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 = p/q phi(0)/S 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.