Probing Chiral-Symmetric Higher-Order Topological Insulators with Multipole Winding Number

Abstract

The interplay between crystalline symmetry and band topology gives rise to unprecedented lower-dimensional boundary states in higher-order topological insulators (HOTIs). However, the measurement of the topological invariants of HOTIs remains a significant challenge. Here, we define a {multipole winding number} (MWN) for chiral-symmetric HOTIs by applying a corner twisted boundary condition. The MWN, arising from both bulk and boundary states, accurately captures the bulk-corner correspondence including boundary-obstructed topological phases. To address the measurement challenge, we leverage the perturbative nature of the corner twisted boundary condition and develop a real-space approach for determining the MWN in both two-dimensional and three-dimensional systems. The real-space formula provides an experimentally viable strategy for directly probing the topology of chiral-symmetric HOTIs through dynamical evolution. Our findings not only highlight the twisted boundary condition as a powerful tool for investigating HOTIs, but also establish a paradigm for exploring real-space formulas for the topological invariants of HOTIs.

References in corpus (66)

• Anyons in an exactly solved model and beyond
• Classification of topological quantum matter with symmetries
• Quantized Electric Multipole Insulators
• Higher-Order Topological Insulators
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Reflection symmetric second-order topological insulators and superconductors
• Observation of a phononic quadrupole topological insulator
• Acoustic higher-order topological insulator on a Kagome lattice
• 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
• Topological protection of photonic mid-gap cavity modes
• Classical higher-order topological insulators
• Photonic quadrupole topological phases
• Corner states of light in photonic waveguides
• Observation of the topological Anderson insulator in disordered atomic wires
• Detection of Zak phases and topological invariants in a chiral quantum walk of twisted photons
• Mapping topological order in coordinate space
• Topological Criticality in the Chiral-Symmetric AIII Class at Strong Disorder
• A General Theorem Relating the Bulk Topological Number to Edge States in Two-dimensional Insulators
• Robust zero-energy modes in an electronic higher-order topological insulator: the dimerized Kagome lattice
• Experimental Observation of Higher-Order Topological Anderson Insulators
• Helical Topological Edge States in a Quadrupole Phase
• Scattering formula for the topological quantum number of a disordered multi-mode wire
• Non-linear second-order topological insulators
• Scattering theory of topological insulators and superconductors
• Observation of an acoustic octupole topological insulator
• Engineering Corner States from Two-Dimensional Topological Insulators
• Demonstration of a quantized acoustic octupole topological insulator
• Topological characterization of chiral models through their long time dynamics
• Topological characterizations of an extended Su-Schrieffer-Heeger model
• Topological phases without crystalline counterparts
• Topological Phase Transitions in Disordered Electric Quadrupole Insulators
• Many-Body Electric Multipole Operators in Extended Systems
• Boundary-obstructed topological phases
• Many-Body Order Parameters for Multipoles in Solids
• K-Theory and Pseudospectra for Topological Insulators
• Dynamical Singularities of Floquet Higher-Order Topological Insulators
• Observation of topological magnon insulator states in a superconducting circuit
• Coupled-wire construction of static and Floquet second-order topological insulators
• Floquet Higher-Order Topological Insulators with Anomalous Dynamical Polarization
• Chiral-Symmetric Higher-Order Topological Phases of Matter
• Topological quantum walks in momentum space with a Bose-Einstein condensate
• Higher-order Topological Anderson Insulators
• Direct Observation of Topology from Single-photon Dynamics on a Photonic Chip
• High-harmonic generation in Su-Schrieffer-Heeger chains
• Higher-Order topological insulator in a dodecagonal quasicrystal
• Photonic quadrupole topological insulator using orbital-induced synthetic flux
• Difficulties in operator-based formulation of the bulk quadrupole moment
• Local invariants identify topology in metals and gapless systems
• Real-space representation of winding number for one-dimensional chiral-symmetric topological insulator
• Topological Anderson insulator phase in a quasicrystal lattice
• Non-Hermitian Floquet second order topological insulators in periodically quenched lattices
• Realization of quasicrystalline quadrupole topological insulators in electrical circuits
• 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
• Corner modes of the breathing kagome lattice: origin and robustness
• Higher-Order Topological Phase in a Honeycomb-Lattice Model with Anti-Kekulé Distortion
• Bulk detection of time-dependent topological transitions in quenched chiral models
• 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
• Generation of higher-order topological insulators using periodic driving
• Detecting Bulk Topology of Quadrupolar Phase from Quench Dynamics
• Floquet second-order topological Anderson insulator hosting corner localized modes
• Third-order topological insulator induced by disorder
• Calculations of Chern number: equivalence of real-space and twisted-boundary-condition formulae

Cited by in corpus (6)

• Family of third-order topological insulators from Su-Schrieffer-Heeger stacking
• Characterization of higher-order topological superconductors using Bott indices
• Topological Corner States in Bilayer and Trilayer Systems with Vertically Stacked Topological Heterostructures
• Scattering theory of higher order topological phases
• Finite-temperature topological invariant for higher-order topological insulators
• Unified Multipole Bott Indices for Non-Hermitian Skin Effect in Different Orders