The Gap Opening and Threshold of Graphene by Shear Strain

In the absence of electron-electron interactions, The energy band-dispersion of graphene are analytic calculated under shear strains using a tight-binding approach and linear elasticity theory. We observe that the shear strain can generate a gap. However, the scenario under shear strain is quite different from the case of uniaxial deformations, the opening of a gap, appear for a shear strain threshold(16%)which is lower than in the case of zigzag uniaxial deformation(a gap is generated by applying an uniaxial strain as large as 23%). The rise of a gap in the energy band-dispersion under the shear strain is due to a peculiar process that involves the merging of two Dirac points, namely, D and D' which move away from the corners K and K' and approach each other inside the BZ. Interestingly enough, the use of a shear strain allows for a gap opening at moderate absolute deformation, safely smaller than the graphene failure strain. Keywords: the tight binding approach; shear strain; the energy dispersion; threshold.