Title: Electronic properties of bilayer sheets forming moiré patterns
Author(s):

	W.S. Wu-Mei (National university of Colombia, Bogota, Colombia),
	R.R. Rey-González (National university of Colombia, Bogota, Colombia)

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 moiré 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.

Key words: tight binding approximation, graphene, boron nitride, bilayer, moire patterns, Van der Waals interactions, commensuration theorem, low energy approximation

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