Investigation of bilayer equivalence of periodic graphene gated structures

We investigate electron transmission through graphene periodic gated structures. Such structures are useful because of their high modulation ability, and low energy consumption. In periodic graphene gated structures the linear dispersion relation of charge carriers is modified and, besides the formation of minibands, electrons and holes acquire a finite effective mass. Because the wavefunction remains spinorial, a periodic graphene gated structure can, in principle, act as a sheet of bilayer graphene. We investigate in this paper if such an equivalence is justified or not.