Low-frequency topological edge and corner states in metamaterial sandwich plates

Recently, topological edge and corner states have attracted significant attention for their unprecedented wave manipulation capabilities. However, most existing advancements in elastic topological wave manipulation have been achieved in metamaterial monolayer plates, operating at high frequencies, which limits their practical applicability. To achieve low-frequency topological edge and corner states, this study presents an innovative topological metamaterial sandwich plate with compression-torsion coupling cores. Mimicking quantum valley Hall effect (QVHE), the gapless topological edge states are achieved by mismatching the sizes of two sandwich cores in C_3v-symmetric rhombic unit cell. To realize higher-order topological corner states, the C_6v-symmetric hexagonal unit cell is constructed by doubling rhombic unit cells. Leveraging quantum spin Hall effect (QSHE), gapped edge states are achieved, laying a critical foundation for the emergence of topological corner states. Eigenstate analysis of rhombic and square lattices presents that corner states can exist at both obtuse and acute angles. Symmetrical topological corner states and anti-symmetrical trivial corner states are observed, with the former being defect-immune. Transmission experiments demonstrate that vibration can be suppressed within the bulk and localized at the edges and corners, validating the presence of edge and corner states. This study could facilitate the development of elastic topological metamaterials and their application in vibration control, energy harvesting, signal sensing, etc.