Classical higher-order topological insulators

Abstract

Topological states nurtures the emergence of devices with unprecedented functions in photonics, plasmonics, acoustics and phononics. As one of the recently discovered members, higher-order topological insulators (HOTIs) have been increasingly explored, featuring lower-dimensional topological boundary states, leading to rich mechanisms for topological manipulation, guiding and trapping of classical waves. Here, we provide an overview of current developments of HOTIs in classical waves including basic principles, unique physical properties, various experimental realizations, novel phenomena and potential applications. Based on these discussions, we remark on the trends and challenges in this field and the impacts of higher-order topology on other research fields.

21 pages, 4 figures

References in corpus (38)

• Topological Photonics
• Two-Dimensional Material Nanophotonics
• Topological Crystalline Insulators
• Scheme to Achieve Silicon Topological Photonics
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Topological Acoustics
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Reflection symmetric second-order topological insulators and superconductors
• Higher-order topological insulators and semimetals on the breathing Kagome and pyrochlore lattices
• Visualization of higher-order topological insulating phases in two-dimensional dielectric photonic crystals
• Direct observation of corner states in second-order topological photonic crystal slabs
• Novel Topological Phase with Zero Berry Curvature
• Topological quantum matter in synthetic dimensions
• Photonic crystal nanocavity based on a topological corner state
• Higher-order Topology of Axion Insulator EuIn${}_2$As${}_2$
• Acoustic realization of quadrupole topological insulators
• Low-threshold topological nanolasers based on second-order corner state
• Surface State Magnetization and Chiral Edge States on Topological Insulators
• Realization of an acoustic third-order topological insulator
• Higher-Order Weyl Semimetals
• Non-Hermitian route to higher-order topology in an acoustic crystal
• Higher-order Weyl Semimetals
• Observation of a phononic higher-order Weyl semimetal
• Topolectrical-circuit octupole insulator with topologically protected corner states
• Higher-order topological phases in tunable $C_3$-symmetric photonic crystals
• Majorana-like zero modes in Kekulé distorted sonic lattices
• Cavity Quantum Electrodynamics with Second-Order Topological Corner State
• Braiding of Majorana corner states in electric circuits and its non-Hermitian generalization
• Evidence for Helical Hinge Zero Modes in an Fe-Based Superconductor
• Observation of symmetry protected zero modes in topolectrical circuits
• Plasmon-polaritonic quadrupole topological insulators
• Spin-orbit-parity coupled superconductivity in topological monolayer WTe${}_2$
• Second-order topological corner states with ultracold atoms carrying orbital angular momentum in optical lattices
• Nonlinear higher-order polariton topological insulator
• Wannier-type photonic higher-order topological corner states induced solely by gain and loss
• Fractional Chiral Hinge Insulator
• Hinge Magnons from Non-collinear Magnetic Order in Honeycomb Antiferromagnet
• Protecting Quantum Superposition and Entanglement with Photonic Higher-Order Topological Crystalline Insulator

Cited by in corpus (137)

