Non-Hermitian route to higher-order topology in an acoustic crystal

He Gao,Jie Zhu,Baile Zhang,Haoran Xue,Tuo Liu,Zhongming Gu

doi:10.1038/s41467-021-22223-y

Abstract

Topological phases of matter are classified based on their Hermitian Hamiltonians, whose real-valued dispersions together with orthogonal eigenstates form nontrivial topology. In the recently discovered higher-order topological insulators (TIs), the bulk topology can even exhibit hierarchical features, leading to topological corner states, as demonstrated in many photonic and acoustic artificial materials. Naturally, the intrinsic loss in these artificial materials has been omitted in the topology definition, due to its non-Hermitian nature; in practice, the presence of loss is generally considered harmful to the topological corner states. Here, we report the experimental realization of a higher-order TI in an acoustic crystal, whose nontrivial topology is induced by deliberately introduced losses. With local acoustic measurements, we identify a topological bulk bandgap that is populated with gapped edge states and in-gap corner states, as the hallmark signatures of hierarchical higher-order topology. Our work establishes the non-Hermitian route to higher-order topology, and paves the way to exploring various exotic non-Hermiticity-induced topological phases.

Highlights

Topological phases of matter are classified based on their Hermitian Hamiltonians, whose real-valued dispersions together with orthogonal eigenstates form nontrivial topology
We present an experimental demonstration of a non-Hermitian route to higher-order topology in an acoustic crystal
Besides the intrinsic loss γ1, the resonators colored in red have an additional loss γ2 − γ1, which is introduced by drilling small holes on the sidewalls of resonators and filling these holes with acoustic absorbing materials

Summary

Introduction

Topological phases of matter are classified based on their Hermitian Hamiltonians, whose real-valued dispersions together with orthogonal eigenstates form nontrivial topology. Many photonic and acoustic TIs have been proposed to emulate the properties of TIs, especially in the classical analogs of quantum Hall[7,8,9,10], quantum spin Hall[11,12,13,14,15,16] and quantum valley Hall[17,18,19] effects While these classical topological systems follow the Hermitian topology definition, they are intrinsically nonHermitian because of the presence of loss and/or gain. With a carefully designed loss configuration, we experimentally identify the loss-induced topological bandgap through local acoustic measurement, followed by the direct observation of gapped edge states and mid-gap corner states, all of which are typical features of the higher-order topology. Our work provides the experimental demonstration of non-Hermiticity-induced higher-order topological phases

Methods

Results

Conclusion