Effect of edge vacancies on localized states in semi-infinite zigzag   graphene sheet
  The effect of vacancies on the robustness of zero-energy edge electronic states in zigzag-type graphene layer is studied at different concentrations and distributions of defects. All calculations are performed by using the Green's function method and the tight-binding approximation. It is found that the arrangement of defects plays a crucial role in the destruction of the edge states. We have specified a critical distance between edge vacancies when their mutual influence becomes significant and affects markedly the density of electronic states at graphene edge. 
A. A. Glebov, V. L. Katkov, V. A. Osipov
cond-mat.mtrl-sci cond-mat.mes-hall