Acoustic corner states in topological insulators with built-in Zeeman-like fields

TL;DR

This paper demonstrates that a phononic crystal can host topological corner states analogous to those in electronic topological insulators with built-in Zeeman fields, providing a new platform for exploring HOTIs without complex magnetic doping.

Contribution

The study introduces a phononic crystal design that simulates the Kane-Mele model with intrinsic Zeeman-like fields, enabling observation of HOTI corner states without experimental magnetic field application.

Findings

Observation of gapped helical edge states in the phononic crystal

Detection of localized corner states within the energy gap

Contrast properties of corner states at different corners

Abstract

The higher-order topological insulators (HOTIs), with such as the topological corner states, emerge as a thriving topic in the field of topological physics. But few connections have been found for the HOTIs with the well explored first-order topological insulators described by the Z_2 index. However, most recently, a proposal asserts that a significant bridge can be established between the HOTIs and the Z_2 topological insulators. When subject to an in-plane Zeeman field, the corner states, the signature of the HOTIs, can be induced in a Z_2 topological insulator. Such Zeeman field can be produced, for example, by the ferromagnetic proximity effect or magnetic atom doping, which obviously involves the drastically experimental complexity. Here we show that, a phononic crystal, designed as a bilayer of coupled acoustic cavities, hosts exactly the Kane-Mele model with built-in in-plane Zeeman fields. We observe that the helical edge states along the zigzag edges are gapped, and the corner states, localized spatially at the corners of the samples, appear in the gap, confirming the effect induced by the Zeeman field. We further demonstrate the intriguing contrast properties of the corner states at the outer and inner corners in a hexagonal ring-shaped sample.