Estudo do transporte eletrônico de uma super-rede de grafeno seguindo o modelo de Aubry-André-Harper

Abstract

Graphene is one of the allotropes of carbon and was discovered in 2004. With its different electronic properties compared to other materials, the scientic community turned its eyes to graphene, where several studies have been carried out until the present day. In this material, the quasiparticles (electrons and holes) behave like massless relativistic fermions. A system that has attracted great attention is the graphene superlattice, as it is possible to control the electronic properties of graphene in this system, leading to the possibility of more varied applications. Superlattice can befinite and infinite, being classified as periodic, random or quasi-periodic. The graphene superlattice structure can be modulated by magnetic barriers, electrostatic potentials, Fermi velocity barriers, etc. In this work, the graphene superlattice is modulated through quasi-periodic potential barriers, more specifically the widths of these barriers, and follows the Aubry-André model. We consider here the continuous model, using the effective Dirac Hamiltonian that describes the low-energy electronic excitations in graphene. Using the transfer matrix method, we obtain the transmission coeffcients, being essential for the analysis of the electronic transport in the system together with the quasi-periodic potentials of Aubry-André.