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According to the tight-binding approximation, we investigate the electronicstructures of graphene ribbons with zigzag shaped edges (ZGRs) and armchairshaped edges (AGRs) drawn by the tensile force, and obtain the analyticrelations between the energy bands of pi-electrons in ZGR, AGR and the tensileforce based on only considering the nearest-neighbor interaction and thehydrogen-like atomic wave function is considered as pi-electron wave function.Importantly, we find the tensile force can open an energy gap at the K pointfor ZGR and AGR, and the force perpendicular to the zigzag edges can openenergy gap more easily besides the gap values of ZGR and AGR at the K pointboth increase as the tensile force increases.

Energy band of graphene ribbons under the tensile force