On distance variation effects on graphene bilayers

• The diagonal distance variation of graphene-like bilayers modifies the electronic structure properties.
• Depending on an intermediate stacking arrangement between the bilayers, the electronic structure properties change.
• The band gap opening depends on the variation of the diagonal distance of the (AB) arrangement.
• The band gap opening is due to the change of states of electrons in the pz orbitals.
• The band gap maximum value, 0.295 eV, is obtained for a vertical distance of 3.6 Å.

The opening of the energy gap and the total energy of the graphene-like bilayers are investigated using ab initio calculations. The studied model consists of a static single layer of graphene interacting with an extra dynamic one placed at a varying vertical distance d in the (AB) stacking arrangement. The effects of the vertical distance variation on the energy gap and the total energy of the system are discussed first. Starting from a distance around the van der Waals length, the energy gap does not depend on the vertical distance variation and the system exhibits graphene-like properties with minor deformations in the lattice size parameter and the energy dispersion behaviour around K points. However, it has been shown that the diagonal distance variation of the graphene-like bilayer modifies the electronic structure properties. This modification depends on an intermediate stacking arrangement between the (AA) and the (AB) configurations. It has been shown that the diagonal distance variation has an influence on the states of pz electrons in the (AB) arrangement and it can be explored to open the energy gap.