Nano Research

, Volume 6, Issue 5, pp 326–334 | Cite as

Highly defective graphene: A key prototype of two-dimensional Anderson insulators

  • Aurélien Lherbier
  • Stephan Roche
  • Oscar A. Restrepo
  • Yann-Michel Niquet
  • Arnaud Delcorte
  • Jean-Christophe Charlier
Research Article


Electronic structure and transport properties of highly defective two-dimensional (2D) sp2 graphene are investigated theoretically. Classical molecular dynamics are used to generate large graphene planes containing a considerable amount of defects. Then, a tight-binding Hamiltonian validated by ab initio calculations is constructed in order to compute quantum transport within a real-space order-N Kubo-Greenwood approach. In contrast to pristine graphene, the highly defective sp2 carbon sheets exhibit a high density of states at the charge neutrality point raising challenging questions concerning the electronic transport of associated charge carriers. The analysis of the electronic wavepacket dynamics actually reveals extremely strong multiple scattering effects giving rise to mean free paths as low as 1 nm and localization phenomena. Consequently, highly defective graphene is envisioned as a remarkable prototype of 2D Anderson insulating materials.


graphene electronic transport Anderson insulators localization 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Kim, K. S.; Zhao, Y.; Jang, H.; Lee, S. Y.; Kim, J. M.; Kim, K. S.; Ahn, J.-H.; Kim, P.; Choi, J.-Y.; Hong, B. H. Large-scale pattern growth of graphene films for stretchable transparent electrodes. Nature 2009, 457, 706–710.CrossRefGoogle Scholar
  2. [2]
    Novoselov, K. S. Nobel lecture: Graphene: Materials in the flatland. Rev. Mod. Phys. 2011, 83, 837–849.CrossRefGoogle Scholar
  3. [3]
    de Heer, W. A.; Berger, C.; Wu, X.; First, P. N.; Conrad, E. H.; Li, X.; Li, T.; Sprinkle, M.; Hass, J.; Sadowski, M. L.; et al. Epitaxial graphene. Solid State Commun. 2007, 143, 92–100.CrossRefGoogle Scholar
  4. [4]
    Wang, X.; Zhi, L.; Müllen, K. Transparent, conductive graphene electrodes for dye-sensitized solar cells. Nano Lett. 2008, 8, 323–327.CrossRefGoogle Scholar
  5. [5]
    Bae, S.; Kim, H.; Lee, Y.; Xu, X.; Park, J.-S.; Zheng, Y.; Balakrishnan, J.; Lei, T.; Kim, H. R.; Song, Y. I.; et al. Roll-to-roll production of 30-inch graphene films for transparent electrodes. Nat. Nanotechnol. 2010, 5, 574–578.CrossRefGoogle Scholar
  6. [6]
    Ferreira, A.; Xu, X.; Tan, C. -L.; Bae, S. -K.; Peres, N. M. R.; Hong, B. -H.; Özyilmaz, B.; Neto, A. H. C. Transport properties of graphene with one-dimensional charge defects. EPL 2011, 94, 28003.CrossRefGoogle Scholar
  7. [7]
    Krasheninnikov, A. V.; Banhart, F. Engineering of nano-structured carbon materials with electron or ion beams. Nat. Mater. 2007, 6, 723–733.CrossRefGoogle Scholar
  8. [8]
    Banhart, F.; Kotakoski, J.; Krasheninnikov, A. V. Structural defects in graphene. ACS Nano 2011, 5, 26–41.CrossRefGoogle Scholar
  9. [9]
    Cockayne, E.; Rutter, G. M.; Guisinger, N. P.; Crain, J. N.; First, P. N.; Stroscio, J. A. Grain boundary loops in graphene. Phys. Rev. B 2011, 83, 195425.CrossRefGoogle Scholar
  10. [10]
    Botello-Méndez, A. R.; Declerck, X.; Terrones, M.; Terrones, H.; Charlier, J.-C. One-dimensional extended lines of divacancy defects in graphene. Nanoscale 2011, 3, 2868–2872.CrossRefGoogle Scholar
  11. [11]
    Lusk, M. T.; Wu, D. T.; Carr, L. D. Graphene nano-engineering and the inverse Stone-Thrower-Wales defect. Phys. Rev. B 2010, 81, 155444.CrossRefGoogle Scholar
  12. [12]
    Yazyev, O. V.; Louie, S. G. Electronic transport in polycrystalline graphene. Nat. Mater. 2010, 9, 806–809.CrossRefGoogle Scholar
  13. [13]
