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Anisotropy of the Stone-Wales Defect and Warping of Graphene Nano-ribbons: A First-principles Analysis

Stone-Wales (SW) defects, analogous to dislocations in crystals, play an important role in mechanical behavior of $sp^2$-bonded carbon based materials. Here, we show using first-principles calculations that a marked anisotropy in the interaction among the SW defects has interesting consequences when such defects are present near the edges of a graphene nano-ribbon: depending on their orientation with respect to edge, they result in compressive or tensile stress, and the former is responsible to depression or warping of the graphene nano-ribbon. Such warping results in delocalization of electrons in the defect states.