Using the density functional theory with generalized gradient approximation, we have studied in detail the cooperative effects of degenerate perturbation and uniaxial strain on bandgap opening in graphene. The uniaxial strain could split π bands into πa and πz bands with an energy interval Es to move the Dirac cone. The inversion symmetry preserved antidot would then further split the πa (πz) bands into πa1 (πz1) and πa2 (πz2) bands with an energy interval Ed, which accounts for the bandgap opening in a kind of superlattices with Dirac cone being folded to Γ point. However, such antidot would not affect the semimetal nature of the other superlattices, showing a novel mechanism for bandstructure engineering as compared to the sublattice-equivalence breaking. For a superlattice with bandgap of ∼Ed opened at Γ point, the Es could be increased by strengthening strain to close the bandgap, suggesting a reversible switch between the high velocity properties of massless Fermions attributed to the linear dispersion relation around Dirac cone and the high on/off ratio properties associated with the sizable bandgap. Moreover, the gap width actually could be continuously tuned by controlling the strain, showing attractive application potentials.
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