(color online) Band structures and the electron density distributions for the edge state in a GNR supercell (N = 23, 2M = 16) with line defect. Panel (a) shows the bands near the Fermi level with a strong defect (). The numbers indicate the p values of the 1D-supercell model; Panels (b) and (c) display the electron density distribution of the edge state for p = 9 band with k = 0 and . Panel (d) exhibits bands near the Fermi level with a weak defect (). Panels (e) and (f) indicate the electron density distribution of the edge state for p = 9 band with k = 0 and . In the density distribution figures, panels (b) and (e) are the overhead views; panels (c) and (f) are the side views of the 3D plot.