Elastic fields and moduli in defected graphene

By means of tight-binding atomistic simulations we study a family of native defects in graphene which have recently been detected experimentally. Their formation energy is found to be as large as several electronvolts, consistent with the empirical evidence of high crystalline quality in most graphene samples. Defects, especially if associated with bond reconstructions, induce sizable deformation and stress fields with a spatial distribution closely related to their actual symmetry. The description of such fields proposed here is believed to be useful for the unambiguous characterization of images obtained by electron microscopy. We also argue that they define the basin of mutual interaction between two nearby defects. Finally, we provide evidence that defects differently affect the linear elastic moduli of monolayer graphene. In general, both the Young modulus and the Poisson ratio are decreased, but their dependence upon the defect surface density is remarkably more pronounced for vacancy-like than for number-like defects.