Spontaneous curling of graphene sheets with reconstructed edges

Recent microscopy experiments have revealed novel reconstructions of the commonly observed zigzag and armchair edges in graphene. We show that tensile edge stresses at these reconstructed edges lead to large-scale curling of graphene sheets into cylindrical surfaces, in contrast to the warping instabilities predicted for unreconstructed edges. Using atomic-scale simulations and large deformation plate models, we have derived scaling laws for the curvature and strain of the curled sheets in terms of the edge stress, shape, and the bending and stretching moduli. For graphene nanoribbons, we show that tensile edge stress leads to periodic ripples, whose morphologies are distinct from those observed due to thermal fluctuations or thermally generated mismatch strains. Since the electronic properties of graphene can be altered by both curvatures and strain, our work provides a route for potentially fabricating nanoelectronic devices such as sensors or switches that can detect stresses induced by dopants at the edges.