Theoretical Study of Band Gap opening in AB- stacked Bi-layer Graphene by Impurity and Electric Field Effects

We report here a tight-binding model calculation for AB-stacked bilayer graphene in the presence of a biased potential between two layers and impurity effects to study the evolution of a band gap near Dirac point. We have calculated the electronic Green's function for both the A and B sub-lattices employing Zubarev's technique. The poles of the Green's functions provide the four band energy dispersions of the bi layer graphene. The imaginary part of Green's function provides the density of states of the electrons. Then the band energy dispersion and density of states are computed for 1000 X 1000 grid points of the electron momentum. The tunable band gap is investigated from the calculated band energy dispersion and electron density of states by varying different physical parameters. The interlayer hopping splits the density of states at the van-Hove singularities with a V shaped gap near Dirac point. Further the biased potential introduces a band gap near Dirac point with a density minimum at the applied potential i.e. at V / 2. The interlayer hopping produces a Mexican hat type gap at K point.