Decay behavior of localized states at reconstructed armchair graphene edges

Department of Physics and Graphene Research Institute, Sejong University, Seoul 143-747, KoreaDensity functional theory calculations are used to investigate the electronic structures of localizedstates at reconstructed armchair graphene edges. We consider graphene nanoribbons with twodifferent edge types and obtain the energy band structures and charge densities of the edge states.By examining the imaginary part of the wavevector in the forbidden energy region, we reveal thedecay behavior of the wavefunctions in graphene. The complex band structures of graphene in thearmchair and zigzag directions are presented in both tight-binding and first-principles frameworks.