Fractal electronic transport in graphene Cantor structures by means of power spectrum analysis

Graphene fractal structures are ideal systems to analyze the impact of self-similar geometries on physical properties. Here, we study the electronic transport in graphene Cantor structures. A transmission scheme for the electronic transport is used. In particular, the zero-temperature linear-regime conductance is computed with the Landauer-B"uttiker formalism. We obtain the conductance for different generations of the graphene Cantor structure. The fractality of the conductance curves is determined by means of power spectrum analysis, while the fractality of the Cantor-like potential profile is calculated with the box-counting method. The fractality of the conductance curves is strongly related to the fractality of the Cantor-like potential profiles. The power spectrum analysis of the conductance curves also allows us to find the dominant Fermi energies of the electronic transport in graphene Cantor structures. These Fermi energies are related to the embedded periodic structures intrinsic to graphene Cantor structures. To the best of our knowledge, this is the first report using the power spectrum analysis to understand the electronic transport in graphene fractal structures.