This paper investigates strain effects on the electronic
properties of single-layer and bilayer graphene using a first-principles
method. The deformation significantly alters energy dispersion, band
overlap, band gap, and the band edges of graphenes. Fermi velocity
behaves both linearly and nonlinearly with the strains, depending
on the types of deformation and the direction of the Fermi velocity.
In bilayer graphene, the uniaxial strain enhances the band overlap
by 2 orders of magnitude. A semimetal–insulator transition
occurs when bilayer graphene is under a compressive uniaxial strain
along the zigzag chain direction. These strain-dependent results are
useful for acquiring the intralayer and interlayer atomic relations
or Slonczewski–Weiss–McClure parameters. The intralayer
coupling γ0 under the H-strain and interlayer couplings
γ1, γ3, and γ4 under
the P-strain decrease dramatically as the strain increases. Nevertheless,
interlayer couplings vary more slowly with the H-strain than the P-strain.
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