Níveis de Landau em grafeno na presença de potenciais unidimensionais

Abstract

Graphene, a monolayer of carbon atoms arranged in a honeycomb lattice, has become a topic of intensive study in recent years and considered a promising candidates for electronic device applications due its unique electronic band structure. Such two-dimensional (2D) material is a zero gap semiconductor, exhibiting a linear energy dispersion, where charge carriers behave as massless Dirac fermions for low energies. In the present work, we investigate within the Dirac continuum model the electronic states of graphene in the presence of a perpendicular uniform magnetic field and by considering the effect of different position-dependent one-dimensional potential. We show that the Landau levels differ from those ones obtained by solving the Schr¨odinger equation for free particles, presenting a square root dependence on magnetic field, instead of being equally spaced as in 2D electron gas. By considering two different shapes of potentials, such as uniform and periodic, we calculate the energy dispersion and magnetic field dependence of those systems in the presence of an external magnetic field. Our solution is performed by using an expansion of the pseudospinor components (wavefunctions for each sub-lattice) in terms of Hermite polynomials and by constructing an eigenvalue equation in which the eigenvalues gives us the energy dispersion.