Bandgap scaling in bilayer graphene antidot lattices

On the basis of a tight binding model we reveal how the bandgap in bilayer graphene antidot lattices (GALs) follows a different scaling law than in monolayer GALs and we provide an explanation using the Dirac model. We show that previous findings regarding the criteria for the appearance of a bandgap in monolayer GALs are equally applicable to the bilayer case. Furthermore, we briefly investigate the optical properties of bilayer GALs and show that estimates of the bandgap using optical methods could lead to overestimates due to weak oscillator strength of the lowest transitions. Finally, we investigate the effect of imposing an electric field perpendicular to the bilayer GAL structure and find that the bandgap tunability may be extended as compared to pristine bilayer graphene.