Vacancy effects on electronic and transport properties of graphene nanoribbons

We analytically study vacancy effects on electronic and transport properties of graphene nanoribbons and nanodots using Green's function approach. For semiconducting systems, the presence of a vacancy induces a zero-energy midgap state. The spatial pattern of the wave functions critically depends on the atomistic edge structures and can be used as an unambiguous probe of the edge structure. For metallic systems, the midgap vacancy state does not exist. In these systems, the vacancy mainly works as a source of electronic scattering and modifies electronic transmission. We derive that the electronic transmission coefficient can be written as T = cos(2)(alpha), where a denotes the phase angle of the on-site Green's function at the vacancy site of the ideal systems. At small energies, T exhibits distinctly different functional form depending on edge structures.