Acoustic higher-order topological insulator on a Kagome lattice

TL;DR

This paper reports the first experimental realization of a second-order topological insulator in an acoustic metamaterial based on a breathing Kagome lattice, featuring shape-dependent topologically protected corner states.

Contribution

It introduces a new type of higher-order topological insulator with nontrivial bulk topology and shape-dependent corner states, expanding the understanding of topological phases in acoustic systems.

Findings

Corner states exist at acute-angled Kagome lattice corners.

Corner states depend on the shape, not just bulk topology.

First experimental realization of a higher-order TI in acoustics.

Abstract

High-order topological insulators (TIs) are a family of recently-predicted topological phases of matter obeying an extended topological bulk-boundary correspondence principle. For example, a two-dimensional (2D) second-order TI does not exhibit gapless one-dimensional (1D) topological edge states, like a standard 2D TI, but instead has topologically-protected zero-dimensional (0D) corner states. So far, higher-order TIs have been demonstrated only in classical mechanical and electromagnetic metamaterials exhibiting quantized quadrupole polarization. Here, we experimentally realize a second-order TI in an acoustic metamaterial. This is the first experimental realization of a new type of higher-order TI, based on a breathing Kagome lattice, that has zero quadrupole polarization but nontrivial bulk topology characterized by quantized Wannier centers (WCs). Unlike previous higher-order TI realizations, the corner states depend not only on the bulk topology but also on the corner shape; we show experimentally that they exist at acute-angled corners of the Kagome lattice, but not at obtuse-angled corners. This shape dependence allows corner states to act as topologically-protected but reconfigurable local resonances.