Corner states of topological fullerenes

Abstract

The unusual electronic properties of the quantum spin Hall or Chern insulator become manifest in the form of robust edge states when samples with boundaries are studied. In this work, we ask if and how the topologically non-trivial electronic structure of these two-dimensional systems can be passed on to their zero-dimensional relatives, namely fullerenes or other closed-cage molecules. To address this question, we study Haldane's honeycomb lattice model on polyhedral nano-surfaces. We find that for sufficiently large surfaces characteristic corner states appear for parameters for which the planar model displays a quantized Hall effect. In the electronic structure, these corner states show up as in-gap modes which are well separated from the quasi-continuum of states. We discuss the role of finite size effects and how the coupling between the corner states lifts the degeneracy in a characteristic way determined by the combined Berry phases which leads to an effective magnetic monopole of charge 2 at the center of the nano-surface. Experimental implications for fullerenes in the large spin-orbit regime are also pointed out.

12 pages, 13 figures

References in corpus (19)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator
• Classification of topological insulators and superconductors in three spatial dimensions
• Large-gap quantum spin Hall insulators in tin films
• Topological Defects and Gapless Modes in Insulators and Superconductors
• The Helical Liquid and the Edge of Quantum Spin Hall Systems
• The space group classification of topological band insulators
• Quantum Spin Hall Effect and Enhanced Magnetic Response by Spin-Orbit Coupling
• Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators
• Electron fractionalization in two-dimensional graphenelike structures
• Helical Metal Inside a Topological Band Insulator
• Spin-charge Separated Solitons in a Topological Band Insulator
• Spin Charge Separation in the Quantum Spin Hall State
• Transport Properties of Graphene Nanoroads in Boron-Nitride Sheets
• Bound States of Conical Singularities in Graphene-Based Topological Insulators
• Quantum anomalous Hall states in the $p$-orbital honeycomb optical lattices
• Topological Invariant and Quantum Spin Models from Magnetic π Fluxes in Correlated Topological Insulators
• Non-abelian gauge fields and quadratic band touchings in molecular graphene

Cited by in corpus (20)

• Quantization of fractional corner charge in $C_n$-symmetric higher-order topological crystalline insulators
• Synthetic three-dimensional atomic structures assembled atom by atom
• Classification of Two Dimensional Topological Crystalline Superconductors and Majorana Bound States at Disclinations
• Stability and properties of high-buckled two-dimensional tin and lead
• Shift insulators: rotation-protected two-dimensional topological crystalline insulators
• Vortex states in an acoustic Weyl crystal with a topological lattice defect
• Quasicrystalline Chern Insulators
• Bulk-Defect Correspondence in Particle-Hole Symmetric Insulators and Semimetals
• Edge states of a three-dimensional topological insulator
• Evolution of Landau levels in graphene-based topological insulators in the presence of wedge disclinations
• Fractional Chern Insulators in Singular Geometries
• Boundary edge networks induced by bulk topology
• Chern Insulators on Singular Geometries
• Confining electrons on a topological insulator surface using potentials and a magnetic field
• Graphene-based topological insulator in the presence of a disclination submitted to a uniform magnetic field
• Gravitational Response of Topological Quantum States of Matter
• Additive rule of real and reciprocal space topologies at disclinations
• Topological Field Theories of Three-Dimensional Rotation Symmetric Insulators: Coupling Curvature and Electromagnetism
• Electronic properties of graphyne-$N$ monolayer and its multilayer: even-odd effect and topological nodal line semimetalic phases
• Designing atomic-scale resistive circuits in topological insulators through vacancy-induced localized modes