  The work presents a study on the quantum theory of periodic graphs applied to
mono- and bilayer hexagonal materials. Different parameters associated with the
atoms present at the vertices of these materials were analyzed, verifying the
existence of gaps in the spectral bands and expressing the width of these
openings according to the parameters. The study was extended to
heterostructures with mixed layers and "sandwiches" of graphene and hexagonal
boron nitride. The dispersion relationships obtained in these models were
analyzed and it was concluded that the inclusion of hBN layers on graphene
layers can induce a gap in the graphene. Furthermore, it was observed that the
inclusion of a single layer of graphene between two layers of hBN reduces the
width of the spectral gap. The interaction between carbon atoms and nitrogen
and boron atoms was pointed out as responsible for these results. Finally, the
inclusion of a magnetic field in the hBN layer was considered, demonstrating
that specific values of magnetic flux can eliminate conical touches in the
dispersion relation of the operator and ensure the existence of gaps.