• Topological acoustics
• Applications of Bound States in the Continuum in Photonics
• Tailoring Structure-borne Sound Through Bandgap Engineering in Phononic Crystals and Metamaterials: A Comprehensive Review
• Controlling mass and energy diffusion with metamaterials
• Experimental realization of single-plaquette gauge flux insertion and topological Wannier cycles
• Acoustic Möbius insulators from projective symmetry
• Photonic quadrupole topological insulator using orbital-induced synthetic flux
• A Universal Mirror-stacking Approach for Constructing Topological Bound States in the Continuum
• Second Order Topological Insulator State in Hexagonal Lattices and its Abundant Material Candidates
• Kekule Lattice in Graphdiyne: Coexistence of Phononic and Electronic Higher-Order Band Topology
• Field-Tunable One-Sided Higher-Order Topological Hinge States in Dirac Semimetals
• Observation of nonlinear disclination states
• Topological thermal transport
• Realization of a Z classified chiral-symmetric higher-order topological insulator in a coupling-inversion acoustic crystal
• Higher-order topological states mediated by long-range coupling in $D_4$-symmetric lattices
• Large-area quantum-spin-Hall waveguide states in a three-layer topological photonic crystal heterostructure
• Non-Hermitian higher-order topological superconductors in two-dimension: statics and dynamics
• Higher-order topological phases in crystalline and non-crystalline systems: a review
• Multifrequency and multimode topological waveguides in a Stampfli-triangle photonic crystal with large valley Chern numbers
• Floquet Weyl semimetal phases in light-irradiated higher-order topological Dirac semimetals
• Acoustic corner states in topological insulators with built-in Zeeman-like fields
• Realization of Surface-Obstructed Topological Insulators
• Ultra-sensitive integrated circuit sensors based on high-order nonHermitian topological physics
• An operator-based approach to topological photonics
• Observation of Topological Corner State Arrays in Photonic Quasicrystals
• Observation of $\pi$ solitons in oscillating waveguide arrays
• Topological photonic crystal fibers based on second-order corner modes
• Systematic generation of the cascade of anomalous dynamical first and higher-order modes in Floquet topological insulators
• Chiral edge modes in evolutionary game theory: a kagome network of rock-paper-scissors
• Higher-order topological Anderson insulators in quasicrystals
• Observation of nonlinear fractal higher-order topological insulator
• Local markers for crystalline topology
• Thouless Pumps and Bulk-Boundary Correspondence in Higher-Order Symmetry-Protected Topological Phases
• Observation of Large-Number Corner Modes in $\mathbb{Z}$-class Higher-Order Topolectrical Circuits
• Generalized bulk-boundary correspondence in periodically driven non-Hermitian systems
• Dynamical construction of Quadrupolar and Octupolar topological superconductors
• Nonlinear photonic disclination states
• Generation of higher-order topological insulators using periodic driving
• A robust and tunable Luttinger liquid in correlated edge of transition-metal second-order topological insulator Ta${}_2$Pd${}_3$Te${}_5$
• Unified characterization for higher-order topological phase transitions
• Sublattice-enriched tunability of bound states in second-order topological insulators and superconductors
• Wannier Function Methods for Topological Modes in 1D Photonic Crystals
• Customizing pseudospin unidirectional states of acoustic and electromagnetic waves in two-dimensional phoxonic topological insulators via multi-objective strategies
• Vortex solitons in topological disclination lattices
• Non-Hermitian Second-Order Topological Phases and Bipolar Skin Effect in Photonic Kagome Crystals
• Dynamical bulk boundary correspondence and dynamical quantum phase transitions in higher order topological insulators
• Density-driven higher-order topological phase transitions in amorphous solids
• Observation of nonlinearity-controlled switching of topological edge states
• Topological properties of two-dimensional photonic square lattice without $C_4$ and $M_{x(y)}$ symmetries
• Exact Solutions Disentangle Higher-Order Topology in 2D Non-Hermitian Lattices
• Engineering non-Hermitian Second Order Topological Insulator in Quasicrystals
• Observation of squeezed Chern insulator in an acoustic fractal lattice
• Non-Hermitian second-order topological superconductors
• Experimental quantum simulation of non-Hermitian dynamical topological states using stochastic Schrödinger equation
• Floquet second-order topological Anderson insulator hosting corner localized modes
• Efficient Design of Helical Higher-Order Topological Insulators in 3D Elastic Medium
• Mirror real Chern insulator in two and three dimensions
• Dirac cones and higher-order topology in quasi-continuous media
• Dynamical Detection of Topological Spectral Density
• Topological solitonic macromolecules
• Observation of gapless corner modes in synthetic translation dimensions
• Observation of Dual-band Topological Corner Modes in Acoustic Kagome Lattice with Long-range Interactions
• Tailoring Quadrupole Topological Insulators with Periodic Driving and Disorder
• Multiple higher-order topological phases with even and odd pairs of zero-energy corner modes in a $C_3$ symmetry broken model
• Realizing and detecting Stiefel-Whitney insulators in an optical Raman lattice
• Time evolution of Majorana corner modes in Floquet second-order topological superconductor
• Generating many Majorana corner modes and multiple phase transitions in Floquet second-order topological superconductors
