Acoustic higher-order topological insulators

Abstract

The concept of topological insulators has recently been transferred into acoustics by designing and constructing acoustic analogues of topological insulators, which nowadays are widely called as “acoustic topological insulators.” As dictated by the conventional bulk-boundary correspondence principle, the topologically nontrivial band structure in a d-dimensional topological insulator shall support (d – 1)-dimensional boundary states. However, recent theories have proposed a new class of higher-order topological insulators which do not satisfy the conventional bulk-boundary correspondence principle. For example, a two-dimensional (2-D) second-order topological insulator does not support one-dimensional (1-D) topological edge states, but has topologically protected zero-dimensional (0D) corner states. Three-dimensional (3-D) second-order and third-order topological insulators do not have 2-D topological surface states, but host 1-D hinge states on edges, and 0D corner states on corners. Here we introduce our recent results of designing and constructing acoustic higher-order topological insulators. Both second-order and third-order topological insulators are discussed in a platform of acoustic metamaterials. By direct acoustic measurement, we demonstrate the acoustic bandgap and the in-gap corner states and hinge states.