Fibonacci quasiregular graphene-based superlattices: Quasiperiodicity and its effects on the transmission, transport and electronic structure properties

We study the transmission, transport and electronic structure properties of aperiodic Fibonacci monolayer graphene-based structures (AFGBSs). The transfer matrix method has been implemented to obtain the transmittance, linear-regime conductance and electronic structure. In particular, we have studied two types of aperiodic graphene-based structures: (1) electrostatic AFGBSs (EAFGBSs), structures formed with electrostatic potentials, and (2) substrate AFGBSs (SAFGBSs), obtained alternating substrates that can open and non-open, such as SiC and SiO2, an energy bandgap on graphene. We have found that the transmission properties can be modulated readily by changing the main parameters of the systems: well and barrier widths, energy and angle of incident electrons and the degree of aperiodicity. In the case of the linear-regime conductance turns out that it diminishes various orders of magnitude increasing the barrier width for SAFGBSs. On the contrary, Klein tunneling sustains the conductance in EAFGBSs. Calculating the electronic structure or miniband-structure formation and its fragmentation we establish a direct connection between the conductance peaks and the opening, closure and degeneration of energy minibands for both EAFGSLs and SAFGSLs.