Dimensional hierarchy of higher-order topology in three-dimensional sonic crystals

Abstract

Topological phases of matter have been extensively studied for their intriguing bulk and edge properties. Recently, higher-order topological insulators with boundary states that are two or more dimensions lower than the bulk states, have been proposed and investigated as novel states of matter. Previous implementations of higher-order topological insulators were based on two-dimensional (2D) systems in which 1D gapped edge states and 0D localized corner states were observed. Here we theoretically design and experimentally realize a 3D higher-order topological insulator in a sonic crystal with a large topological band gap. We observe the coexistence of third-, second- and first-order topological boundary states with codimension three, two and one, respectively, indicating a dimensional hierarchy of higher-order topological phenomena in 3D crystals. Our acoustic metamaterial goes beyond the descriptions of tight-binding model and possesses a band structure which automatically breaks the chiral symmetry, leading to the separation of bulk, surface, hinge and corner states. Our study opens a new route toward higher-order topological phenomena in three-dimensions and paves the way for topological wave trapping and manipulation in a hierarchy of dimensions in a single system.

arXiv comment29 pages, 4 figures

References in corpus (43)

• Topological Insulators
• Topological insulators and superconductors
• Topological Photonics
• Classification of topological quantum matter with symmetries
• Possible Realization of Directional Optical Waveguides in Photonic Crystals with Broken Time-Reversal Symmetry
• Topological Crystalline Insulators
• 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
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Topological Acoustics
• Acoustic topological insulator and robust one-way sound transport
• $(d-2)$-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
• Higher-Order Topology in Bismuth
• Demonstration of a quantized microwave quadrupole insulator with topologically protected corner states
• Quantization of fractional corner charge in $C_n$-symmetric higher-order topological crystalline insulators
• Visualization of higher-order topological insulating phases in two-dimensional dielectric photonic crystals
• Topological protection of photonic mid-gap cavity modes
• Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide
• Second-order photonic topological insulator with corner states
• Observation of second-order topological insulators in sonic crystals
• Topologically protected acoustic helical edge states and interface states in strongly coupled metamaterial ring lattices
• Topological negative refraction of surface acoustic waves in a Weyl phononic crystal
• Second-order topological insulators and superconductors with an order-two crystalline symmetry
• Synthetic gauge fields and Weyl point in Time-Reversal Invariant Acoustic Systems
• Topological Sound
• Valley Topological Phases in Bilayer Sonic Crystals
• Realization of an acoustic third-order topological insulator
• Accidental degeneracy and topological phase transitions in two-dimensional core-shell dielectric photonic crystals
• Observation of acoustic Landau quantization and quantum-Hall-like edge states
• Topological light-trapping on a dislocation
• Axial-field-induced chiral channels in an acoustic Weyl system
• Topological triply-degenerate point with double Fermi arcs
• Experimental Observation of Acoustic Weyl Points and Topological Surface States
• Boundaries of boundaries: a systematic approach to lattice models with solvable boundary states of arbitrary codimension

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• Nonlinear imaging of nanoscale topological corner states
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• $C_n$-symmetric higher-order topological crystalline insulators in atomically thin transition-metal dichalcogenides
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• Extended Haldane model -- a modern gateway to topological insulators
• Dynamical transition in non-Hermitian Chern insulator
• Floquet first- and higher-order topological superconductors: A review