Chiral-Symmetric Higher-Order Topological Phases of Matter

Abstract

We introduce novel higher-order topological phases of matter in chiral-symmetric systems (class AIII of the tenfold classification), most of which would be misidentified as trivial by current theories. These phases are protected by "multipole chiral numbers", bulk integer topological invariants that in 2D and 3D are built from sublattice multipole moment operators, as defined herein. The integer value of a multipole chiral number indicates how many degenerate zero-energy states localize at each corner of a system. These higher-order phases of matter are generally boundary-obstructed and robust in the presence of chiral-symmetry-preserving disorder.

arXiv commentMain Text: 7 pages, 3 figures. Supp. Info: 11 pages, 7 figures

References in corpus (79)

• Classification of topological insulators and superconductors in three spatial dimensions
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Experimental realisation of the topological Haldane model
• Quantized Electric Multipole Insulators
• Periodic table for topological insulators and superconductors
• Higher-Order Topological Insulators
• Topological quantum chemistry
• Realization of the Hofstadter Hamiltonian with ultracold atoms in optical lattices
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Realizing the Harper Hamiltonian with Laser-Assisted Tunneling in Optical Lattices
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Topolectrical circuit realization of topological corner modes
• Reflection symmetric second-order topological insulators and superconductors
• Higher-Order Topology in Bismuth
• Demonstration of a quantized microwave quadrupole insulator with topologically protected corner states
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Quantization of fractional corner charge in $C_n$-symmetric higher-order topological crystalline insulators
• The Quantum-Mechanical Position Operator in Extended Systems
• Topological Origin of Zero-Energy Edge States in Particle-Hole Symmetric Systems
• The effects of interactions on the topological classification of free fermion systems
• Topological protection of photonic mid-gap cavity modes
• Photonic quadrupole topological phases
• Higher-order topological insulators and superconductors protected by inversion symmetry
• High-throughput calculations of magnetic topological materials
• Second-order topological insulators and superconductors with an order-two crystalline symmetry
• Photonic crystal nanocavity based on a topological corner state
• Higher-order Topology of Axion Insulator EuIn${}_2$As${}_2$
• Higher-Order Topology, Monopole Nodal Lines, and the Origin of Large Fermi Arcs in Transition Metal Dichalcogenides XTe${}_2$ (X=Mo,W)
• Higher-order bulk-boundary correspondence for topological crystalline phases
• Hyperbolic Lattices in Circuit Quantum Electrodynamics
• Symmetry indicators and anomalous surface states of topological crystalline insulators
• Magnetic Topological Quantum Chemistry
• Topological Criticality in the Chiral-Symmetric AIII Class at Strong Disorder
• Low-threshold topological nanolasers based on second-order corner state
• Building Blocks of Topological Quantum Chemistry: Elementary Band Representations
• Band Topology and Linking Structure of Nodal Line Semimetals with Z2 Monopole Charges
• Realization of an acoustic third-order topological insulator
• Lasing from multipole topological corner states
• Strong and Fragile Topological Dirac Semimetals with Higher-Order Fermi Arcs
• Observation of Quadrupole Transitions and Edge Mode Topology in an LC network
• Weak-Pairing Higher Order Topological Superconductors
• Majorana Kramers pairs in higher-order topological insulators
• Higher-order topological insulators protected by inversion and rotoinversion symmetries
• Classification of Two Dimensional Topological Crystalline Superconductors and Majorana Bound States at Disclinations
• Observation of an acoustic octupole topological insulator
• Topological Quadrupolar Semimetals
• Material design with the van der Waals stacking of bismuth-halide chains realizing a higher-order topological insulator
• Demonstration of a quantized acoustic octupole topological insulator
• Tunable Majorana corner states in a two-dimensional second-order topological superconductor induced by magnetic fields
• Majorana corner states in a two-dimensional magnetic topological insulator on a high-temperature superconductor
• Higher-order Weyl Semimetals
• Second Order Topological Superconductivity in $\pi$-Junction Rashba Layers
• Symmetry Enforced Chiral Hinge States and Surface Quantum Anomalous Hall Effect in Magnetic Axion Insulator ${\text{Bi}}_{2-x}{\text{Sm}}_x{\text{Se}}_3$
• Topolectrical-circuit octupole insulator with topologically protected corner states
• Topological Phase Transitions in Disordered Electric Quadrupole Insulators
• Higher-order topological insulators in amorphous solids
• Many-Body Electric Multipole Operators in Extended Systems
• Boundary-obstructed topological phases
• Quadrupole Topological Photonic Crystals
• Many-Body Order Parameters for Multipoles in Solids
• Higher-order topological odd-parity superconductors
• Higher-order Topological Anderson Insulators
• On the robustness of topological corner modes in photonic crystals
• General corner charge formula in two-dimensional C_n-symmetric higher-order topological insulators
• Boundary-obstructed topological high-T${}_c$ superconductivity in iron pnictides
• Phase tunable second-order topological superconductor
• Almost Commuting Matrices, Localized Wannier Functions, and the Quantum Hall Effect
• Chiral Dirac Superconductors: Second-order and Boundary-obstructed Topology
• Difficulties in operator-based formulation of the bulk quadrupole moment
• Real-space representation of winding number for one-dimensional chiral-symmetric topological insulator
• Vortex and Surface Phase Transitions in Superconducting Higher-order Topological Insulators
• Majorana Corner Modes in a Second-Order Kitaev Spin Liquid
• Filling anomaly for general 2D and 3D $C_4$ symmetric lattices
• Edge-Corner Correspondence: Boundary-Obstructed Topological Phases with Chiral Symmetry
• Pairing Obstructions in Topological Superconductors
• Topological Crystalline Phases in a Disordered Inversion-Symmetric Chain
• Time-reversal-invariant $C_2$-symmetric higher-order topological superconductors
• Boundary-obstructed topological phases of a massive Dirac fermion in a magnetic field
• Chaos-Assisted Long-Range Tunneling for Quantum Simulation

