Magneto-optical properties of Fibonacci graphene superlattices

We have studied the transition strength and magneto-optical absorption in Fibonacci graphene superlattices under the effects of perpendicularly applied magnetic field. It is shown that the former quantity present self-similarity and anti-self-similarity behavior at magnetic field strengths connected via τ4 and τ2, respectively, τ being the golden mean. In order to be able to observe this effect, it is necessary that for a particular field the transition strength curve is displaced laterally as a rigid body so that the adjustment is achieved with that corresponding to the other field. It was found that this shifting is determined by the symmetry and scaling properties of the Fibonacci structure. For all the magnetic fields and polarizations of the incident radiation considered here, it is observed that the absorption spectra have the characteristic of self-similarity and also that they show resonant peak structures that satisfy selection rules that keep, in very good approximation, the same characteristics of graphene monolayers. We showed analytically that the similarity properties of both the transition strength and optical absorption are a direct consequence of those of the magnetic subbands.