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

TL;DR

This paper demonstrates that deliberate loss (non-Hermiticity) in an acoustic crystal can induce higher-order topological phases, leading to observable corner states, thus expanding the understanding of topological matter beyond Hermitian systems.

Contribution

It experimentally shows that non-Hermitian effects, specifically loss, can induce higher-order topological phases in acoustic materials, a novel approach in topological physics.

Findings

Identification of a topological bulk bandgap with corner states

Experimental realization of non-Hermitian higher-order topological insulator

Loss-induced hierarchy in topological states

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.