Graphene – A Two-Dimensional Dirac Material

Abstract: Graphene is a two-dimensional material, whose popularity has soared in both condensedmatter physics and material science the past decade. Due to its unique properties, graphene can be used in a vast array of new and interesting applications that could fundamentally change the material industry. This report reviews the current research and literature in order to trace the historical development of graphene. Then, in order to better understand the material, the unique properties of graphene are explained and potential applications are listed. From a theoretical physics perspective, the tight-binding approximation is used to calculate the energy bands formed by the -electrons. Then, the electrons close to the Fermi energy are shown to satisfy the relativistic Dirac equation of a massless fermion and additionally, the Landau energy levels of graphene are calculated. Finally, the band gap structure of graphene is modelled and compared to that of silicon