Novel version of the Fibonacci superlattices formed of graphene nanoribbons: Transmission spectra

Abstract

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.

Transmission of the Relativistic Fermions With the Pseudospin Equal to One Through the Quasi‐Periodic Barriers

“…The trace map depicted in Figure reveals properties that are in some aspects essentially different from the analogous trace maps of the graphene structures: Particular attention is attracted to the point of energy E = U /2. For all Fibonacci generations, the super Klein tunneling is observed for this energy.…”

“…It should be noted that in the barrier region, that is, within the energy range [0, U ], the number of the allowed bands in each following sequence is subjected to the Fibonacci rule: Z n = Z n‐1 + Z n‐2 , namely, the number of zones for the 3rd, 4th, 5th, 6th …, generations are equal to 2, 4, 6, 10…, respectively. For the stronger quasi‐periodic factor, that is, for greater difference between the values of U A and U B , we observe the following changes in the trace‐map: 1) more significant reduction of the allowed bands; 2) a shift of the bands toward higher energies. It differs greatly from the graphene‐based SL, in which the trace map composition (i.e., mutual arrangement of bands) does not change with amplification of the quasi‐periodic factor (there is no shift of the bands, see, e.g.,).…”

“…Various types of the SL are considered: strictly periodic ones, disordered ones, lattices with defects, etc. Structures intermediate between the periodic and the disordered ones (in particular the quasi‐periodic lattices, such as the Fibonacci and the Thue‐Morse superlattices) occupy a notable place among the SL . This is determined by their unique properties, such as the self‐similarity, the Cantor nature of the energy spectrum, and others (see, e.g.,).…”

“…Structures intermediate between the periodic and the disordered ones (in particular the quasiperiodic lattices, such as the Fibonacci and the Thue-Morse superlattices) occupy a notable place among the SL. [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39] This is determined by their unique properties, such as the selfsimilarity, the Cantor nature of the energy spectrum, and others (see, e.g., [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39]). There is a surge of interest in exploring transport properties of the quasi-periodic superlattices (refs.…”

“…There is a surge of interest in exploring transport properties of the quasi-periodic superlattices (refs. [25,[29][30][31][32][33][34][35][36][37][38][39]). The quasi-periodical SL can have different application areas, in particular as the convenient and effective energy filter for the quasiparticles.…”