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.

References in corpus (53)

• Topological Insulators
• Topological insulators and superconductors
• Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Edge states and topological invariants of non-Hermitian systems
• Quantized Electric Multipole Insulators
• Photonic Analogue of Two-dimensional Topological Insulators and Helical One-Way Edge Transport in Bi-Anisotropic Metamaterials
• Imaging topological edge states in silicon photonics
• Scheme to Achieve Silicon Topological Photonics
• Higher-Order Topological Insulators
• Colloquium: Topological Band Theory
• Robust optical delay lines via topological protection
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Topological Acoustics
• Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems
• Acoustic topological insulator and robust one-way sound transport
• Anomalous edge state in a non-Hermitian lattice
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Topolectrical circuit realization of topological corner modes
• Reflection symmetric second-order topological insulators and superconductors
• Observation of a phononic quadrupole topological insulator
• Observation of topological valley transport of sound in sonic crystals
• Higher-order topological insulators and semimetals on the breathing Kagome and pyrochlore lattices
• Acoustic higher-order topological insulator on a Kagome lattice
• Zoo of quantum-topological phases of matter
• Demonstration of a quantized microwave quadrupole insulator with topologically protected corner states
• Anatomy of skin modes and topology in non-Hermitian systems
• Non-Hermitian robust edge states in one-dimension: Anomalous localization and eigenspace condensation at exceptional points
• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• All-Si Valley-Hall Photonic Topological Insulator
• Topological protection of photonic mid-gap cavity modes
• Topologically-protected refraction of robust kink states in valley photonic crystals
• Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide
• Hybrid higher-order skin-topological modes in non-reciprocal systems
• Second-Order Topological Phases in Non-Hermitian Systems
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• New topological invariants in non-Hermitian systems
• Experimental Realization of Acoustic Chern Insulator
• Higher-order topological corner states induced by gain and loss
• Non-Hermitian extensions of higher-order topological phases and their biorthogonal bulk-boundary correspondence
• Observation of an acoustic octupole topological insulator
• Demonstration of a quantized acoustic octupole topological insulator
• Non-Hermitian higher-order topological states in nonreciprocal and reciprocal systems with their electric-circuit realization
• Spin and orbital angular momenta of acoustic beams
• Non-Hermitian boundary and interface states in nonreciprocal higher-order topological metals and electrical circuits
• Topological non-Hermitian origin of surface Maxwell waves
• Observation of acoustic spin
• Constant-pressure sound waves in non-Hermitian disordered media
• Transverse spin and surface waves in acoustic metamaterials
• Digitally virtualized atoms for acoustic metamaterials
• Klein-Gordon representation of acoustic waves and topological origin of surface acoustic modes
• Wannier-type photonic higher-order topological corner states induced solely by gain and loss
• Edge modes in 2D electromagnetic slab waveguides: analogues of acoustic plasmons

Cited by in corpus (35)

• Classical higher-order topological insulators
• Topological acoustics
• Roadmap on structured waves
• Hybrid skin-topological modes without asymmetric couplings
• Projectively enriched symmetry and topology in acoustic crystals
• Dimensional transmutation from non-Hermiticity
• Non-Hermitian waves in a continuous periodic model and application to photonic crystals
• Observation of dynamical degeneracy splitting for the non-Hermitian skin effect
• Universal competitive spectral scaling from the critical non-Hermitian skin effect
• 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
• Topological energy braiding of the non-Bloch bands
• 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