• Planar Hall Plateau in Magnetic Weyl Semimetals
• Nonlinear Corner States in Topologically Nontrivial Kagome Lattice
• Observation of nonlinear topological corner states originating from different spectral charges
• Magnetic field filtering of the hinge supercurrent in unconventional metal NiTe${}_2$-based Josephson junctions
• Topological gap solitons in Rabi Su-Schrieffer-Heeger lattices
• Topological Wannier cycles for the bulk and edges
• Topological edge states in photonic Floquet insulator with unpaired Dirac cones
• Probing Chiral-Symmetric Higher-Order Topological Insulators with Multipole Winding Number
• Gapless higher-order topology and corner states in Floquet systems
• Transport features of topological corner states in honeycomb lattice with multihollow structure
• Remote control of spin polarization of topological corner states
• Topological Corner Modes by Composite Wannier States in Glide-Symmetric Photonic Crystal
• Competing topological phases in a non-Hermitian time-reversal symmetry-broken Bernevig-Hughes-Zhang model
• Two-Dimensional Altermagnetic Iron Oxyhalides: Real Chern Topology and Valley-Spin-Lattice Coupling
• Bulk-boundary-transport correspondence of the second-order topological insulators
• Microwave hinge states in a simple-cubic-lattice photonic crystal insulator
• Corner modes in non-Hermitian next-nearest-neighbor hopping model
• Generic Approach to Intrinsic Magnetic Second-order Topological Insulators via Inverted $p-d$ Orbitals
• Higher-order topology in twisted multilayer systems: a review
• Orbital Edelstein effect of electronic itinerant orbital motion at edges
• Dissipation Enhanced Unidirectional Transport in Topological Systems
• Pentagonal nanowires from topological crystalline insulators: a platform for intrinsic core-shell nanowires and higher-order topology
• Corner states of two-dimensional second-order topological insulators with a chiral symmetry and broken time reversal and charge conjugation
• Tailoring higher-order topological phases via orbital hybridization
• Topological physics in quantum critical systems
• Generalization of the Nested Wilson Loop Formalism in Topological Dirac Semimetals with Higher-order Fermi Arcs
• Higher-order topological superconductor phases in a multilayer system
• On the role of geometric phase in the dynamics of elastic waveguides
• Observation of nonlinear higher-order topological insulators with unconventional boundary truncations
• Optical Berry Curvature of Hinge State and Its Detection
• Hybrid-Order Topological Phase And Transition in 1H Transition Metal Compounds
• Sub-symmetry Protected Topology in Topological Insulators and Superconductors
• Hinge States of Second-Order Topological Insulators as a Mach-Zehnder Interferometer
• Dimensional hierarchy of topological bound states in the continuum
• Extrinsic higher-order topological corner states in AB-stacked transition-metal dichalcogenides
• Topological phases in discrete stochastic systems
• Takagi Topological Insulator on the Honeycomb Lattice
• Mirror-symmetry protected higher-order topological zero-frequency boundary and corner modes in Maxwell lattices
• Topological semimetal with coexisting nodal points and nodal lines
• Hinge non-Hermitian skin effect in the single-particle properties of a strongly correlated f-electron system
• Polariton Topological Insulators with Disclinations
• Third-order Orbital Corner State and its Realization in Acoustic Crystals
• C*-framework for higher-order bulk-boundary correspondences
• Dynamically Characterizing the Structures of Dirac Points via Wave Packets
• RKKY interaction in helical higher-order topological insulators
• Thresholdless corner vortex solitons in fractal Sierpiński topological insulators
• Spin separation and filtering assisted by topological corner states in the Kekulé lattice
• Quadratic solitons in higher-order topological insulators
• Observation of Embedded Topology in a Trivial Bulk via Projective Crystal Symmetry
• Quantum Coherent Transport of 1D ballistic states in second order topological insulator Bi${}_4$Br${}_4$
• Network model for magnetic higher-order topological phases
• 3D Topologically Polarized Elastic Metamaterials Enable Asymmetric Energy Isolation at Low Frequencies
• Anomalous Topological Bloch Oscillations under Non-Abelian Gauge Fields
• Higher-order topological insulators in two-dimensional antiferromagnetic and altermagnetic chromium-based group-IV chalcogenides
• Nonlinearity-induced corner states in a kagome lattice
• Intrinsic higher-order topological states in 2D honeycomb Z_2 quantum spin Hall insulators
• Floquet states on disclinations
• Interaction-Induced Higher-Order Topological Insulator via Floquet Engineering
• Topological Optical Pseudospin Injection Beyond Weyl Semimetals
• Zeeman field induced corner states in the Kane-Mele-Hubbard model
• Fractal Polariton Topological Insulator
• Continuum Landau surface states in a non-Hermitian Weyl semimetal
• Stable vortex soliton arrays in disclination-fractal systems
• Topological Pseudospin Hall Effect and Multi-frequency Corner Modes in Kagome-based Lattices
• Coupled-wire construction of non-Abelian higher-order topological phases
• Floquet second-order topological insulator in strained graphene
• Layer-number parity induced topological phase transition
• Wilson loop invariants and bulk-boundary correspondence in higher-order topological insulators with two anticommuting mirror symmetries
• Non-Hermitian physics and topological phenomena in convective thermal metamaterials
• Topological energy pumping in a quasi-periodically driven four-level system