Microscopic theoretical model study of band gap opening in AA-stacked bi-layer graphene

We address here a tight-binding theoretical model calculation for AA-stacked bi-layer graphene taking into account of a biased potential between two layers to study the density of states and the band dispersion within the total Brillouin zone. We have calculated the electronic Green's function for electron operator corresponding to A and B sub lattices by Zubarev's Green's function technique from which the electronic density of states and the electron band energy dispersion are calculated. The numerically computed density of states and band energy dispersions are investigated by tuning the biased potential to exhibit the band gap by varying the different physical parameters.