Transmission and transport properties in Cantor graphene structures: The case of magnetoelectric modulation

We discuss theoretically the transmission and transport properties of Dirac electrons in a Cantor graphene system under magnetoelectric effects. The transfer matrix method and the Landauer-Büttiker formalism have been implemented to compute the transmittance and the linear-regime conductance, respectively. The fractal order of Cantor type together with the magnetic and electric field are used to distribute and generate the magnetoelectric barriers. This system give us the possibility of compare the mentioned physical properties for magnetic and magnetoelectric barriers. We found a bifurcation process in the transmission spectra which is observable when the generation increases. Also, an asymmetrical and symmetrical behavior is presented for magnetic and magnetoelectric barriers, respectively. In general, an oscillatory behavior is manifested in the conductance. Moreover, we can describe the peaks (form and location) that give rise to the oscillations through the contour plots of the transmittance in the (E,ky) space. Likewise, by increasing the generation of the system the conductance is enhanced, the oscillations reduced and less pronounced. In short, the magnetoelectric modulation along with the fractal order can be used to control the transmission and transport properties in graphene-based structures.