摘要 According to band folding analyses, the graphene superlattices can be differed by whether the Dirac points are folded to Γ point or not. In previous studies, the inversion symmetry preserved defects open bandgap in the former superlattices while they cannot in the latter ones. In this paper, by using density functional theory with generalized gradient approximation, we have carefully studied the electronic properties of the latter graphene superlattices, in which the defects would induce π-band splitting to get the π_{a1}-π_{a2} and π_{z1}-π_{z2} band sets. Based on our detailed studies, such splitting could be attributed to the geometrically induced bond-symmetry breaking. In addition, these band sets could be shifted toward each other by the methodology of strain engineering. A bandgap would be opened once the band sets start to overlap. Then, its gap width could be continuously enlarged by enhancing strain until reaching the maximum value determined by the defect density. These studies contribute to the bandstructure engineering of graphene-based nanomaterials, which would be interesting to call for further investigations on both theory and experiment.

Abstract：According to band folding analyses, the graphene superlattices can be differed by whether the Dirac points are folded to Γ point or not. In previous studies, the inversion symmetry preserved defects open bandgap in the former superlattices while they cannot in the latter ones. In this paper, by using density functional theory with generalized gradient approximation, we have carefully studied the electronic properties of the latter graphene superlattices, in which the defects would induce π-band splitting to get the π_{a1}-π_{a2} and π_{z1}-π_{z2} band sets. Based on our detailed studies, such splitting could be attributed to the geometrically induced bond-symmetry breaking. In addition, these band sets could be shifted toward each other by the methodology of strain engineering. A bandgap would be opened once the band sets start to overlap. Then, its gap width could be continuously enlarged by enhancing strain until reaching the maximum value determined by the defect density. These studies contribute to the bandstructure engineering of graphene-based nanomaterials, which would be interesting to call for further investigations on both theory and experiment.

基金资助:Project jointly supported by the Natural Science Foundation of Shandong Province (Grant NO. TSHW20101004) and the National Natural Science Foundation of China (Grant Nos. 11374128 and 11674129).