Localized vibrational, edges and breathing modes of graphene nanoribbons with topological line defects

  • Minggang XiaEmail author
  • Zhidan Su
  • Yang Song
  • Jinyun Han
  • Shengli Zhang
  • Baowen Li
Regular Article


Peculiar vibrational modes of graphene nanoribbons (GNRs) with topological line defects were presented. We find that phonon dispersion relations of the topological defective GNRs are more similar to those of perfect armchair-edge GNR than to zigzag-edge GNR in spite of their zigzag edge. All vibrational modes at Γ point are assigned in detail by analyzing their eigenvectors and are presented by video. Three types of characteristic vibrational modes, namely, localized vibrational modes in defect sites, edges, and breathing modes, are observed. Five localized vibrational modes near the defect sites are found to be robust against the width of the topological line-defective GNR. The Raman D’ band just originates from one localized mode, 1622 cm-1. The vibrational mode is sensitive to symmetry. The edge modes are related with structural symmetry but not with widths. Two edge modes are asymmetrical and only one is symmetrical. The breathing modes are inversely proportional to the width for wide-defect GNRs, and inversely proportional to the square root of the width for narrow-defect GNRs. The breathing mode frequencies of defective GNRs are slightly higher than those of perfect GNRs. These vibrational modes may be useful in the manipulation of thermal conductance and implementation of single phonon storage.


