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

Abstract

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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References

  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)

  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)

  3. 3.

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

  4. 4.

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

  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)

  6. 6.

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

  7. 7.

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

  8. 8.

    A.H. Castro Neto, F. Guinea, N.M.R. Peres, K.S. Novoselov, A.K. Geim, Rev. Mod. Phys. 81, 109 (2009)

  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)

  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)

  11. 11.

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

  12. 12.

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

  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)

  14. 14.

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

  15. 15.

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

  16. 16.

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

  17. 17.

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

  18. 18.

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

  19. 19.

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

  20. 20.

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

  21. 21.

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

  22. 22.

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

  23. 23.

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

  24. 24.

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

  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)

  26. 26.

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

  27. 27.

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

  28. 28.

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

  29. 29.

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

  30. 30.

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

  31. 31.

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

  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)

  35. 35.

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

  36. 36.

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

  37. 37.

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

  38. 38.

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

  39. 39.

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

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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) doi:10.1140/epjb/e2013-40068-5

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Keywords

  • Mesoscopic and Nanoscale Systems