Transmission properties of Dirac electrons through Cantor monolayer graphene superlattices

Abstract

In this work we use the transfer matrix method to study the tunneling of Dirac electrons through aperiodic monolayer graphene superlattices. We consider a graphene sheet deposited on top of slabs of Silicon-Oxide (SiO2) and Silicon-Carbide (SiC) substrates, in which we applied the Cantor's series. We calculate the transmittance for different fundamental parameters such as: starting width, incident energy, incident angle and generation number of the Cantor's series. In this case, the transmittance as function of energy presents self-similar features as a function of the generation number. We also compute the angular distribution of the transmittance for fixed energies finding a self-similar patterns between generations. Finally, we calculate the scaling factor for some transmittance spectra, which effectively show scalability.