Higher-order topological states in locally resonant elastic metamaterials

Higher-order topological insulators (HOTIs), capable of hosting topological states over multiple dimensionalities, have received considerable attention recently, providing unprecedented platforms for robust wave manipulation. Aiming at applications of HOTIs for integrated sensing, energy harvesting, or control of structural vibration propagation, challenges remain in achieving topological states at low frequencies with ample flexibility and tunability. Here, we report the theoretical modeling and experimental realization of HOTIs in elastic locally resonant metamaterials (LRMs). By exploring the interplay between local resonance couplings and nontrivial band topology, a variety of higher-order topological corner states (TCSs) are constructed in deep sub-wavelength regime with high efficiency in energy confinement. More importantly, we reveal that the TCSs are dependent on localization mechanisms of interacting sites at interfaces, which endows our HOTIs with unique frequency-selective and dimension-switching abilities. We further design complex domain walls to demonstrate the TCSs can be selectively switched on at desired frequencies or geometric corners. Our findings not only offer effective routes for the design of deep sub-wavelength topological devices but also enrich the understandings of higher-order topological physics that can be extended to other classic systems.