Geometric and Electronic structures of deformed bilayer graphenes

The electronic properties of bilayer AB-stacked graphene are investigated with a first-principles method when homogeneous and uniaxial strains are exerted. The two types of strains can be either tensile or compressive. The maximum deformation ratio is 36{\%} for tensile strain, and 20{\%} for compressive strain. The uniaxial strains along the armchair (A strain) or zigzag (Z strain) directions are considered. Bilayer AB-stacked graphene belongs to semimetal essentially. One pair of $\pi $ bands owns two intersections near the Fermi level. One intersection lies at K point; the other one is near K point along the path of $\Gamma $ to K. The $\pi $ band overlap is approximately 2.6meV. No gap will be developed for bilayer graphene under homogenous strain or A strain. Nevertheless, tensile Z strain results in a tiny indirect band gap near R point.