Graphene-based topological insulator in the presence of a disclination submitted to a uniform magnetic field

Highlights: • Quantum dynamics of quasiparticle in graphene-based topological. • Haldane model in the presence of disclination. • Landau levels in Haldane model in the presence of topological defects. • Topological insulator with topological defect. In this paper we investigate quasiparticles in graphene-based topological insulator with a wedge disclination in the presence of a uniform magnetic field. In particular, we consider a massive spinless model. The Landau levels are analytically found for the described system. We show that the Landau levels are lifted for a specific range of the parameter $\nu$. In addition, we also show that, for appropriate parameter values, one finds gapless and gapped states.