Harmonic model of graphene based on a tight binding interatomic potential

Like in many other materials, the presence of topological defects in graphene has been demonstrated to modify its behavior, thus enhancing features aimed at several technological applications, more specifically, its electronic and transport properties. In particular, pristine defect-free graphene has been shown to be of limited use for semiconductor-based electronics, whereas the presence of individual or cluster defect rings along grain boundaries hinders electron transport and introduce a transport gap, unveiling the possibility of novel electronic device applications based on the structural engineering of graphene-based materials. In this work, we present an atomic bondwise force-constant model from the tight binding potential by Xu et al. (1992), that accounts for the electron-mechanical coupling effects in graphene. First we verify that this computational scheme is capable of accurately predicting the defect energies and core structures of dislocation dipoles based on the theory of discrete dislocations of Ariza and Ortiz (2005). In order to demonstrate our ability to characterize the effect of patterned distributions of structural defects on the electronic structure of graphene, we present the electronic band structures and density of states curves of several defective graphene sheets.