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We consider the gapped graphene superlattice (SL) constructed in accordance with the Fibonacci rule. Quasi-periodic modulation is due to the difference in the values of the energy gap in different SL elements. It is shown that the effective splitting of the allowed bands and thereby forming a series of gaps is realized under the normal incidence of electrons on the SL as well as under oblique incidence. Energy spectra reveal periodical character on the whole energy scale. The splitting of allowed bands is subjected to the inflation Fibonacci rule. The gap associated with the new Dirac point is formed in every Fibonacci generation. The location of this gap is robust against the change in the SL period but at the same time it is sensitive to the ratio of barrier and well widths; also it is weakly dependent on values of the mass term in the Hamiltonian.
Based on first-principles calculations we predict that periodically repeated junctions of armchair graphene nanoribbons of different widths form superlattice structures. In these superlattice heterostructures the width and the energy gap are modulate
We study the conductance of disordered graphene superlattices with short-range structural correlations. The system consists of electron- and hole-doped graphenes of various thicknesses, which fluctuate randomly around their mean value. The effect of
Twisting van der Waals heterostructures to induce correlated many-body states provides a novel tuning mechanism in solid-state physics. In this work, we theoretically investigate the fate of the surface Dirac cone of a three-dimensional topological i
We explore the effect of mechanical strain on the electronic spectrum of patterned graphene based heterostructures. We focus on the competition of Kekule-O type distortion favoring a trivial phase and commensurate Kane-Mele type spin-orbit coupling g
The moire superlattice induced in graphene by the hexagonal boron nitride substrate modifies strongly the bandstructure of graphene, which manifests itself by the appearance of new Dirac points, accompanied by van Hove singularities. In this work, we