(color online) Atomic structures for the armchair graphene or graphene-like nanoribbons. Panel (a) shows the simple aGNR, each unit cell contains N A- and B-carbon atoms. The dashed lines in the top/bottom region indicate the boundaries of the standing wave. Panel (b) shows the reduced 1D aGNR supercell with sub-unit cells; panel (c) shows the aGNR supercell with an elongation-type line defect (indicated by the dash lines in the middle region); panel (d) shows the supercell of a boron-nitride nanoribbon. The boron atoms are green and the nitride atoms are red.