We find a systematic reappearance of massive Dirac features at the edges of consecutive minibands formed at magnetic fields $B_{p/q}=\frac{p}{q}{\varphi }_0/S$ 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.

• Received 31 October 2013

DOI:https://doi.org/10.1103/PhysRevB.89.075401