Higher-order elastic topological insulators with reconfigurable route and tunable corner states

In recent years, topological insulators (TIs) have been introduced in classical wave systems as a new type of quantum material, opening up new ways and approaches for manipulating the propagation of acoustic/elastic waves. The excellent topological protection characteristics of the edge states and corner states in TIs have the potential to significantly impact various scientific and technological advancements, which has attracted widespread attention from the academic community. However, in the case of the majority of elastic TIs, the application is significantly restricted by the fixed interface path and corner state frequency once the structural materials are prepared. To overcome this limitation, this paper presents an elastic TI with reconfigurable topological paths. By manipulating the rotation angle of each unit cell's eccentric cylinder, it becomes feasible to achieve interface paths of any desired shape. Numerical simulation and experimental results indicate that elastic waves exclusively propagate along topological interface paths of different configurations, demonstrating excellent robustness to defects. Furthermore, by incorporating magnetorheological elastomers into the structure, it becomes possible to generate higher-order corner states by adjusting the width of the connected narrow bands. For a structure composed of nontrivial unit cells, it is possible to generate edge states as well as two distinct types of corner states. Elastic waves exhibit strong confinement to edges or corner points and have topological protection properties. By harnessing the magnetorheological effect, it becomes possible to overcome the limitations of traditional higher-order topological insulators, where the corner state frequency is fixed. This approach allows for active manipulation of the working frequency by applying different magnetic fields. Consequently, this research provides valuable insights and serves as a reference for designing intelligent elastic waveguide devices and energy harvesting devices.