Higher-Order Topological Insulators in Quasicrystals

Abstract

Current understanding of higher-order topological insulators (HOTIs) is based primarily on crystalline materials. Here, we propose that HOTIs can be realized in quasicrystals. Specifically, we show that two distinct types of second-order topological insulators (SOTIs) can be constructed on the quasicrystalline lattices (QLs) with different tiling patterns. One is derived by using a Wilson mass term to gap out the edge states of the quantum spin Hall insulator on QLs. The other is the quasicrystalline quadrupole insulator (QI) with a quantized quadrupole moment. We reveal some unusual features of the corner states (CSs) in the quasicrystalline SOTIs. We also show that the quasicrystalline QI can be simulated by a designed electrical circuit, where the CSs can be identified by measuring the impedance resonance peak. Our findings not only extend the concept of HOTIs into quasicrystals but also provide a feasible way to detect the topological property of quasicrystals in experiments.

5 pages, 4 figures, 8 pages of supplementary materials, accepted by Physical Review Letters

References in corpus (13)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Classification of topological insulators and superconductors in three spatial dimensions
• 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
• 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
• Topological properties of linear circuit lattices
• Topological Photonic Quasicrystals: Fractal Topological Spectrum and Protected Transport
• Topological phases without crystalline counterparts
• Topological Hofstadter Insulators in a Two-Dimensional Quasicrystal
• Difficulties in operator-based formulation of the bulk quadrupole moment

Cited by in corpus (148)

