Impurities in graphene

We report the transport properties of graphene in the presence of topological and (non-topological) long-range impurities, in the framework of a tight-binding model. We first investigate the electronic transport properties of a zigzag edge graphene nanoribbon with several kinds topological defects: a pentagon, a heptagon, and a pentagon-heptagon pair at the center. On the aspect of non-topological impurities, we perform systematic calculations to investigate the effect of the impurity potential range and its density on the conductance of graphene nanoribbon. Moreover, we demonstrate that the nonlinear dependence in the recent experiment can also be explained when scattering due to the low density and long-range impurities are accounted. We also calculate the scaling properties of disordered graphene with long-range impurities in the framework of finite-size scaling. On the marginal metallic side, we find that the conductance is independent of the system size, which is a characteristic of the Kosterlitz-Thouless type transition in conventional 2D systems with random magnetic field. We explicitly probe the K-T transition nature of the MIT by identifying the bounding and unbounding vortex-anti-vortex local currents in the system.