Fractional charge bound to a vortex in two dimensional topological crystalline insulators

Abstract

We establish the correspondence between the fractional charge bound to a vortex in a textured lattice and the relevant bulk band topology in two-dimensional (2D) topological crystalline insulators. As a representative example, we consider the Kekule textured graphene whose bulk band topology is characterized by a 2D ${\mathbb{Z}}_2$ topological invariant ${\nu }_{2D}$ protected by inversion symmetry. The fractional charge localized at a vortex in the Kekule texture is shown to be related to the change in the bulk topological invariant ${\nu }_{2D}$ around the vortex, as in the case of the Su-Schriefer-Heeger model in which the fractional charge localized at a domain wall is related to the change in the bulk charge polarization between degenerate ground states. We show that the effective three-dimensional (3D) Hamiltonian, where the angle $\theta$ around a vortex in Kekule-textured graphene is a third coordinate, describes a 3D axion insulator with a quantized magnetoelectric polarization. The spectral flow during the adiabatic variation of $\theta$ corresponds to the chiral hinge modes of an axion insulator and determines the accumulated charge localized at the vortex, which is half-quantized when chiral symmetry exists. When chiral symmetry is absent, electric charge localized at the vortex is no longer quantized, but the vortex always carries a half-quantized Wannier charge as long as inversion symmetry exists. For the cases when magnetoelectric polarization is quantized due to the presence of symmetry that reverses the space-time orientation, we classify all possible topological crystalline insulators whose vortex defect carries a fractional charge.

5+8 pages, 3+6 figures, 1+1 tables

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• Fragile Topology Protected by Inversion Symmetry: Diagnosis, Bulk-Boundary Correspondence, and Wilson Loop
• General corner charge formula in two-dimensional C_n-symmetric higher-order topological insulators
• Corner modes of the breathing kagome lattice: origin and robustness
• Identifying Higher Order Topology and Fractional Corner Charge Using Entanglement Spectra
• Topological states in a dimerized system with staggered magnetic fluxes
• Competition of First-Order and Second-Order Topology on the Honeycomb Lattice
• Electric Polarization in Inhomogeneous Crystals
• Edge states in a non-Hermitian topological crystalline insulator
• Remote control of spin polarization of topological corner states
• Spin separation and filtering assisted by topological corner states in the Kekulé lattice
• Extended Haldane model -- a modern gateway to topological insulators