    Lherbier, A.; Dubois, S. M.-M.; Declerck, X.; Roche, S.; Niquet, Y. M.; Charlier, J.-C. Two-dimensional graphene with structural defects: Elastic mean free path, minimum conductivity, and Anderson transition. Phys. Rev. Lett. 2011, 106, 046803.CrossRefGoogle Scholar
  14. [14]
    Kotakoski, J.; Krasheninnikov, A. V.; Kaiser, U.; Meyer, J. C. From point defects in graphene to two-dimensional amorphous carbon. Phys. Rev. Lett. 2011, 106, 105505.CrossRefGoogle Scholar
  15. [15]
    Kapko, V.; Drabold, D. A.; Thorpe, M. F. Electronic structure of a realistic model of amorphous graphene. Phys. Stat. Solidi B 2010, 247, 1197–1200.CrossRefGoogle Scholar
  16. [16]
    Li, Y.; Inam, F.; Kumar, A.; Thorpe, M. F.; Drabold, D. A. Pentagonal puckering in a sheet of amorphous graphene. Phys. Status Solidi B 2011, 248, 2082–2086.Google Scholar
  17. [17]
    Holmström, E.; Fransson, J.; Eriksson, O.; Lizárraga, R.; Sanyal, B.; Bhandary, S.; Katsnelson, M. I. Disorder-induced metallicity in amorphous graphene. Phys. Rev. B 2011, 84, 205414.CrossRefGoogle Scholar
  18. [18]
    Tuan, D. V.; Kumar, A.; Roche, S.; Ortmann, F.; Thorpe, M. F.; Ordejon, P. Insulating behavior of an amorphous graphene membrane. Phys. Rev. B 2012, 86, 121408.CrossRefGoogle Scholar
  19. [19]
    Brenner, D. W.; Shenderova, O. A.; Harrison, J. A.; Stuart, S. J.; Ni, B.; Sinnott, S. B. A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons. J. Phys. Condes.Matter. 2002, 14, 783–802.CrossRefGoogle Scholar
  20. [20]
    Stuart, S. J.; Tutein, A. B.; Harrison, J. A. A reactive potential for hydrocarbons with intermolecular interactions. J. Chem. Phys. 2000, 112, 6472–6486.CrossRefGoogle Scholar
  21. [21]
    Hoffmann, R.; Alder, R. W.; Wilcox, C. F. Planar tetracoor-dinate carbon. J. Am. Chem. Soc. 1970, 92, 4992–4993.CrossRefGoogle Scholar
  22. [22]
    Ajayan, P. M.; Ravikumar, V.; Charlier, J.-C. Surface reconstructions and dimensional changes in single-walled carbon nanotubes. Phys. Rev. Lett. 1998, 81, 1437–1440.CrossRefGoogle Scholar
  23. [23]
    Wang, B.; Puzyrev, Y.; Pantelides, S. T. Strain enhanced defect reactivity at grain boundaries in polycrystalline graphene. Carbon 2011, 49, 3983–3988.CrossRefGoogle Scholar
  24. [24]
    Dean, C. R.; Young, A. F.; Meric, I.; Lee, C.; Wang, L.; Sorgenfrei, S.; Watanabe, K.; Taniguchi, T.; Kim. P.; Shepard, K. L.; et al. Boron nitride substrates for high-quality graphene electronics. Nat. Nanotechnol. 2010, 5, 722–726.CrossRefGoogle Scholar
  25. [25]
    Xue, J.; Sanchez-Yamagishi, J.; Bulmash, D.; Jacquod, P.; Deshpande, A.; Watanabe, K.; Taniguchi, T.; Jarillo-Herrero, P.; Leroy, B. J. Scanning tunnelling microscopy and spectroscopy of ultra-flat graphene on hexagonal boron nitride. Nat. Mater. 2011, 10, 282–285.CrossRefGoogle Scholar
  26. [26]
    Pereira, V.M.; Neto, A. H. C.; Peres, N. M. R. Tight-binding approach to uniaxial strain in graphene. Phys. Rev. B 2009, 80, 045401.CrossRefGoogle Scholar
  27. [27]
    Lherbier, A.; Dubois, S. M.-M.; Declerck, X.; Niquet, Y. M.; Roche, S.; Charlier, J.-C. Transport properties of graphene containing structural defects. Phys. Rev. B 2012, 86, 075402.CrossRefGoogle Scholar
  28. [28]
    Lherbier, A.; Biel, B.; Niquet, Y. M.; Roche, S. Transport length scales in disordered graphene-based materials: Strong localization regimes and dimensionality effects. Phys. Rev. Lett. 2008, 100, 036803.CrossRefGoogle Scholar
  29. [29]
    Roche, S.; Mayou, D. Conductivity of quasiperiodic systems: A numerical study. Phys. Rev. Lett. 1997, 79, 2518–2521.CrossRefGoogle Scholar
  30. [30]
    Roche, S. Quantum transport by means of O(N) real-space methods. Phys. Rev. B 1999, 59, 2284–2291.CrossRefGoogle Scholar
  31. [31]
