Band structures of zigzag graphene nanoribbons

Based on the pi-electron tight-binding model, for zigzag graphene nanoribbons(ZGNRs) the influence of boundary structure on band structure, specially the electrons of the valence band and the conductor band near the Fermi level, are studied in detail. We investigate the band structures and the distributions of electrons of different atoms in a unit cell of the valence band near the Fermi level of ZGNRs with seven reasonable boundary structures. We find NN-ZGNRs with no dangling atoms on both edges, DN-ZGNRs with dangling atoms only on one edge, SPP-ZGNRs and ASPP-ZGNRs each with pentagons on both two edges and being metallic, DD-ZGNRs with dangling atoms on both two edges, PN-ZGNRs each with a defective structure of pentagons on one edge and no dangling atoms on the other edge, PD-ZGNRs with a pentagon on one edge and dangling atoms on the other edge being semiconducting, and the energy gap being inversely proportional to the width of nanoribbons. But for DD-ZGNRs and PD-ZGNRs, the energy gaps quickly reduce to zero with the increase of width; for PN-ZGNRs, the energy gaps decrease exponentially to a limited value of 0.154 eV. It is found that different boundary structures have different effects on the distribution of electrons in the valence band near the Fermi level. And the probability for electrons staying in the atoms on two edges of nanoribbons is relatively large.