Higher-Order topological insulator in a dodecagonal quasicrystal

Abstract

Higher-order topological insulators (HOTIs) are a newly discovered class of topological insulators which exhibit unconventional bulk-boundary correspondence. Very recently, the concept of HOTIs has been extended to aperiodic quasicrystalline systems, where the topological band theory fails to describe topological phases. More importantly, a novel HOTI phase protected by an eightfold rotational symmetry, not found in crystalline materials, was identified in the Ammann-Beenker tiling quasicrystals. Here we report the discovery of a quasicrystalline HOTI in a dodecagonal quasicrystal. The quasicrystalline HOTI supports twelve in-gap zero-energy modes symmetrically distributed at the corners of the quasicrystal dodecagon. These zero-energy corner modes are protected by a combination of a twelvefold rotational symmetry and mirror symmetry, as well as particle-hole symmetry, which has no crystalline counterpart.

arXiv commentpublished version, accepted as a Rapid Communication in Phys. Rev. B

References in corpus (107)

• Topological Insulators
• Topological insulators and superconductors
• Classification of topological insulators and superconductors in three spatial dimensions
• Classification of topological quantum matter with symmetries
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Topological Crystalline Insulators
• Quantized Electric Multipole Insulators
• Higher-Order Topological Insulators
• Colloquium: Topological Band Theory
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Topological States and Adiabatic Pumping in Quasicrystals
• $(d-2)$-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
• Higher-order topological insulators and semimetals on the breathing Kagome and pyrochlore lattices
• Acoustic higher-order topological insulator on a Kagome lattice
• Zoo of quantum-topological phases of matter
• 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
• Topological Crystalline Insulators and Topological Superconductors: From Concepts to Materials
• The space group classification of topological band insulators
• Topological classification of crystalline insulators through band structure combinatorics
• Topological protection of photonic mid-gap cavity modes
• Photonic quadrupole topological phases
• Higher-order topological insulators and superconductors protected by inversion symmetry
• Topology of crystalline insulators and superconductors
• Hybrid higher-order skin-topological modes in non-reciprocal systems
• Second-Order Topological Phases in Non-Hermitian Systems
• Observation of second-order topological insulators in sonic crystals
• Topological phase transition in non-Hermitian quasicrystals
• Corner states of light in photonic waveguides
• Second-order topological insulators and superconductors with an order-two crystalline symmetry
• Failure of Nielsen-Ninomiya theorem and fragile topology in two-dimensional systems with space-time inversion symmetry: application to twisted bilayer graphene at magic angle
• Elastic higher-order topological insulator with topologically protected corner states
• Higher-order Topology of Axion Insulator EuIn${}_2$As${}_2$
• Classification of topological insulators and superconductors in the presence of reflection symmetry
• Dirac Electrons in a Dodecagonal Graphene Quasicrystal
• Higher-Order Topology, Monopole Nodal Lines, and the Origin of Large Fermi Arcs in Transition Metal Dichalcogenides XTe${}_2$ (X=Mo,W)
• Two-dimensional second-order topological insulator in graphdiyne
• Classification of Topological Insulators and Superconductors
• Topological Zero-Energy Modes in Gapless Commensurate Aubry-André-Harper Models
• Higher-order bulk-boundary correspondence for topological crystalline phases
• Majorana corner modes in a high-temperature platform
• Topological Equivalence between the Fibonacci Quasicrystal and the Harper Model
• Surface State Magnetization and Chiral Edge States on Topological Insulators
• Topological classification with additional symmetries from Clifford algebras
• Higher-Order Topological Insulator in Twisted Bilayer Graphene
• High-Temperature Majorana Corner States
• Quasicrystalline 30° Twisted Bilayer Graphene as an Incommensurate Superlattice with Strong Interlayer Coupling
• Robust zero-energy modes in an electronic higher-order topological insulator: the dimerized Kagome lattice
• Higher-Order Topological Insulators in Quasicrystals
• Impurity Bound States and Greens Function Zeroes as Local Signatures of Topology
• Higher Order Topological Phases: A General Principle of Construction
• Topological Photonic Quasicrystals: Fractal Topological Spectrum and Protected Transport
• Weak-Pairing Higher Order Topological Superconductors
• Helical Topological Edge States in a Quadrupole Phase
• Majorana Kramers pairs in higher-order topological insulators
• Higher-order topological insulators protected by inversion and rotoinversion symmetries
• An anomalous higher-order topological insulator
• Topological Quadrupolar Semimetals
• Minimal model for higher-order topological insulators and phosphorene
• Quantum Spin Hall Effect and Spin Bott Index in a Quasicrystal Lattice
• Two-dimensional higher-order topology in monolayer graphdiyne
• Majorana corner states in a two-dimensional magnetic topological insulator on a high-temperature superconductor
• Second Order Topological Superconductivity in $\pi$-Junction Rashba Layers
• Topology of nonsymmorphic crystalline insulators and superconductors
• Symmetry Enforced Chiral Hinge States and Surface Quantum Anomalous Hall Effect in Magnetic Axion Insulator ${\text{Bi}}_{2-x}{\text{Sm}}_x{\text{Se}}_3$
• Lattice models with exactly solvable topological hinge and corner states
• Topological phases without crystalline counterparts
• Higher-order topological insulators in amorphous solids
• Higher-order topological odd-parity superconductors
• Topological switch between second-order topological insulators and topological crystalline insulators
• Higher-order Floquet topological phases with corner and bulk bound states
• Topological Hofstadter Insulators in a Two-Dimensional Quasicrystal
• Quasicrystalline electronic states in 30${}^{\circ }$ rotated twisted bilayer graphene
• Second-order Topological Superconductors with Mixed Pairing
• Inversion-protected higher order topological superconductivity in monolayer WTe${}_2$
• Magnetic second-order topological insulators and semimetals
• Theory of spin Bott index for quantum spin Hall states in non-periodic systems
• Aperiodic Weak Topological Superconductors
• Higher order symmetry-protected topological states for interacting bosons and fermions
• Lattice symmetry assisted second order topological superconductors and Majorana patterns
• Topological crystalline superconductivity and second-order topological superconductivity in nodal-loop materials
• Fragile Topology Protected by Inversion Symmetry: Diagnosis, Bulk-Boundary Correspondence, and Wilson Loop
• Majorana corner and hinge modes in second-order topological insulator-superconductor heterostructures
• Higher-order Topological Mott Insulators
• Dodecagonal bilayer graphene quasicrystal and its approximants
• Second-order topological phases protected by chiral symmetry
• Phase tunable second-order topological superconductor
• Amorphous topological superconductivity in a Shiba glass
• Topological models in rotationally symmetric quasicrystals
• Three-dimensional superconductors with hybrid higher order topology
• Hofstadter butterfly of a quasicrystal
• Quantization in chiral higher order topological insulators: circular dichroism and local Chern marker
• Topological Anderson insulator phase in a quasicrystal lattice
• Strong and weak second-order topological insulators with hexagonal symmetry and ${\mathbb{Z}}_3$ index
• Quasicrystalline Chern Insulators
• Inversion-symmetry protected chiral hinge states in stacks of doped quantum Hall layers
• Majorana Corner Modes in a Second-Order Kitaev Spin Liquid
• Fibonacci Topological Superconductor
• Kane-Mele with a twist: Quasicrystalline higher-order topological insulators with fractional mass kinks
• Topological mechanics in quasicrystals
• Bott periodicity for the topological classification of gapped states of matter with reflection symmetry
• Hinged Quantum Spin-Hall Effect in Antiferromagnetic Topological Insulators

