Efeitos de campo magnético dependente da posição em monocamadas e bicamadas de grafeno

Abstract

In the past few years graphene has been shown to be an interesting object of investigation to scientists around the world, due to its peculiar characteristics as well as its electronics properties. Much research have been done in order to unveil this still newly discovered carbon allotrope, having already rendered a Nobel prize in 2010. Here it'll be discussed some of these graphene characteristics focusing on the structural lattice properties and also on the electronics properties. The interaction of Dirac fermions, massless relativistic particles, under an external homogeneous magnetic eld in one and two layers of graphene will be studied, based on the low-energy Dirac theory and the tight-binding approximation model, stating an equivalence between these two models. By writing the Hamiltonian for a single sheet of graphene, an eigenvalue problem is set up, and the energy band dispersion of the material and the so called Landau levels are found, the latter, originated by the presence of a magnetic eld perpendicular to the interaction plane. Next, these same steps were performed to the bilayer sistem. In addition, the e ects of a position dependent magnetic eld will be presented here, so that the Landau levels can be written. This work will demonstrate that one of the factors that make graphene so attractive to research is precisely the particle interaction in this material.