Dirac edges of fractal magnetic minibands in graphene with hexagonal moire superlattices

We find a systematic reappearance of massive Dirac features at the edges of consecutive minibands formed at magnetic fields B_{p/q}= pφ_0/(qS) providing rational magnetic flux through a unit cell of the moire 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.