Bound States of Conical Singularities in Graphene-Based Topological Insulators

TL;DR

This paper explores how conical singularities in graphene topological insulators induce robust bound electronic states, revealing a correspondence with flux and defect types, applicable to both Chern insulators and time-reversal invariant systems.

Contribution

It establishes a novel correspondence between bound states of disclinations, fluxes, and defects in graphene topological insulators, demonstrating their robustness and generalization to time-reversal invariant cases.

Findings

Bound states are robust against perturbations.

Correspondence between flux, defect, and bound states.

Generalization to time-reversal invariant 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.