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The energy spectra of a novel version of graphene‐based Fibonacci superlattices (SL) are calculated. A new quasiperiodical factor is considered. The SL is built of graphene nanoribbons (GNR) and the quasi‐periodicity is formed due to the fact that different ribbons are used as individual elements of the SL and are placed along the lattice growth axis in accordance with the Fibonacci inflation rule. In one case, the SL is composed of smooth‐edges and a metal‐like armchair NR, and we propose to use a metal‐like and a semiconductor armchair NR for another case. It is shown that: (i) the difference in values of the quantized transverse quasi‐momentum of electrons for different NR is fully enough to form an effective quasi‐periodic modulation in the given structure (no additional factors are needed), and the range of the ribbon widths for this purpose is determined; (ii) it is important that this range is suitable for practice. We also analyze the dependence of the energy spectra of the studied structure on the geometric parameters of the superlattice as well as on the external electrostatic potential. Attention is drawn, in particular, that in each Fibonacci generation there is the Dirac superlattice gap. Varying the nanoribbons width one can change the spectra investigated flexibly. The conductance of the structure studied is also calculated. The results obtained can be useful in determining the optimum parameters of devices of the graphene‐based nanoelectronics.

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