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

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Abstract

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.

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References

  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.

    Article  CAS  Google Scholar 

  2. Novoselov, K. S. Nobel lecture: Graphene: Materials in the flatland. Rev. Mod. Phys. 2011, 83, 837–849.

    Article  CAS  Google Scholar 

  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.

    Article  Google Scholar 

  4. Wang, X.; Zhi, L.; Müllen, K. Transparent, conductive graphene electrodes for dye-sensitized solar cells. Nano Lett. 2008, 8, 323–327.

    Article  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

    Article  Google Scholar 

  7. Krasheninnikov, A. V.; Banhart, F. Engineering of nano-structured carbon materials with electron or ion beams. Nat. Mater. 2007, 6, 723–733.

    Article  CAS  Google Scholar 

  8. Banhart, F.; Kotakoski, J.; Krasheninnikov, A. V. Structural defects in graphene. ACS Nano 2011, 5, 26–41.

    Article  CAS  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  12. Yazyev, O. V.; Louie, S. G. Electronic transport in polycrystalline graphene. Nat. Mater. 2010, 9, 806–809.

    Article  CAS  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

    CAS  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  21. Hoffmann, R.; Alder, R. W.; Wilcox, C. F. Planar tetracoor-dinate carbon. J. Am. Chem. Soc. 1970, 92, 4992–4993.

    Article  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  23. Wang, B.; Puzyrev, Y.; Pantelides, S. T. Strain enhanced defect reactivity at grain boundaries in polycrystalline graphene. Carbon 2011, 49, 3983–3988.

    Article  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  29. Roche, S.; Mayou, D. Conductivity of quasiperiodic systems: A numerical study. Phys. Rev. Lett. 1997, 79, 2518–2521.

    Article  CAS  Google Scholar 

  30. Roche, S. Quantum transport by means of O(N) real-space methods. Phys. Rev. B 1999, 59, 2284–2291.

    Article  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  Google Scholar 

  35. Shon, N. H.; Ando, T. Quantum transport in two-dimensional graphite system. J. Phys. Soc. Jpn. 1998, 67, 2421–2429.

    Article  CAS  Google Scholar 

  36. Peres, N. M. R.; Guinea, F.; Neto, A. H. C. Electronic properties of disordered two-dimensional carbon. Phys. Rev. B 2006, 73, 125411.

    Article  Google Scholar 

  37. Ostrovsky, P. M.; Gornyi, I. V.; Mirlin, A. D. Electron transport in disordered graphene. Phys. Rev. B 2006, 74, 235443.

    Article  Google Scholar 

  38. Nomura, K.; MacDonald, A. H. Quantum transport of massless Dirac fermions. Phys. Rev. Lett. 2007, 98, 076602.

    Article  Google Scholar 

  39. Geim, A. K.; Novoselov, K. S. The rise of graphene. Nat. Mater. 2007, 6, 183–191.

    Article  CAS  Google Scholar 

  40. Lee, P. A.; Ramakrishnan, T. V. Disordered electronic systems. Rev. Mod. Phys. 1985, 57, 287–337.

    Article  CAS  Google Scholar 

  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.

    Article  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

    Article  CAS  Google Scholar 

  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.

    Article  Google Scholar 

  45. Teweldebrhan, D.; Balandin, A. A. Modification of graphene properties due to electron beam irradiation. Appl. Phys. Lett. 2009, 94, 013101.

    Article  Google Scholar 

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Authors and Affiliations

  1. Institute of Condensed Matter and Nanoscience (IMCN), Université catholique de Louvain (UCL), NAPS-ETSF, Chemin des étoiles 8, 1348, Louvain-la-Neuve, Belgium

    Aurélien Lherbier & Jean-Christophe Charlier

  2. Catalan Institute of Nanotechnology, CIN2 (ICN-CSIC) and Universitat Autónoma de Barcelona, Campus UAB, 08193, Bellaterra (Barcelona), Spain

    Stephan Roche

  3. Institució Catalana de Recerca i Estudis Avançats, ICREA, 08070, Barcelona, Spain

    Stephan Roche

  4. Institute of Condensed Matter and Nanoscience (IMCN), BSMA, Université catholique de Louvain (UCL), Place Croix du Sud 1 (Boltzmann), 1348, Louvain-la-Neuve, Belgium

    Oscar A. Restrepo & Arnaud Delcorte

  5. L_Sim, SP2M, UMR-E CEA/UJF-Grenoble 1, INAC, 17 rue des Martyrs, 38054, Grenoble Cedex 9, France

    Yann-Michel Niquet

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  1. Aurélien Lherbier
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  2. Stephan Roche
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Correspondence to Aurélien Lherbier.

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Lherbier, A., Roche, S., Restrepo, O.A. et al. Highly defective graphene: A key prototype of two-dimensional Anderson insulators. Nano Res. 6, 326–334 (2013). https://doi.org/10.1007/s12274-013-0309-7

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  • DOI: https://doi.org/10.1007/s12274-013-0309-7

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