  In this article, we report the electronic band structures of hexagonal
bilayer systems, specifically, rotated graphene-graphene and boron
nitride-boron nitride bilayers, by introducing an angle between the layers and
forming new periodic structures, known as moir\'e patterns. Using a
semi-empirical tight-binding approach with a parametrized hopping parameter
between the layers, using one orbital per-site approximation, and taking into
account nearest-neighbor interactions only, we found he electronic dispersion
relations to be around K points in a low energy approximation. Our results show
that graphene bilayers exhibit zero band gap for all angles tested in this
work. In boron nitride bilayers, the results reveal a tunable bandgap that
satisfies the prediction of the bandgap found in one-dimensional diatomic
systems presented in the literature.
