Landau levels for massive disclinated graphene-based topological insulator

TL;DR

This paper studies the Landau levels in massive disclinated graphene-based topological insulators under magnetic fields, revealing zero modes and sublattice-dependent gap variations through a decoupled Dirac equation approach.

Contribution

It introduces a method to decouple the Dirac equation in disclinated graphene, deriving Landau levels and identifying zero modes and sublattice gap differences in this topological insulator model.

Findings

Zero modes emerge as edge states due to inversion symmetry breaking.

Different sublattices can have different gap widths.

Landau levels are characterized in the disclinated graphene framework.

Abstract

In this work, we investigate the massive Kane-Mele model for graphene in the presence of disclination and an external magnetic field, where graphene behaviors as a topological insulator. In the low-energy limit, the effective field equation for graphene is described by a Dirac equation with three different degrees of freedom. We succeed to decouple the set of eight components of the Dirac equation by using the spin projector \hat{C} in the disclinated geometry. As consequence, we obtain the Landau levels in this framework, in which we note the emergence of zero modes as edge states due to the inversion symmetry breaking. We also note that for different sites in sublattices \mathcal{A/B}, one can have different values of gap width.