Demonstration of a 3rd order hierarchy of topological states in a three-dimensional acoustic metamaterial (Conference Presentation)

Abstract

Higher-order topological (HOT) states are topological states localized in more than one dimension of a D-dimensional system. In the recent years, HOT states have been shown to exist in classical wave-systems such as photonics and acoustics and have been used to explore a host of topological phenomena that have typically been associated with condensed matter systems. In our work, we construct the 3D acoustic metamaterial with HOT states through a rapid prototyping process and manufacture the individual metaatoms and metamolecules, which can then be snapped together to form 3D metamaterials with complex geometries. The assembled 3D topological metamaterial represents the acoustic analogue of the pyrochlore lattice with acoustic modes strongly bound to the individual resonant cavities and a design that only allows for nearest neighbor coupling. This provides us with the framework to explore the topological nature of the structure in a semi-analytical way (tight-binding model) while comparing it to the first-principles finite element method (FEM) model, and then comparing both theoretical results to the experiment. Consistent with the models, we observe the third-order (0-D) topological corner states along with second-order (1D) edge states and first-order (2D) surface states within the same topological bandgap, thus establishing a full hierarchy of HOT states in three dimensions. Additionally, we experimentally measure the field profile of each topological mode, which are in excellent agreement with the numerically calculated profiles of the HOT states.