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• Local invariants identify topology in metals and gapless systems
• Topological Phases of Photonic Crystals under Crystalline Symmetries
• Topologically protected vortex transport via chiral-symmetric disclination
• Realization of a Z classified chiral-symmetric higher-order topological insulator in a coupling-inversion acoustic crystal
• Non-Hermitian higher-order topological superconductors in two-dimension: statics and dynamics
• Higher-order topological phases in crystalline and non-crystalline systems: a review
• An operator-based approach to topological photonics
• Observation of Topological Corner State Arrays in Photonic Quasicrystals
• Observation of Large-Number Corner Modes in $\mathbb{Z}$-class Higher-Order Topolectrical Circuits
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• Unified characterization for higher-order topological phase transitions
• Tutorial: Classifying Photonic Topology Using the Spectral Localizer and Numerical $K$-Theory
• Hybrid-order topological odd-parity superconductors via Floquet engineering
• Generalization of Benalcazar-Bernevig-Hughes model to arbitrary dimensions
• Floquet second-order topological Anderson insulator hosting corner localized modes
• Dynamical Detection of Topological Spectral Density
• Calculations of Chern number: equivalence of real-space and twisted-boundary-condition formulae
• Probing Bulk Band Topology from Time Boundary Effect in Synthetic Dimension
• Wannier Topology and Quadrupole Moments for a generalized Benalcazar-Bernevig-Hughes Model
• Mean-chiral displacement in coherently driven photonic lattices and its application to synthetic frequency dimensions
• Multi higher-order Dirac and nodal line semimetals
• Probing Chiral-Symmetric Higher-Order Topological Insulators with Multipole Winding Number
• Mode-Shell correspondence, a unifying phase space theory in topological physics -- Part I: Chiral number of zero-modes
• Crystalline-electromagnetic responses of higher order topological semimetals
• Unveiling Higher-Order Topology via Polarized Topological Charges
• Corner modes in non-Hermitian next-nearest-neighbor hopping model
• Direct demonstration of bulk-boundary correspondence in higher-order topological superconductors with chiral symmetry
• Hierarchical Topological States in Thermal Diffusive Networks
• Josephson current signature of Floquet Majorana and topological accidental zero modes in altermagnet heterostructures
• Chiral crossroads in $\mathrm{H}{\mathrm{o}}_3\mathrm{Sc}{\mathrm{O}}_6$: a tale of frustration in maple leaf lattice
• Topological Corner States in Bilayer and Trilayer Systems with Vertically Stacked Topological Heterostructures
• Mixed higher-order topology and nodal and nodeless flat band topological phases in a superconducting multiorbital model
• Family of third-order topological insulators from Su-Schrieffer-Heeger stacking
• Unconventional hybrid-order topological insulators
• Characterization of higher-order topological superconductors using Bott indices
• A new class of higher-order topological insulators that localize energy at arbitrary multiple sites
• An index theorem for quarter-plane Toeplitz operators via extended symbols and gapped Invariants related to corner states
• Hinge Majorana Flat Band in Type-II Dirac Semimetals
• Floquet topological phases with time-reversal and space inversion symmetries and dynamical detection of topological charges
• Multiple topological corner states in the continuum of extended kagome lattice
• Thresholdless corner vortex solitons in fractal Sierpiński topological insulators
• Quasiperiodic Quadrupole Insulators
• Topology reconstruction for asymmetric systems by isomorphic mapping or perturbation approximation
• Disorder-induced instability of a Weyl nodal loop semimetal towards a diffusive topological metal with protected multifractal surface states
• Topological edge states of continuous Hamiltonians
• The Quadrupole Moment of Higher-Order Topological Insulator at Finite temperature
• Breakdown of Non-Bloch Bulk-Boundary Correspondence and Emergent Topology in Floquet Non-Hermitian Systems
• Current switching behavior mediated via hinge modes in higher-order topological phases using altermagnets
• Recent progress on disorder-induced topological phases
• Unified Multipole Bott Indices for Non-Hermitian Skin Effect in Different Orders
• Breakdown of the symmetry constraint in a Floquet topological insulator
• Higher-order topological phases protected by noninvertible and subsystem symmetries
• Non-Hermitian second-order topological insulator with point gap
• Wilson loop invariants and bulk-boundary correspondence in higher-order topological insulators with two anticommuting mirror symmetries
• Coupled-wire construction of non-Abelian higher-order topological phases
• Topological superconductivity and superconducting diode effect mediated via unconventional magnet and Ising spin-orbit coupling