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A tight-binding analytic framework is combined with first-principles calculations to reveal the mechanism underlying the strain effects on electronic structures of graphene and graphene nanoribbons (GNRs). It provides a unified and precise formulation of the strain effects under various circumstances—including the shift of the Fermi (Dirac) points, the change in band gap of armchair GNRs with uniaxial strain in a zigzag pattern and its insensitivity to shear strain, and the variation of the k-range of edge states in zigzag GNRs under uniaxial and shear strains which determine the gap behavior via the spin polarization interaction.
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