https://doi.org/10.1140/epjp/s13360-025-06153-y
Regular Article
Landau levels for massive disclinated graphene-based topological insulator
1
Departamento de Física, Universidade Federal da Paraíba, Caixa Postal 5008, 58051-970, João Pessoa, PB, Brazil
2
Centro de Ciências, Tecnologia e Saúde, Universidade Estadual da Paraíba, 58233-000, Araruna, PB, Brazil
Received:
18
July
2024
Accepted:
19
February
2025
Published online:
19
March
2025
In this work, we investigate the massive Kane–Mele model for graphene in the presence of disclination and an external magnetic field, where graphene behaves 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 in decoupling the set of eight components of the Dirac equation by using the spin projector 
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 
, one can have different values of gap width.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
