The transmission spectra of the graphene-based Fibonacci superlattice

TL;DR

This paper investigates the electronic transmission spectra of a Fibonacci-structured graphene superlattice, revealing band splitting, gap formation, and the influence of structural parameters on electronic properties.

Contribution

It introduces a model of a Fibonacci-based graphene superlattice with energy gap modulation and analyzes its spectral properties and band structure behavior.

Findings

Allowed band splitting follows Fibonacci inflation rules

Energy gaps form at each Fibonacci generation

Gap location is robust to period changes but sensitive to barrier/well ratio

Abstract

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.