Mesoscopic and Nanoscale Systems 

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  1. 1.
    K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, Y. Zhang, S.V. Dubonos, I.V. Grigorieva, A.A. Firsov, Science 306, 666 (2004)ADSCrossRefGoogle Scholar
  2. 2.
    K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, M.I. Katsnelson, I.V. Grigorieva, S.V. Dubonos, A.A. Firsov, Nature 438, 197 (2005)ADSCrossRefGoogle Scholar
  3. 3.
    Y.B. Zhang, Y.W. Tan, H.L. Stormer, P. Kim, Nature 438, 201 (2005)ADSCrossRefGoogle Scholar
  4. 4.
    K.I. Bolotin, F. Ghahari, M.D. Shulman, H.L. Storme, P. Kim, Nature 462, 196 (2009)ADSCrossRefGoogle Scholar
  5. 5.
    J.S. Bunch, A.M. van der Zande, S.S. Verbridge, I.W. Frank, D.M. Tanenbaum, J.M. Parpia, H.G. Craighead, P.L. McEuen, Science 315, 490 (2007)ADSCrossRefGoogle Scholar
  6. 6.
    C. Lee, X.C. Wei, J.W. Kysar, J. Hone, Science 321, 385 (2008)ADSCrossRefGoogle Scholar
  7. 7.
    E. Cadelano, P.L. Palla, S. Giordano, L. Colombo, Phys. Rev. Lett. 102, 235502 (2009)ADSCrossRefGoogle Scholar
  8. 8.
    A.H. Castro Neto, F. Guinea, N.M.R. Peres, K.S. Novoselov, A.K. Geim, Rev. Mod. Phys. 81, 109 (2009)ADSCrossRefGoogle Scholar
  9. 9.
    S. Ghosh, I. Calizo, D. Teweldebrhan, E.P. Pokatilov, D.L. Nika, A.A. Balandin, W. Bao, F. Miao, C.N. Lau, Appl. Phys. Lett. 92, 151911 (2008)ADSCrossRefGoogle Scholar
  10. 10.
    J.H. Seol, I. Jo, A.L. Moore, L. Lindsay, Z.H. Aitken, M.T. Pettes, X. Li, Z. Yao, R. Huang, D. Broido, N. Mingo, R.S. Ruoffs, L. Shi, Science 328, 213 (2010)ADSCrossRefGoogle Scholar
  11. 11.
    L.D. Carr, M.T. Lusk, Nature Nanotech. 5, 316 (2010)ADSCrossRefGoogle Scholar
  12. 12.
    J. Lahiri, Y. Lin, P. Bozkurt, I.I. Oleynik, M. Batzill, Nature Nanotech. 5, 326 (2010)ADSCrossRefGoogle Scholar
  13. 13.
    G. Otero, C. González, A.L. Pinardi, P. Merino, S. Gardonio, S. Lizzit, M. Blanco-Rey, K. Van de Ruit, C.F.J. Flipse, J. Méndez, P.L. de Andrés, J.A. Martín-Gago, Phys. Rev. Lett. 105, 216102 (2010)ADSCrossRefGoogle Scholar
  14. 14.
    J. Kotakoski, A.V. Krasheninnikov, U. Kaiser, J.C. Meyer, Phys. Rev. Lett. 106, 105505 (2011)ADSCrossRefGoogle Scholar
  15. 15.
    P. Recher, B. Trauzettel, Physics 4, 25 (2011)CrossRefGoogle Scholar
  16. 16.
    X.Q. Lin, J. Ni, Phys. Rev. B 84, 075461 (2011)ADSCrossRefGoogle Scholar
  17. 17.
    L.Z. Kou, C. Tang, W.L. Guo, C.F. Chen, ACS Nano 5, 1012 (2011)CrossRefGoogle Scholar
  18. 18.
    S. Okada, T. Kawai, K. Nakada, J. Phys. Soc. Jpn 80, 013709 (2011)ADSCrossRefGoogle Scholar
  19. 19.
    O.V. Yazyev, S.G. Louie, Nat. Mater. 9, 806 (2010)ADSCrossRefGoogle Scholar
  20. 20.
    D. Gunlycke, C.T. White, Phys. Rev. Lett. 106, 136806 (2011)ADSCrossRefGoogle Scholar
  21. 21.
    O.V. Yazyev, S.G. Louie, Phys. Rev. B 81, 195420 (2010)ADSCrossRefGoogle Scholar
  22. 22.
    A.R. Botello-Méndez, X. Declerck, M. Terrones, H. Terrones, J.C. Charlier, Nanoscale 3, 2868 (2011)ADSCrossRefGoogle Scholar
  23. 23.
    J.W. Jiang, B.S. Wang, J.S. Wang, Appl. Phys. Lett. 98, 113114 (2011)ADSCrossRefGoogle Scholar
  24. 24.
    X.F. Peng, X.J. Wang, Z.Q. Gong, K.Q. Chen, Appl. Phys. Lett. 99, 233105 (2011)ADSCrossRefGoogle Scholar
  25. 25.
    M. Mohr, J. Maultzsch, E. Dobardžić, S. Reich, I. Milošević, M. Damnjanović, A. Bosak, M. Krisch, C. Thomsen, Phys. Rev. B 76, 035439 (2007)ADSCrossRefGoogle Scholar
  26. 26.
    J. Tersoff, Phys. Rev. Lett. 56, 632 (1986)ADSCrossRefGoogle Scholar
  27. 27.
    D.W. Brenner, Phys. Rev. B 42, 9458 (1990)ADSCrossRefGoogle Scholar
  28. 28.
    D.W. Brenner, O.A. Shenderova, J.A. Harrison, J. Phys.: Condens. Matter 14, 783 (2002)ADSCrossRefGoogle Scholar
  29. 29.
    V.P. Sokhan, D. Nicholson, N. Quirke, J. Chem. Phys. 113, 2007 (2000)ADSCrossRefGoogle Scholar
  30. 30.
    M.G. Xia, S.L. Zhang, Eur. Phys. J. B 84, 385 (2011)MathSciNetADSCrossRefGoogle Scholar
  31. 31.
    F. Mazzamuto, J. Saint-Martin, A. Valentin, C. Chassat, P. Dollfus, J. Appl. Phys. 109, 064516 (2011)ADSCrossRefGoogle Scholar
  32. 32.
    R.M. Martin, L.M. Falicov, in Light Scattering in Solids I, Topics in Applied Physics, edited by M. Cardona (Springer, Berlin, 1983), Vol. 8, p. 79Google Scholar
  33. 33.
    S. Reich, C. Thomsen, J. Maultzsch, Carbon Nanotubes: Basic Concepts and Physical Properties (Wiley, Weinheim, 2004), p. 128.Google Scholar
  34. 34.
    R. Saito, M. Hofmann, G. Dresselhaus, A. Jorio, M.S. Dresselhaus, Adv. Phys. 60, 413 (2011)ADSCrossRefGoogle Scholar
  35. 35.
    J. Zhou, J.M. Dong, Appl. Phys. Lett. 91, 173108 (2007)ADSCrossRefGoogle Scholar
  36. 36.
    J. Zhou, J.M. Dong, Phys. Lett. A 372, 7183 (2008)ADSzbMATHCrossRefGoogle Scholar
  37. 37.
    L. Wang, B. Li, Phys. Rev. Lett. 101, 267203 (2008)ADSCrossRefGoogle Scholar
  38. 38.
    N. Li, J. Ren, L. Wang, G. Zhang, P. Hänggi, B. Li, Rev. Mod. Phys. 84, 1045 (2012)ADSCrossRefGoogle Scholar
  39. 39.
    M. Pedram, S. Nazarian, Proc. IEEE 94, 1487 (2006)CrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Minggang Xia
    • 1
    • 2
    Email author
  • Zhidan Su
    • 3
  • Yang Song
    • 3
  • Jinyun Han
    • 3
  • Shengli Zhang
    • 1
    • 3
  • Baowen Li
    • 4
    • 5
  1. 1.MOE Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, School of ScienceXi’an Jiaotong UniversityShaanxiP.R. China
  2. 2.Center on Experimental Physics, School of ScienceXi’an Jiaotong UniversityShaanxiP.R. China
  3. 3.Department of Applied Physics, School of ScienceXi’an Jiaotong UniversityShaanxiP.R. China
  4. 4.Centre for Computational Science and Engineering, Graphene Research Center, and Department of PhysicsNational University of SingaporeSingaporeRepublic of Singapore
  5. 5.NUS-Tongji Center for Phononics and Thermal Energy Science, Department of PhysicsTongji UniversityShanghaiP.R. China

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