• Non-Hermitian Physics
• Classical higher-order topological insulators
• Topological Phase Transitions in Disordered Electric Quadrupole Insulators
• Higher-order topological odd-parity superconductors
• Topolectric circuits: Theory and construction
• Majorana corner and hinge modes in second-order topological insulator-superconductor heterostructures
• Structural Disorder Induced Second-order Topological Insulators in Three Dimensions
• Higher-order topological phases on fractal lattices
• Higher-Order topological insulator in a dodecagonal quasicrystal
• Experimental identification of the second-order non-Hermitian skin effect with physics-graph-informed machine learning
• Higher-Order Weyl-Exceptional-Ring Semimetals
• Higher-order topological insulators and semimetals in generalized Aubry-André-Harper models
• Topological models in rotationally symmetric quasicrystals
• Observation of symmetry protected zero modes in topolectrical circuits
• Effective Model for Fractional Topological Corner Modes in Quasicrystals
• Topological states in quasicrystals
• 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
• Higher-order topological insulators in hyperbolic lattices
• Non-Hermitian Floquet second order topological insulators in periodically quenched lattices
• Realization of quasicrystalline quadrupole topological insulators in electrical circuits
• Quasicrystalline Chern Insulators
• Topological superconductivity in quasicrystals
• Higher-order Topological Hyperbolic Lattices
• Corner charge and bulk multipole moment in periodic systems
• Kane-Mele with a twist: Quasicrystalline higher-order topological insulators with fractional mass kinks
• Weyl nodes with higher-order topology in an optically driven nodal-line semimetal
• Hybrid skin-topological effect induced by eight-site cells and arbitrary adjustment of the localization of topological edge states
• Higher-order topological phases in crystalline and non-crystalline systems: a review
• Floquet Weyl semimetal phases in light-irradiated higher-order topological Dirac semimetals
• Topological Gaps by Twisting
• Observation of Topological Corner State Arrays in Photonic Quasicrystals
• A Higher-Order Topological Insulator Phase in a Modulated Haldane Model
• Higher-order topological Anderson insulators in quasicrystals
• Disorder-Induced Quantum Phase Transitions in Three-Dimensional Second-Order Topological Insulators
• Experimental realization of two-dimensional weak topological insulators
• Second-Order Bulk-Boundary Correspondence in Rotationally Symmetric Topological Superconductors from Stacked Dirac Hamiltonians
• Coulomb instabilities of 3D higher-order topological insulators
• Quantum many-body topology of quasicrystals
• Layer-Dependent Topological Phase in a Two-Dimensional Quasicrystal and Approximant
• Transition from metal to higher-order topological insulator driven by random flux
• Higher-order topological phases emerging from the Su-Schrieffer-Heeger stacking
• Topological Random Fractals
• Noncrystalline topological superconductors
• Fractional Corner Charge of Sodium Chloride
• Bulk-boundary correspondence in disordered higher-order topological insulators
• Topological excitonic corner states and nodal phase in bilayer quantum spin Hall insulators
• Theory of inversion-${\mathbb{Z}}_4$ protected topological chiral hinge states and its applications to layered antiferromagnets
• Appearance of hinge states in second-order topological insulators via the cutting procedure
• Magnon corner states in twisted bilayer honeycomb magnets
• Corner- and sublattice-sensitive Majorana zero modes on the kagome lattice
• Topological Anderson insulators in an Ammann-Beenker quasicrystal and a snub-square crystal
• Many-Body Invariants for Chern and Chiral Hinge Insulators
• Length scale formation in the Landau levels of quasicrystals
• Klein-bottle quadrupole insulators and Dirac semimetals
• Quasicrystalline second-order topological semimetals
• Intrinsic vortex pinning in superconducting quasicrystals
• Sublattice-enriched tunability of bound states in second-order topological insulators and superconductors
• Average Symmetry Protected Higher-order Topological Amorphous Insulators
• Projected Topological Branes
• Out-of-Time-Order Correlation as a Witness for Topological Phase Transitions
• Density-driven higher-order topological phase transitions in amorphous solids
• Topological Gaps in Quasi-Periodic Spin Chains: A Numerical and K-Theoretic Analysis
• Robustness of Helical Hinge States of Weak Second-Order Topological Insulators
• Higher-order Weyl superconductors with anisotropic Weyl-point connectivity
• Quasicrystalline Bose glass in the absence of disorder and quasidisorder
• Mechanics and dynamics of two-dimensional quasiperiodic composites
• Topological States in Two-Dimensional Su-Schrieffer-Heeger Models
• Josephson effect in a Fibonacci quasicrystal
• A Kitaev-type spin liquid on a quasicrystal
• Engineering non-Hermitian Second Order Topological Insulator in Quasicrystals
• Second-Order Topological Insulator in van der Waals Heterostructures of CoBr${}_2$/Pt${}_2$HgSe${}_3$/CoBr${}_2$
• Topological states in a dimerized system with staggered magnetic fluxes
• Hybrid-order topological odd-parity superconductors via Floquet engineering
• Quasicrystalline Weyl points and dense Fermi-Bragg arcs
• Observation of type-III corner states induced by long-range interactions
• Role of the edges in a quasicrystalline Haldane model
• Generalization of Benalcazar-Bernevig-Hughes model to arbitrary dimensions
• Engineering topological states and quantum-inspired information processing using classical circuits
