L?vy flight for electrons in graphene: Superdiffusive-to-diffusive transport transition

In this paper we propose an electronic Levy glass, analogous to a recent optical realization. To that end, we investigate the transmission of electrons in graphene nanoribbons in the presence of circular electrostatic clusters, whose diameter follow a power-law distribution. We analyze the effect of the electrostatic clusters on the electronic transport regime of the nanoribbons, in terms of its diffusion behavior. Our numerical calculations show that the presence of circular electrostatic clusters induces a transition from Levy (superdiffusive) to diffu-sive transport as the energy increases. Furthermore, we argue that in our electronic Levy glass, superdiffusive transport is an exclusive feature of the low-energy quantum regime, while diffusive transport is a feature of the semiclassical regime. We thus attribute the observed transition to the chiral symmetry breaking, once the energy moves away from the Dirac point of graphene.