Gap opening in graphene nanoribbons by application of simple shear strain and in-plane electric field

The effects of shear strain and applied in plane electric field on the electronic properties of monolayer graphene nanoribbons (GNRs) are theoretically investigated. Band structures and the probability densities are calculated within the tight-binding model and the mechanical stresses submitted to the GNRs are taken into account by using the theory of linear elasticity with joint modifications in the elongation of the nearest-neighbor vectors and the modification of the hopping parameters. The energy gaps for specific widths of (semiconducting) armchair nanoribbons are verified also in the presence of either strain or field, whereas zigzag nanoribbons are metallic for any value of strain and exhibit a small gap for any value of field. However, our results demonstrate that when both strain and electric field are combined, a significant energy gap is always observed in the band structure, for any width or edge type of the ribbon. Moreover, the obtained total wave function is asymmetric along the ribbon width due to the applied electric field that pushes the electrons to one side of the ribbon and, under shear strain, a peak at the center of the ribbon in the spatial distribution is also observed owing to the preferable localization around the almost undeformed carbon bonds at ribbon center.