• Colloquium: Synthetic quantum matter in non-standard geometries
• Statistical mechanics of dimers on quasiperiodic Ammann-Beenker tilings
• Structural disorder-induced topological phase transitions in quasicrystals
• Correlation Effects in Quadrupole Insulators: a Quantum Monte Carlo Study
• Effects of Disorder On Thouless Pumping In Higher-Order Topological Insulators
• Higher-order Topological Insulators and Semimetals in Three Dimensions without Crystalline Counterparts
• Quantized charge-pumping in higher-order topological insulators
• Topological superconductivity in Fibonacci quasicrystals
• Interlayer Coupling Induced Topological Phase Transition to Higher Order
• Third-order topological insulator induced by disorder
• Fractional hinge and corner charges in various crystal shapes with cubic symmetry
• Transport Induced Dimer State from Topological Corner States
• Intertwined Weyl phases emergent from higher-order topology and unconventional Weyl fermions via crystalline symmetry
• Topological quantum transition driven by charge-phonon coupling in higher-order topological insulators
• Quasiperiodic pairing in graphene quasicrystals
• Bulk Localised Transport States in Infinite and Finite Quasicrystals via Magnetic Aperiodicity
• Decagonal Sn clathrate on $d$-Al-Ni-Co
• Rotoinversion-symmetric bulk-hinge correspondence and its applications to higher-order Weyl semimetals
• Floquet higher-order topological phases in momentum space
• Higher-dimensional Hofstadter butterfly on Penrose lattice
• Transport features of topological corner states in honeycomb lattice with multihollow structure
• Majorana corner modes and flat-band Majorana edge modes in superconductor/topological-insulator/superconductor junctions
• Higher-order topological corner states induced solely by onsite potentials with mirror symmetry
• Fibonacci-Modulation-Induced Multiple Topological Anderson Insulators
• Confined states and topological phases in two-dimensional quasicrystalline $\pi$-flux model
• Fractal Surface States in Three-Dimensional Topological Quasicrystals
• Unveiling Higher-Order Topology via Polarized Topological Charges
• Higher-order topology in twisted multilayer systems: a review
• Hierarchical Topological States in Thermal Diffusive Networks
• Self-consistent study of topological superconductivity in two-dimensional quasicrystals
• The Fibonacci quasicrystal: case study of hidden dimensions and multifractality
• Effects of first- and second-order topological phases on equilibrium crystal shapes
• Chiral Hinge Transport in Disordered Non-Hermitian Second-Order Topological Insulators
• Unveiling Correlated Two-dimensional Topological Insulators through Fermionic Tensor Network States -- Classification, Edge Theories and Variational Wavefunctions
• Weyl superconductivity and quasiperiodic Majorana arcs in quasicrystals
• Topological phases of amorphous matter
• Optical Berry Curvature of Hinge State and Its Detection
• General corner charge formulas in various tetrahedral and cubic space groups
• Quasiperiodic gallium adlayer on i-Al-Pd-Mn
• Tunable corner states in topological insulators with long-range hoppings and diverse shapes
• Experimental realization of Majorana hinge and corner modes in intrinsic organic topological superconductor without magnetic field at room temperature
• Theory of fractional corner charges in cylindrical crystal shapes
• Finite-temperature topological invariant for higher-order topological insulators
• Second-order topological insulator and fragile topology in topological circuitry simulation
• Quasiperiodic Quadrupole Insulators
• Boundary topological insulators and superconductors of Altland-Zirnbauer tenfold classes
• Missing link between the 2D Quantum Hall problem and 1D quasicrystals
• Higher-Order Topology in Monolayer FeSe
• Local expression of fractional corner charges in obstructed atomic insulators and relationship with the fractional disclination charges
• Gapless States Localized along a Staircase Edge in Second-Order Topological Insulators
• Interaction-Induced Higher-Order Topological Insulator via Floquet Engineering
• Zeeman field induced corner states in the Kane-Mele-Hubbard model
• Intrinsic higher-order topological states in 2D honeycomb Z_2 quantum spin Hall insulators
• Tunable cornerlike states in topological type-II hyperbolic lattices
• Higher order topology in a Creutz ladder
• Superconducting order parameter in aperiodic binary systems
• First-principles evidence for conventional superconductivity in a quasicrystal approximant
• Disorder-induced chiral and helical Majorana edge modes in a two-dimensional Ammann-Beenker quasicrystal
• Three-nodal surface phonons in solid-state materials: Theory and material realization
• One-dimensional topological quasiperiodic chain for directional wireless power transfer
• Efficient algorithm for simulating particles in real quasiperiodic environments
• Projected branes as platforms for crystalline, superconducting, and higher-order topological phases
• Non-Hermitian second-order topological insulator with point gap
• Hinge modes of three-dimensional Euler insulators
• Floquet second-order topological insulator in strained graphene
• Second-order topological insulator induced by compensated altermagnetism without bulk spin splitting
• Magnetic-Field Tunable Möbius and Higher-Order Topological Insulators in Three-Dimensional Layered Octagonal Quasicrystals
• Topological states and flat bands in exactly solvable decorated Cayley trees
• Breakdown of the symmetry constraint in a Floquet topological insulator