We find a systematic reappearance of massive Dirac features at the edges of consecutive minibands formed at magnetic fields Bp/q=p/qφ₀/S providing rational magnetic flux through a unit cell of the moir\'e superlattice created by a hexagonal substrate for electrons in graphene. The Dirac-type features in the minibands at B=Bp/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 Bp/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.
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Chen et al. (2014) studied this question.