Please wait a minute...
Chin. Phys. B, 2010, Vol. 19(11): 117105    DOI: 10.1088/1674-1056/19/11/117105
CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES Prev   Next  

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
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.
Keywords:  armchair graphene nanoribbons      complex band structure      edge bond relaxation      third nearest neighbour interaction  
Received:  20 May 2010      Revised:  28 May 2010      Accepted manuscript online: 
PACS:  71.15.Ap (Basis sets (LCAO, plane-wave, APW, etc.) and related methodology (scattering methods, ASA, linearized methods, etc.))  
  73.22.-f (Electronic structure of nanoscale materials and related systems)  
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

[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)
[1] Structural, electronic, elastic, and thermal properties of CaNiH3 perovskite obtained from first-principles calculations
S Benlamari, H Bendjeddou, R Boulechfar, S Amara Korba, H Meradji, R Ahmed, S Ghemid, R Khenata, S Bin Omran. Chin. Phys. B, 2018, 27(3): 037104.
[2] First principles investigation of protactinium-based oxide-perovskites for flexible opto—electronic devices
Nazia Erum, Muhammad Azhar Iqbal. Chin. Phys. B, 2017, 26(4): 047102.
[3] Electronic transport of bilayer graphene with asymmetry line defects
Xiao-Ming Zhao(赵小明), Ya-Jie Wu(吴亚杰), Chan Chen(陈婵), Ying Liang(梁颖), Su-Peng Kou(寇谡鹏). Chin. Phys. B, 2016, 25(11): 117303.
[4] Investigations of mechanical, electronic, and magnetic properties of non-magnetic MgTe and ferro-magnetic Mg0.75TM0.25Te (TM=Fe, Co, Ni): An ab-initio calculation
Mahmood Q, Alay-e-Abbas S M, Mahmood I, Asif Mahmood, Noor N A. Chin. Phys. B, 2016, 25(4): 047101.
[5] Synthesis, structure, optical, and electric properties of Ce-doped CuInTe2 compound
Fu Li (付丽), Guo Yong-Quan (郭永权). Chin. Phys. B, 2014, 23(12): 127801.
[6] Investigations of the half-metallic behavior and the magnetic and thermodynamic properties of half-Heusler CoMnTe and RuMnTe compounds:A first-principles study
T. Djaafri, A. Djaafri, A. Elias, G. Murtaza, R. Khenata, R. Ahmed, S. Bin Omran, D. Rached. Chin. Phys. B, 2014, 23(8): 087103.
[7] First-principles study of structural, electronic and optical properties of ZnF2
Wu Jian-Bang (吴建邦), Cheng Xin-Lu (程新路), Zhang Hong (张红), Xiong Zheng-Wei (熊政伟). Chin. Phys. B, 2014, 23(7): 077102.
[8] Electronic and optical properties of Au-doped Cu2O:A first principles investigation
Jiang Zhong-Qian (姜中钱), Yao Gang (姚钢), An Xin-You (安辛友), Fu Ya-Jun (符亚军), Cao Lin-Hong (曹林洪), Wu Wei-Dong (吴卫东), Wang Xue-Min (王雪敏). Chin. Phys. B, 2014, 23(5): 057104.
[9] Numerical simulation of a triple-junction thin-film solar cell based on μc-Si1-xGex:H
Huang Zhen-Hua (黄振华), Zhang Jian-Jun (张建军), Ni Jian (倪牮), Cao Yu (曹宇), Hu Zi-Yang (胡子阳), Li Chao (李超), Geng Xin-Hua (耿新华), Zhao Ying (赵颖). Chin. Phys. B, 2013, 22(9): 098803.
[10] Differences in adsorption of FePc on coinage metal surfaces
R.A. Rehman, Cai Yi-Liang (蔡亦良), Zhang Han-Jie (张寒洁), Wu Ke (吴珂), Dou Wei-Dong (窦卫东), Li Hai-Yang (李海洋), He Pi-Mo (何丕模), Bao Shi-Ning (鲍世宁). Chin. Phys. B, 2013, 22(6): 063101.
[11] Structural, electronic, and magnetic properties of Co-doped ZnO
Bakhtiar Ul Haq, A. Afaq, R. Ahmed, S. Naseem. Chin. Phys. B, 2012, 21(9): 097101.
[12] Effects of N-doping concentration on the electronic structure and optical properties of N-doped β-Ga2O3
Zhang Li-Ying(张丽英), Yan Jin-Liang(闫金良), Zhang Yi-Jun(张易军), and Li Ting(李厅) . Chin. Phys. B, 2012, 21(6): 067102.
[13] Theoretical prediction of structural, electronic and optical properties of quaternary alloy Zn1-xBexSySe1-y
Hacini K, Meradji H, Ghemid S, and El Haj Hassan F . Chin. Phys. B, 2012, 21(3): 036102.
[14] Investigation of the guided-mode characteristics of hollow-core photonic band-gap fibre with interstitial holes
Yuan Jin-Hui(苑金辉), Yu Chong-Xiu(余重秀), Sang Xin-Zhu(桑新柱), Zhang Jin-Long(张锦龙), Zhou Gui-Yao(周桂耀), Li Shu-Guang(李曙光), and Hou Lan-Tian(侯蓝田). Chin. Phys. B, 2011, 20(6): 064203.
[15] Theoretical investigation of band-gap and mode characteristics of anti-resonance guiding photonic crystal fibres
Yuan Jin-Hui(苑金辉), Sang Xin-Zhu(桑新柱), Yu Chong-Xiu(余重秀), Xin Xiang-Jun(忻向军), Zhang Jin-Long(张锦龙), Zhou Gui-Yao(周桂耀), Li Shu-Guang(李曙光), and Hou Lan-Tian(侯蓝田). Chin. Phys. B, 2011, 20(2): 024213.
No Suggested Reading articles found!