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• Classical higher-order topological insulators
• Effective Model for Fractional Topological Corner Modes in Quasicrystals
• Topological states in quasicrystals
• Field-Tunable One-Sided Higher-Order Topological Hinge States in Dirac Semimetals
• Higher-order topological insulators in hyperbolic lattices
• Realization of quasicrystalline quadrupole topological insulators in electrical circuits
• 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
• Observation of Topological Corner State Arrays in Photonic Quasicrystals
• Higher-order topological Anderson insulators in quasicrystals
• Amorphous topological phases protected by continuous rotation symmetry
• Higher-order topological phases emerging from the Su-Schrieffer-Heeger stacking
• Topological Random Fractals
• Noncrystalline topological superconductors
• Bulk-boundary correspondence in disordered higher-order topological insulators
• Topological excitonic corner states and nodal phase in bilayer quantum spin Hall insulators
• Topological Anderson insulators in an Ammann-Beenker quasicrystal and a snub-square crystal
• Length scale formation in the Landau levels of quasicrystals
• Average Symmetry Protected Higher-order Topological Amorphous Insulators
• Quasicrystalline second-order topological semimetals
• Physical properties of an Aperiodic monotile: Graphene-like features, chirality and zero-modes
• Density-driven higher-order topological phase transitions in amorphous solids
• Topological States in Two-Dimensional Su-Schrieffer-Heeger Models
• Second-Order Topological Insulator in van der Waals Heterostructures of CoBr${}_2$/Pt${}_2$HgSe${}_3$/CoBr${}_2$
• Generalization of Benalcazar-Bernevig-Hughes model to arbitrary dimensions
• Structural disorder-induced topological phase transitions in quasicrystals
• Higher-order Topological Insulators and Semimetals in Three Dimensions without Crystalline Counterparts
• Topological quantum transition driven by charge-phonon coupling in higher-order topological insulators
• Bulk Localised Transport States in Infinite and Finite Quasicrystals via Magnetic Aperiodicity
• Quasiperiodic pairing in graphene quasicrystals
• Higher-order topological corner states induced solely by onsite potentials with mirror symmetry
• Majorana corner modes and flat-band Majorana edge modes in superconductor/topological-insulator/superconductor junctions
• Probing Chiral-Symmetric Higher-Order Topological Insulators with Multipole Winding Number
• Transport features of topological corner states in honeycomb lattice with multihollow structure
• Confined states and topological phases in two-dimensional quasicrystalline $\pi$-flux model
• Hierarchical Topological States in Thermal Diffusive Networks
• Higher-order topology in twisted multilayer systems: a review
• Weyl superconductivity and quasiperiodic Majorana arcs in quasicrystals
• Boundary topological insulators and superconductors of Altland-Zirnbauer tenfold classes
• Quasiperiodic Quadrupole Insulators
• Zeeman field induced corner states in the Kane-Mele-Hubbard model
• Tunable cornerlike states in topological type-II hyperbolic lattices
• Magnetic-Field Tunable Möbius and Higher-Order Topological Insulators in Three-Dimensional Layered Octagonal Quasicrystals
• Disorder-induced chiral and helical Majorana edge modes in a two-dimensional Ammann-Beenker quasicrystal