CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES |
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The complex band structure for armchair graphene nanoribbons |
Zhang Liu-Jun(张留军)† and Xia Tong-Sheng(夏同生) |
School of Electronic Information Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China |
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Abstract Using a tight binding transfer matrix method, we calculate the complex band structure of armchair graphene nanoribbons. The real part of the complex band structure calculated by the transfer matrix method fits well with the bulk band structure calculated by a Hermitian matrix. The complex band structure gives extra information on carrier's decay behaviour. The imaginary loop connects the conduction and valence band, and can profoundly affect the characteristics of nanoscale electronic device made with graphene nanoribbons. In this work, the complex band structure calculation includes not only the first nearest neighbour interaction, but also the effects of edge bond relaxation and the third nearest neighbour interaction. The band gap is classified into three classes. Due to the edge bond relaxation and the third nearest neighbour interaction term, it opens a band gap for N=3M-1. The band gap is almost unchanged for N=3M+1, but decreased for N=3M. The maximum imaginary wave vector length provides additional information about the electrical characteristics of graphene nanoribbons, and is also classified into three classes.
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Received: 20 May 2010
Revised: 28 May 2010
Accepted manuscript online:
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PACS:
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71.15.Ap
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(Basis sets (LCAO, plane-wave, APW, etc.) and related methodology (scattering methods, ASA, linearized methods, etc.))
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73.22.-f
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(Electronic structure of nanoscale materials and related systems)
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Fund: Project supported by the Fundamental Research Funds for the Central Universities (Grant No. YWF-10-02-040). |
Cite this article:
Zhang Liu-Jun(张留军) and Xia Tong-Sheng(夏同生) The complex band structure for armchair graphene nanoribbons 2010 Chin. Phys. B 19 117105
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[1] |
Novoselov K S, Geim A K, Morozov S V, Jiang D, Zhang Y, Dubonos S V, Grigorieva I V and Firsov A A 2004 wxScience306 666
|
[2] |
Zhang Y B, Tan Y W, Stormer H L and Kim P 2005 wxNature438 201
|
[3] |
Durkop T, Getty S A, Cobas E and Fuhrer M S 2004 wxNano Lett.4 35
|
[4] |
Nakada K, Fujita M, Dresselhaus G and Dresselhaus M S 1996 wxPhys. Rev. B54 17954
|
[5] |
Barone V, Hod O and Scuseria G E 2006 wxNano Lett.6 2748
|
[6] |
Zhou B H, Duan Z G, Zhou B L and Zhou G H 2010 wxChin. Phys. B19 037204
|
[7] |
Miyamoto Y, Nakada K and Fujita M 1999 wxPhys. Rev. B59 9858
|
[8] |
Son Y W, Cohen M L and Louie S G 2006 wxPhys. Rev. Lett.97 216803
|
[9] |
White C T, Li J, Gunlycke D and Mintmire J W 2007 wxNano Lett.7 825
|
[10] |
Reich S, Maultzsch J, Thomsen C and Ordejon P 2002 wxPhys. Rev. B66 035412
|
[11] |
Brey L and Fertig H A 2006 wxPhys. Rev. B73 235411
|
[12] |
Lee D H and Joannopoulos J D 1981 wxPhys. Rev. B23 4997
|
[13] |
Fujita M, Wakabayashi K, Nakada K and Kusakabe K 1996 wxJ. Phys. Soc. Jpn.65 1920
|
[14] |
Gunlycke D and White C T 2008 wxPhys. Rev. B77 115116
|
[15] |
Yu S S, Wen Q B, Zheng W T and Jiang Q 2008 wxMolecular Simulation34 1085
|
[16] |
Bowen R C 1995 Full Bandstructure Modeling of Quantum Transport in Nanoscaled Devices Ph.D. Thesis The University of Texas at Dallas, Dallas, USA)
|
[17] |
Heine V 1965 wxPhys. Rev.138 A1689
|
[18] |
Schulman J N and Chang Y C 1983 wxPhys. Rev. B27 2346
|
[19] |
Chang Y C and Schulman J N 1982 wxPhys. Rev. B25 3975
|
[20] |
Tomfohr J K and Sankey O F 2002 wxPhys. Rev. B65 245105
|
[21] |
Xia T S, Register L F and Banerjee S K 2004 wxJ. Appl. Phys.95 1597
|
[22] |
Xia T S, Register L F and Banerjee S K 2004 wxPhys. Rev. B70 045322
|
[23] |
Boykin T B 1996 wxPhys. Rev. B54 8107
|
[24] |
St'ovneng J A and Lipavsk'y P 1994 wxPhys. Rev. B49 16494
|
[25] |
Bowen R C, Frensley W R, Klimeck G and Lake R K 1995 wxPhys. Rev. B52 2754
|
[26] |
Ting D Z Y, Yu E T and McGill T C 1992 wxPhys. Rev. B45 3583
|
[27] |
Mintmire J W and White C T 1995 wxCarbon33 893
|
[28] |
Lee D H and Joannopoulos J D 1981 wxPhys. Rev. B23 4988
|
[29] |
Zheng H X, Wang Z F, Luo T, Shi Q W and Chen J 2007 wxPhys. Rev. B75 165414
|
[30] |
Hu H X, Zhang Z H, Liu X H, Qiu M and Ding K H 2009 wxActa Phys. Sin.58 7156 (in Chinese)
|
[31] |
Jin Z F, Tong G P and Jiang Y J 2009 wxActa Phys. Sin.58 8537(in Chinese)
|
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