Abstract
A new self-similar graphene structure with different construction parameters is created to investigate the scalability of transmission coefficient. The transfer matrix formalism is used to calculate transmission spectra for generations of the self-similar structure. Two cases are analyzed: In the first case, the barriers were created by substrates, which induce a gap in the graphene. In the second case, the barriers were created by electric fields that can produce a displacement of the Dirac cones. We find that both cases show self-similarity patterns in their transmission spectra, which can be demonstrated through analytical equations called scaling rules, those rules connecting the generations of the structure. It results when the height of the barriers (V 0) is scaled or not, it gives different scaling rules, which shows that V 0 can be a revealing factor to find alternatives to scaling the transmission coefficient. Scaling rules can be useful because one can determine the transmission coefficient of generation i + 1 only by knowing a generation i.
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