Disorder in self-similar structure based graphene monolayer

We studied the impact of structural disorder on the transport of massive electrons in self-similar structures based on graphene monolayers. For each generation of the structure, we calculated the transmission coefficient using the transfer matrix formalism. The self-similar structure we studied follows a scaling rule that relates the transmission coefficient across different generations. We introduced disorder in three ways: by modifying the total width of the structure, changing the barrier energy, and altering each barrier independently. Our results indicate that disorder significantly impacts both the transport properties and self-similar characteristics of graphene, mainly when it affects the total width of the structure. In contrast, introducing disorder solely to the barrier energy did not influence the electronic or self-similar properties, demonstrating the robustness of the scaling rule against fabrication-induced disturbances. When disorder was independently introduced to the energy of each barrier, the electronic properties and behavior of massive electrons remained stable, although the scaling rule was slightly affected.