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We find a systematic reappearance of massive Dirac features at the edges of consecutive minibands formed at magnetic fields B p/q =pq ϕ 0 /S providing rational magnetic flux through a unit cell of the moiré superlattice created by a hexagonal substrate for electrons in graphene. The Dirac-type features in the minibands at B=B p/q determine a hierarchy of gaps in the surrounding fractal spectrum and show that these minibands have topological insulator properties. Using the additional q -fold degeneracy of magnetic minibands at B p/q , we trace the hierarchy of the gaps to their manifestation in the form of incompressible states upon variation of the carrier density and magnetic field.
Chen, X., Wallbank, J. R., Patel, A. A., Mucha-Kruczynski, M., McCann, E., & Fal'ko, V. I. (2014). Dirac edges of fractal magnetic minibands in graphene with hexagonal moiré superlattices. Physical Review B, 89(7), 1 - 5. . https://doi.org/10.1103/PhysRevB.89.075401