enormous attentions these years. A significant hallmark of quantum spin Hall effect is that it can support interface modes that are protected by topology and robust to structural disturbance. However, researches on this topic are often limited to the passive structures that manifest topologically protected interface modes at fixed and narrow frequency ranges. In view of the shortage of non-passive topological metamaterial systems, this work has a primary motive to study the active control of quantum spin Hall effect in soft membrane-type metamaterials (MAM). After introducing sandwiched membrane-type acoustic metamaterials, the plane wave expansion method is adopted to analytically capture the system dispersion properties. A finite element model is further developed and a very good convergence with analytical result is presented. Further, by adjusting locations of spraying discs in the honeycomb lattice without violating the C6v symmetry, topological phase inversion is observed around a double Dirac cone at the center of the Brillouin zone, separating the topologically trivial state from the nontrivial counterpart. The topologically protected interface modes (TPIMs) around the interface between metamaterials of trivial and nontrivial states are observed. Additionally, to actively control working frequency of the TPIM, an electrical voltage that lies within the locking-up limit is applied to MAM. It is concluded that the topological interface state and the topological bandgaps are very sensitive to the applied voltage, while the system localization behavior is not influenced by the voltage. Utilizing this topologically protected interface state analysis, a straight path and a zig-zag path are designed to control wave propagation in the structure. Conclusively, a voltage-controlled topological metamaterial system is designed to broaden the working frequency range of TPIM.