Field modulation in bilayer graphene band structure

Using an external electric field, one can modulate the band gap of Bernal stacked bilayer graphene by breaking the A-(B) over tilde symmetry. We analyze strain effects on the bilayer graphene using the extended Huckel theory and find that reduced interlayer distance results in higher band gap modulation, as expected. Furthermore, above about 2.5 angstrom interlayer distance, the band gap is direct, follows a convex relation with the electric field and saturates to a value determined by the interlayer distance. However, below about 2.5 angstrom, the band gap is indirect, the trend becomes concave and a threshold electric field is observed, which also depends on the stacking distance.