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


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.

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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)

    ADS  Article  Google 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)

    ADS  Article  Google Scholar 

  3. 3.

    Y.B. Zhang, Y.W. Tan, H.L. Stormer, P. Kim, Nature 438, 201 (2005)

    ADS  Article  Google Scholar 

  4. 4.

    K.I. Bolotin, F. Ghahari, M.D. Shulman, H.L. Storme, P. Kim, Nature 462, 196 (2009)

    ADS  Article  Google 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)

    ADS  Article  Google Scholar 

  6. 6.

    C. Lee, X.C. Wei, J.W. Kysar, J. Hone, Science 321, 385 (2008)

    ADS  Article  Google Scholar 

  7. 7.

    E. Cadelano, P.L. Palla, S. Giordano, L. Colombo, Phys. Rev. Lett. 102, 235502 (2009)

    ADS  Article  Google 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)

    ADS  Article  Google 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)

    ADS  Article  Google 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)

    ADS  Article  Google Scholar 

  11. 11.

    L.D. Carr, M.T. Lusk, Nature Nanotech. 5, 316 (2010)

    ADS  Article  Google Scholar 

  12. 12.

    J. Lahiri, Y. Lin, P. Bozkurt, I.I. Oleynik, M. Batzill, Nature Nanotech. 5, 326 (2010)

    ADS  Article  Google 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)

    ADS  Article  Google Scholar 

  14. 14.

    J. Kotakoski, A.V. Krasheninnikov, U. Kaiser, J.C. Meyer, Phys. Rev. Lett. 106, 105505 (2011)

    ADS  Article  Google Scholar 

  15. 15.

    P. Recher, B. Trauzettel, Physics 4, 25 (2011)

    Article  Google Scholar 

  16. 16.

    X.Q. Lin, J. Ni, Phys. Rev. B 84, 075461 (2011)

    ADS  Article  Google Scholar 

  17. 17.

    L.Z. Kou, C. Tang, W.L. Guo, C.F. Chen, ACS Nano 5, 1012 (2011)

    Article  Google Scholar 

  18. 18.

    S. Okada, T. Kawai, K. Nakada, J. Phys. Soc. Jpn 80, 013709 (2011)

    ADS  Article  Google Scholar 

  19. 19.

    O.V. Yazyev, S.G. Louie, Nat. Mater. 9, 806 (2010)

    ADS  Article  Google Scholar 

  20. 20.

    D. Gunlycke, C.T. White, Phys. Rev. Lett. 106, 136806 (2011)

    ADS  Article  Google Scholar 

  21. 21.

    O.V. Yazyev, S.G. Louie, Phys. Rev. B 81, 195420 (2010)

    ADS  Article  Google Scholar 

  22. 22.

    A.R. Botello-Méndez, X. Declerck, M. Terrones, H. Terrones, J.C. Charlier, Nanoscale 3, 2868 (2011)

    ADS  Article  Google Scholar 

  23. 23.

    J.W. Jiang, B.S. Wang, J.S. Wang, Appl. Phys. Lett. 98, 113114 (2011)

    ADS  Article  Google Scholar 

  24. 24.

    X.F. Peng, X.J. Wang, Z.Q. Gong, K.Q. Chen, Appl. Phys. Lett. 99, 233105 (2011)

    ADS  Article  Google 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)

    ADS  Article  Google Scholar 

  26. 26.

    J. Tersoff, Phys. Rev. Lett. 56, 632 (1986)

    ADS  Article  Google Scholar 

  27. 27.

    D.W. Brenner, Phys. Rev. B 42, 9458 (1990)

    ADS  Article  Google Scholar 

  28. 28.

    D.W. Brenner, O.A. Shenderova, J.A. Harrison, J. Phys.: Condens. Matter 14, 783 (2002)

    ADS  Article  Google Scholar 

  29. 29.

    V.P. Sokhan, D. Nicholson, N. Quirke, J. Chem. Phys. 113, 2007 (2000)

    ADS  Article  Google Scholar 

  30. 30.

    M.G. Xia, S.L. Zhang, Eur. Phys. J. B 84, 385 (2011)

    MathSciNet  ADS  Article  Google Scholar 

  31. 31.

    F. Mazzamuto, J. Saint-Martin, A. Valentin, C. Chassat, P. Dollfus, J. Appl. Phys. 109, 064516 (2011)

    ADS  Article  Google 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. 79

  33. 33.

    S. Reich, C. Thomsen, J. Maultzsch, Carbon Nanotubes: Basic Concepts and Physical Properties (Wiley, Weinheim, 2004), p. 128.

  34. 34.

    R. Saito, M. Hofmann, G. Dresselhaus, A. Jorio, M.S. Dresselhaus, Adv. Phys. 60, 413 (2011)

    ADS  Article  Google Scholar 

  35. 35.

    J. Zhou, J.M. Dong, Appl. Phys. Lett. 91, 173108 (2007)

    ADS  Article  Google Scholar 

  36. 36.

    J. Zhou, J.M. Dong, Phys. Lett. A 372, 7183 (2008)

    ADS  MATH  Article  Google Scholar 

  37. 37.

    L. Wang, B. Li, Phys. Rev. Lett. 101, 267203 (2008)

    ADS  Article  Google Scholar 

  38. 38.

    N. Li, J. Ren, L. Wang, G. Zhang, P. Hänggi, B. Li, Rev. Mod. Phys. 84, 1045 (2012)

    ADS  Article  Google Scholar 

  39. 39.

    M. Pedram, S. Nazarian, Proc. IEEE 94, 1487 (2006)

    Article  Google Scholar 

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Correspondence to Minggang Xia.

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Xia, M., Su, Z., Song, Y. et al. Localized vibrational, edges and breathing modes of graphene nanoribbons with topological line defects. Eur. Phys. J. B 86, 344 (2013). https://doi.org/10.1140/epjb/e2013-40068-5

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