    Ishii, H.; Triozon, F.; Kobayashi, N.; Hirose, K.; Roche, S. Charge transport in carbon nanotubes based materials: A Kubo-Greenwood computational approach. C. R. Phys. 2009, 10, 283–296.CrossRefGoogle Scholar
  32. 32]
    Leconte, N.; Moser, J.; Ordejón, P.; Tao, H.; Lherbier, A.; Bachtold, A.; Alsina, F.; Torres, C. M. S.; Charlier, J.-C.; Roche, S. Damaging graphene with ozone treatment: A chemically tunable metal-insulator transition. ACS Nano 2010, 4, 4033–4038.CrossRefGoogle Scholar
  33. [33]
    Radchenko, T. M.; Shylau, A. A.; Zozoulenko, I. V. Influence of correlated impurities on conductivity of graphene sheets: Time-dependent real-space Kubo approach. Phys. Rev. B 2012, 86, 035418.CrossRefGoogle Scholar
  34. [34]
    Tan, Y.-W.; Zhang, Y.; Bolotin, K.; Zhao, Y.; Adam, S.; Hwang, E. H.; Das Sarma, S.; Stormer, H. L.; Kim, P. Measurement of scattering rate and minimum conductivity in graphene. Phys. Rev. Lett. 2007, 99, 246803.CrossRefGoogle Scholar
  35. [35]
    Shon, N. H.; Ando, T. Quantum transport in two-dimensional graphite system. J. Phys. Soc. Jpn. 1998, 67, 2421–2429.CrossRefGoogle Scholar
  36. [36]
    Peres, N. M. R.; Guinea, F.; Neto, A. H. C. Electronic properties of disordered two-dimensional carbon. Phys. Rev. B 2006, 73, 125411.CrossRefGoogle Scholar
  37. [37]
    Ostrovsky, P. M.; Gornyi, I. V.; Mirlin, A. D. Electron transport in disordered graphene. Phys. Rev. B 2006, 74, 235443.CrossRefGoogle Scholar
  38. [38]
    Nomura, K.; MacDonald, A. H. Quantum transport of massless Dirac fermions. Phys. Rev. Lett. 2007, 98, 076602.CrossRefGoogle Scholar
  39. [39]
    Geim, A. K.; Novoselov, K. S. The rise of graphene. Nat. Mater. 2007, 6, 183–191.CrossRefGoogle Scholar
  40. [40]
    Lee, P. A.; Ramakrishnan, T. V. Disordered electronic systems. Rev. Mod. Phys. 1985, 57, 287–337.CrossRefGoogle Scholar
  41. [41]
    Lherbier, A.; Blase, X.; Niquet, Y. M.; Triozon, F.; Roche, S. Charge transport in chemically doped 2D graphene. Phys. Rev. Lett. 2008, 101, 036808.CrossRefGoogle Scholar
  42. [42]
    Ferrari, A. C.; Meyer, J. C.; Scardaci, V.; Casiraghi, C.; Lazzeri, M.; Mauri, F.; Piscanec, S.; Jiang, D.; Novoselov, K. S.; Roth, S.; et al. Raman spectrum of graphene and graphene layers. Phys. Rev. Lett. 2006, 97, 187401.CrossRefGoogle Scholar
  43. [43]
    Casiraghi, C.; Hartschuh, A.; Qian, H.; Piscanec, S.; Georgi, C.; Fasoli, A.; Novoselov, K. S.; Basko, D. M.; Ferrari, A. C. Raman spectroscopy of graphene edges. Nano Lett. 2009, 9, 1433–1441.CrossRefGoogle Scholar
  44. [44]
    Liu, G.; Teweldebrhan, D.; Balandin, A. A.; Tuning of graphene properties via controlled exposure to electron beams. IEEE Trans. Nanotechnol. 2011, 10, 865–870.CrossRefGoogle Scholar
  45. [45]
    Teweldebrhan, D.; Balandin, A. A. Modification of graphene properties due to electron beam irradiation. Appl. Phys. Lett. 2009, 94, 013101.CrossRefGoogle Scholar

Copyright information

© Tsinghua University Press and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Aurélien Lherbier
    • 1
  • Stephan Roche
    • 2
    • 3
  • Oscar A. Restrepo
    • 4
  • Yann-Michel Niquet
    • 5
  • Arnaud Delcorte
    • 4
  • Jean-Christophe Charlier
    • 1
  1. 1.Institute of Condensed Matter and Nanoscience (IMCN)Université catholique de Louvain (UCL)Louvain-la-NeuveBelgium
  2. 2.Catalan Institute of NanotechnologyCIN2 (ICN-CSIC) and Universitat Autónoma de Barcelona, Campus UABBellaterra (Barcelona)Spain
  3. 3.Institució Catalana de Recerca i Estudis AvançatsICREABarcelonaSpain
  4. 4.Institute of Condensed Matter and Nanoscience (IMCN), BSMAUniversité catholique de Louvain (UCL)Louvain-la-NeuveBelgium
  5. 5.L_Sim, SP2M, UMR-E CEA/UJF-Grenoble 1INACGrenoble Cedex 9France

Personalised recommendations