Protected Gapless Edge States In Trivial Topology

Abstract

Bulk-boundary correspondence serves as an important feature of the strong topological insulators, including Chern insulators and $Z_2$ topological insulators. Under nontrivial band topology, the protected gapless edge states correspond to the Wannier obstruction or Wilson-loop winding in the bulk. Recent studies show that the bulk topological features may not imply the existence of protected gapless edge states. Here we address the opposite question: Does the existence of protected gapless edge states necessarily imply the Wannier obstruction or Wilson-loop winding? We provide an example where the protected gapless edge states arise without the aforementioned bulk topological features. This trivialized topological insulator belongs to a new class of systems with non-delta-like Wannier functions. Interestingly, the gapless edge states are not protected by the crystalline symmetry; instead the protection originates from the mirror antisymmetry, a combination of chiral and mirror symmetries. Although the protected gapless edge states cannot be captured by the bulk topological features, they can be characterized by the spectral flow in the entanglement spectrum.

arXiv comment7 pages, 4 figures

References in corpus (81)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Topological Insulators in Three Dimensions
• Topological Insulators with Inversion Symmetry
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Maximally localized Wannier functions: Theory and applications
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Topological Crystalline Insulators
• Quantized Electric Multipole Insulators
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Higher-Order Topological Insulators
• Topological quantum chemistry
• Topological Crystalline Insulators in the SnTe Material Class
• 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 Topology in Bismuth
• Symmetry-based Indicators of Band Topology in the 230 Space Groups
• Quantization of fractional corner charge in $C_n$-symmetric higher-order topological crystalline insulators
• The Helical Liquid and the Edge of Quantum Spin Hall Systems
• Surface States of the Topological Insulator Bi_{1-x}Sb_x
• Topological classification of crystalline insulators through band structure combinatorics
• Direct observation of corner states in second-order topological photonic crystal slabs
• Stability of the quantum spin Hall effect: effects of interactions, disorder, and Z_2 topology
• Inversion Symmetric Topological Insulators
• Higher-order topological insulators and superconductors protected by inversion symmetry
• Topology of crystalline insulators and superconductors
• Second-order photonic topological insulator with corner states
• All "Magic Angles" Are "Stable" Topological
• Second-order topological insulators and superconductors with an order-two crystalline symmetry
• Faithful Tight-binding Models and Fragile Topology of Magic-angle Bilayer Graphene
• Entanglement spectrum of topological insulators and superconductors
• Fragile Topology and Wannier Obstructions
• Spin-filtered Edge States with an Electrically Tunable Gap in a Two-Dimensional Topological Crystalline Insulator
• 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
• Symmetry indicators and anomalous surface states of topological crystalline insulators
• Higher-Order Topological Insulator in Twisted Bilayer Graphene
• Building Blocks of Topological Quantum Chemistry: Elementary Band Representations
• Wilson loop approach to fragile topology of split elementary band representations and topological crystalline insulators with time reversal symmetry
• Wannier Center Sheets in Topological Insulators
• Higher-order topological insulators protected by inversion and rotoinversion symmetries
• Engineering Corner States from Two-Dimensional Topological Insulators
• Universal Approach to Magnetic Second-Order Topological Insulator
• Topological non-symmorphic crystalline insulators
• Real Space Invariants: Twisted Bulk-Boundary Correspondence of Fragile Topology
• Topology of Disconnected Elementary Band Representations
• Boundary-obstructed topological phases
• Disconnected Elementary Band Representations, Fragile Topology, and Wilson Loops as Topological Indices: An Example on the Triangular Lattice
• Topological switch between second-order topological insulators and topological crystalline insulators
• Spinless Topological Insulators without Time-Reversal Symmetry
• Topological Insulators from Group Cohomology
• Edge modes in band topological insulators
• Fractional corner charges in spin-orbit coupled crystals
• Fragile Topology Protected by Inversion Symmetry: Diagnosis, Bulk-Boundary Correspondence, and Wilson Loop
• Berry-phase description of Topological Crystalline Insulators
• Entanglement Spectrum Classification of $C_n$-invariant Noninteracting Topological Insulators in Two Dimensions
• Shift insulators: rotation-protected two-dimensional topological crystalline insulators
• General corner charge formula in two-dimensional C_n-symmetric higher-order topological insulators
• Fragile Phases As Affine Monoids: Classification and Material Examples
• Symmetry indicators of band topology
• Crystallographic splitting theorem for band representations and fragile topological photonic crystals
• Free-fermion Entanglement Spectrum through Wannier Interpolation
• Multicellularity of delicate topological insulators
• Adiabatic Pumping of Chern-Simons Axion Coupling
• CPT theorem and classification of topological insulators and superconductors
• Corner charge and bulk multipole moment in periodic systems
• Delicate topology protected by rotation symmetry: Crystalline Hopf insulators and beyond
• Axion coupling in the hybrid Wannier representation
• Classification of crystalline insulators without symmetry indicators: atomic and fragile topological phases in twofold rotation symmetric systems
• Fractional Corner Charge of Sodium Chloride
• Bulk-and-edge to corner correspondence
• Symmetry-protected entangling boundary zero modes in crystalline topological insulators
• Non-Compact Atomic Insulators
• Identifying Higher Order Topology and Fractional Corner Charge Using Entanglement Spectra
• Quantized surface magnetism and higher-order topology: Application to the Hopf insulator
• Fractional hinge and corner charges in various crystal shapes with cubic symmetry
• Gapless hinge states from adiabatic pumping of axion coupling

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