Abstract
In this paper, we investigated the Fano factor in two types of self-similar potential structures in a graphene monolayer. These structures are substrate-based potential and electrostatic-based potential. However, in order to determine the Fano factor in such structures, we solved the Dirac Hamiltonian by using the transfer matrix method. We found that the self-similar substrate-based potential structure manifests a self-similar behavior in the Fano factor and conductance. Therefore, we proposed scaling rules that represent a scale invariance between generations, main barrier heights, and total lengths of the structures. In particular, the maximum Fano factor value was reported for the self-similar electrostatic-based potentials. More analysis was given in terms of the generation, main barrier heights, and structure’s total lengths. These kinds of structures could be used to control the Fano factor.
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