Quasiperiodic graphene superlattices: Self-similarity of the Landau level spectra

We have numerically calculated the magnetic subbands of a quasiperiodic Fibonacci graphene superlattice subject to a perpendicular magnetic field. It is shown that, when all energies and lengths are written in units of the cyclotron energy and cyclotron radius, respectively, these subbands exhibit a self-similar behavior at two magnetic fields related by τ4. To see explicitly that behavior, the energy spectrum corresponding to one of the fields must be rigidly shifted upwards in energy and in the lateral direction. It was also found that to obtain a good coincidence between both spectra, one of them must be properly rescaled in energy.