Bound States of Conical Singularities in Graphene-Based Topological Insulators

Abstract

We investigate the electronic structure induced by wedge-disclinations (conical singularities) in a honeycomb lattice model realizing Chern numbers $\gamma =\pm 1$. We establish a correspondence between the bound state of (i) an isolated ${\Phi }_0/2$-flux, (ii) an isolated pentagon $(n=1)$ or heptagon $(n=-1)$ defect with an external flux of magnitude $n\gamma {\Phi }_0/4$ through the center and (iii) an isolated square or octagon defect without external flux, where ${\Phi }_0=h/e$ is the flux quantum. Due to the above correspondence, the existence of isolated electronic states bound to the disclinations is robust against various perturbations. These results are also generalized to graphene-based time-reversal invariant topological insulators.

5+4 pages, 4+3 figures, revised introduction and Fig. 4

References in corpus (40)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Effect in Graphene
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Quantum Spin Hall Effect in Silicene
• Topological Crystalline Insulators
• Energy gaps, topological insulator state and zero-field quantum Hall effect in graphene by strain engineering
• Gauge fields in graphene
• Topological crystalline insulator states in Pb(1-x)Sn(x)Se
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Topological Defects in Graphene: Dislocations and Grain Boundaries
• Aharonov-Bohm interference in topological insulator nanoribbons
• Antiferromagnetic topological insulators
• Inversion Symmetric Topological Insulators
• Impurity induced spin-orbit coupling in graphene
• Boundary conditions for Dirac fermions on a terminated honeycomb lattice
• Electron fractionalization in two-dimensional graphenelike structures
• Helical Metal Inside a Topological Band Insulator
• Aharonov-Bohm effect and broken valley-degeneracy in graphene rings
• The Electronic Spectrum of Fullerenes from the Dirac Equation
• Quantum Anomalous Hall Effect in Single-layer and Bilayer Graphene
• Magnetic and Electronic Properties of Metal-Atom Adsorbed Graphene
• Effects of topological defects and local curvature on the electronic properties of planar graphene
• Aharonov-Bohm oscillations in disordered topological insulator nanowires
• Giant topological insulator gap in graphene with 5d adatoms
• Two-Dimensional Topological Insulator State and Topological Phase Transition in Bilayer Graphene
• Grain Boundary Loops in Graphene
• Anomalous Aharonov-Bohm conductance oscillations from topological insulator surface states
• Edge solitons of topological insulators and fractionalized quasiparticles in two dimensions
• Topological insulators in three dimensions from spontaneous symmetry breaking
• Universal probes of two-dimensional topological insulators: Dislocation and pi-flux
• Topological Phases in Graphitic Cones
• Spin-charge Separated Solitons in a Topological Band Insulator
• Wormhole Effect in a Strong Topological Insulator
• Spin Charge Separation in the Quantum Spin Hall State
• Fractional topological phases and broken time reversal symmetry in strained graphene
• Topological Order and Semions in a Strongly Correlated Quantum Spin Hall Insulator
• Parallel Transport of Electrons in Graphene Parallels Gravity
• Fullerenes, Zero-modes, and Self-adjoint Extensions
• Aharonov-Bohm effect in relativistic and nonrelativistic 2D electron gas: a comparative study

Cited by in corpus (29)

• Quantization of fractional corner charge in $C_n$-symmetric higher-order topological crystalline insulators
• Experimental discovery of bulk-disclination correspondence
• Correlation effects in two-dimensional topological insulators
• Majorana Fermions and Disclinations in Topological Crystalline Superconductors
• Observation of Protected Photonic Edge States Induced By Real-Space Topological Lattice Defects
• Shift insulators: rotation-protected two-dimensional topological crystalline insulators
• Vortex states in an acoustic Weyl crystal with a topological lattice defect
• Partial lattice defects in higher order topological insulators
• Topological states in multi-orbital HgTe honeycomb lattices
• Observation of nonlinear disclination states
• Kane-Mele with a twist: Quasicrystalline higher-order topological insulators with fractional mass kinks
• Bulk-Defect Correspondence in Particle-Hole Symmetric Insulators and Semimetals
• Corner states of topological fullerenes
• Topological Invariant and Quantum Spin Models from Magnetic π Fluxes in Correlated Topological Insulators
• Fractional charge and inter-Landau level states at points of singular curvature
• Disclination classes, fractional excitations, and the melting of quantum liquid crystals
• Observation of Large-Number Corner Modes in $\mathbb{Z}$-class Higher-Order Topolectrical Circuits
• Nonlinear photonic disclination states
• Evolution of Landau levels in graphene-based topological insulators in the presence of wedge disclinations
• Quantum oscillation and wave packet revival in conical graphene structure
• Chern Insulators on Singular Geometries
• Fractional Chern Insulators in Singular Geometries
• Boundary edge networks induced by bulk topology
• Graphene with wedge disclination in the presence of intrinsic and Rashba spin orbit couplings
• Graphene-based topological insulator in the presence of a disclination submitted to a uniform magnetic field
• Electronic Properties of Graphene Quantum Ring with Wedge Disclination
• Topological Field Theories of Three-Dimensional Rotation Symmetric Insulators: Coupling Curvature and Electromagnetism
• Observation of dislocation-induced topological modes in a three-dimensional acoustic topological insulator
• Zero-energy states in graphene quantum dot with wedge disclination