Quasicrystalline Chern Insulators

Abstract

Chern insulator or quantum anomalous Hall state is a topological state with integer Hall conductivity but in absence of Landau level. It had been well established on various two-dimensional lattices with periodic structure. Here, we report similar Chern insulators can also be realized on the quasicrystal with $5$-fold rotational symmetry. Providing the staggered flux through plaquettes, we propose two types of quasicrystalline Chern insulators. Their topological characterizations are well identified by the robustness of edge states, non-zero real-space Chern number, and quantized conductance. We further find the failure of integer conductivity but with quantized Chern number at some special energies. Our study therefore provide a new opportunity to searching topological materials in aperiodic system.

10 pages, 9 figures

References in corpus (43)

• Topological Insulators
• Topological insulators and superconductors
• Anyons in an exactly solved model and beyond
• Experimental realisation of the topological Haldane model
• Topological Crystalline Insulators
• Kwant: a software package for quantum transport
• High temperature fractional quantum Hall states
• The (High Quality) Topological Materials In The World
• Nearly-flat bands with nontrivial topology
• Catalogue of Topological Electronic Materials
• Topological quantization of the spin Hall effect in two-dimensional paramagnetic semiconductors
• Towards ideal topological materials: Comprehensive database searches using symmetry indicators
• Spin Anisotropy and Quantum Hall Effect in the Kagome Lattice - Chiral Spin State based on a Ferromagnet-
• Topological insulator on the kagome lattice
• Observation of Topological Phase Transitions in Photonic Quasicrystals
• An exact chiral spin liquid with non-Abelian anyons
• Dirac Electrons in a Dodecagonal Graphene Quasicrystal
• Mapping topological order in coordinate space
• Topological Insulators on the Lieb and Perovskite Lattices
• Topological Phases for Fermionic Cold Atoms on the Lieb Lattice
• Higher-Order Topological Insulators in Quasicrystals
• Disordered Topological Insulators via $C^{\ast }$-Algebras
• Topological Photonic Quasicrystals: Fractal Topological Spectrum and Protected Transport
• Quantum Spin Hall Effect and Spin Bott Index in a Quasicrystal Lattice
• Fractional Quantum Hall Effect in Topological Flat Bands with Chern Number Two
• Topological phases without crystalline counterparts
• Topological phase transitions driven by next-nearest-neighbor hopping in two-dimensional lattices
• Topological Hofstadter Insulators in a Two-Dimensional Quasicrystal
• Topological insulators and fractional quantum Hall effect on the ruby lattice
• Theory of spin Bott index for quantum spin Hall states in non-periodic systems
• Aperiodic Weak Topological Superconductors
• Topological phases and phase transitions on the square-octagon lattice
• Topology in the Sierpiński-Hofstadter problem
• Topological Insulators on the Decorated Honeycomb Lattice
• Failure of conductance quantization in two-dimensional topological insulators due to non-magnetic impurities
• Hofstadter butterfly of a quasicrystal
• Topological Anderson insulator phase in a quasicrystal lattice
• Corner states of topological fullerenes
• Nontrivial interplay of strong disorder and interactions in quantum spin-Hall insulators doped with dilute magnetic impurities
• Nontrivial topological states on a Möbius band
• Landau levels in quasicrystals
• Fractional Chern Insulators in Singular Geometries
• Chern Insulators on Singular Geometries

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• Layer-Dependent Topological Phase in a Two-Dimensional Quasicrystal and Approximant
• Topological Anderson insulators in an Ammann-Beenker quasicrystal and a snub-square crystal
• Quasicrystalline second-order topological semimetals
• Physical properties of an Aperiodic monotile: Graphene-like features, chirality and zero-modes
• Quasicrystalline Bose glass in the absence of disorder and quasidisorder
• Fermionic Chern insulator from twisted light with linear polarization
• Topological states in a dimerized system with staggered magnetic fluxes
• Topological charge pumping in quasiperiodic systems characterized by Bott index
• Non-Hermitian topological phases and skin effects in kagome lattices
• Higher-dimensional Hofstadter butterfly on Penrose lattice
• Confined states and topological phases in two-dimensional quasicrystalline $\pi$-flux model
• Chebyshev Polynomial Method to Landauer-Büttiker Formula of Quantum Transport in Nanostructures
• Interlaced wire medium with quasicrystal lattice
• Weyl superconductivity and quasiperiodic Majorana arcs in quasicrystals
• Family of Aperiodic Tilings with Tunable Quantum Geometric Tensor
• Global and Local Topological Crystalline Markers for Rotation-Symmetric Insulators
• Real-space formulation of the Chern invariant and topological phases in a disordered Chern insulator
• Disorder-induced chiral and helical Majorana edge modes in a two-dimensional Ammann-Beenker quasicrystal