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

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.

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• Non-Hermitian waves in a continuous periodic model and application to photonic crystals
• Observation of dynamical degeneracy splitting for the non-Hermitian skin effect
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• Demonstration of acoustic high-order Stiefel-Whitney semimetal in bilayer graphene sonic crystals
• Non-Hermitian Squeezed Polarons
• Experimental observation of non-Hermitian higher-order skin interface states in topological electric circuits
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• Always-Real-Eigenvalued Non-Hermitian Topological Systems
• Generalized bulk-boundary correspondence in periodically driven non-Hermitian systems
• Observation of a topological edge state stabilized by dissipation
• Experimental realization of stable exceptional chains protected by non-Hermitian latent symmetries unique to mechanical systems
• Non-Hermitian Second-Order Topological Phases and Bipolar Skin Effect in Photonic Kagome Crystals
• Exact Solutions Disentangle Higher-Order Topology in 2D Non-Hermitian Lattices
• Engineering non-Hermitian Second Order Topological Insulator in Quasicrystals
• Engineering topologically protected zero-dimensional interface end states in antiferromagnetic heterojunction graphene nanoflakes
• Topological quantum transition driven by charge-phonon coupling in higher-order topological insulators
• Acoustic circular dichroism in a three-dimensional chiral metamaterial
• Non-Hermitian Quantum Fractals
• Intrinsic-perturbation induced anomalous higher-order boundary states in non-Hermitian systems
• Multiple topological transitions and spectral singularities in non-Hermitian Floquet systems
• Tunable corner states in topological insulators with long-range hoppings and diverse shapes
• Observation of dislocation-induced topological modes in a three-dimensional acoustic topological insulator
• Topology and criticality in non-Hermitian multimodal optical resonators through engineered losses
• An unusual phase transition in a non-Hermitian Su-Schrieffer-Heeger model
• Observation of Embedded Topology in a Trivial Bulk via Projective Crystal Symmetry
• Unveiling Topological Hinge States in the Higher-Order Topological Insulator WTe${}_2$ Based on the Fractional Josephson Effect
• Non-Hermitian Higher-Order Dirac Semimetals
• Quasiperiodic Skin Criticality in an Exactly Solvable Non-Hermitian Quasicrystal
• Non-Hermitian Higher-Order Weyl Semimetals