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Based on the π-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.
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Keywords:
- zigzag graphen nanoribbons /
- tight-binding model /
- the distribution of electrons /
- the defective structure
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[29] Zheng X H, Dai Z X, Wang X L, Zeng Z 2009 Acta Phys. Sin. 58 S259 (in Chinese) [郑小宏、戴振翔、王贤龙、曾 雉 2009 物理学报 58 S259]
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[1] Novoselov K S , Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V, Firsov A A 2004 Science 306 666
[2] Katsnelson M I, Novoselov K S, Geim A K 2006 Nat. Phys. 2 620
[3] Castro Neto A H, Guinea F, Peres N M R, Novoselov K S, Geim A K 2009 Rev. Mod. Phys. 81 110
[4] Zhang Y B, Tan Y W, Stormer H L, Kim P 2005 Nature 438 201
[5] Nomura K, MacDonald A H 2006 Phys. Rev. Lett. 96 256602
[6] Brey L, Fertig H A 2006 Phys. Rev. B 73 195408
[7] Westervelt R M 2008 Science 320 324
[8] Matulis A, Peeters F M 2008 Phys. Rev. B 77 115423
[9] Pedersen T G, Flindt C, Pedersen J, Mortensen N A, Jauho A P, Pedersen K 2008 Phys. Rev. Lett. 100 136804
[10] Xu H Y, Heinzel T, Zozoulenko I V 2009 Phys. Rev. B 80 045308
[11] Sahu B, Min H, MacDonald A H, Banerjee1 S K 2008 Phys. Rev. B 78 045404
[12] Castro E V, Peres N M R, Lopes dos Santos J M B, Castro Neto A H, Guinea F 2008 Phys. Rev. Lett. 100 026802
[13] Jin Z F, Tong G P, Jiang Y J 2009 Acta Phys. Sin. 58 8537 (in Chinese) [金子飞、童国平、蒋永进 2009 物理学报 58 8537]
[14] Wimmer M, Adagideli I, Berber S, Tomanek D, Richter K 2008 Phys. Rev. Lett. 100 177207
[15] Yang L, Cohen M L, Louie S G 2007 Nano Lett. 7 3112
[16] Son Y W, Cohen M L, Louie S G 2006 Phys Rev. Lett. 97 216803
[17] Barone V, Hod O, Scuseria G E 2006 Nano Lett. 6 2748
[18] Son Y W, Cohen M L, Louie S G 2006 Nature 444 347
[19] Brey L, Fertig H A 2006 Phys. Rev. B 73 235411
[20] Zhou B H, Duan Z G, Zhou B L, Zhou G H 2010 Chin. Phys. B 19 037204
[21] Rozhkov A V, Savel’ev S, Nori F 2009 Phys. Rev. B 79 125420
[22] Areshkin D A, Gunlycke D, White C T 2007 Nano Lett. 7 204
[23] Ezawa M 2006 Phys. Rev. B 73 045432
[24] Han M Y, zyilmaz B, Zhang Y, Kim Philip 2007 Phys. Rev. Lett. 98 206805
[25] Ouyang F P, Wang H Y, Li M J, Xiao J, Xu H 2008 Acta Phys. Sin. 57 7132 (in Chinese) [欧阳方平、王焕友、李明君、肖 金、徐 慧 2008 物理学报 57 7132]
[26] Cresti A, Roche S 2009 Phys. Rev. B 79 233404
[27] Lee G D, Wang C Z, Yoon E, Hwang N M, Ho K M 2010 Phys. Rev. B 81 195419
[28] Li Z Z 2002 Solid State Theory (2nd ed) (Beijing: Higher Education Press) p67 (in Chinese) [李正中 2002 固体理论(第二版)(北京:高等教育出版社)第67页]
[29] Zheng X H, Dai Z X, Wang X L, Zeng Z 2009 Acta Phys. Sin. 58 S259 (in Chinese) [郑小宏、戴振翔、王贤龙、曾 雉 2009 物理学报 58 S259]
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