iBet uBet web content aggregator. Adding the entire web to your favor.
iBet uBet web content aggregator. Adding the entire web to your favor.



Link to original content: https://doi.org/10.1038/nature05545
The structure of suspended graphene sheets | Nature
Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

The structure of suspended graphene sheets

Abstract

The recent discovery of graphene has sparked much interest, thus far focused on the peculiar electronic structure of this material, in which charge carriers mimic massless relativistic particles1,2,3. However, the physical structure of graphene—a single layer of carbon atoms densely packed in a honeycomb crystal lattice—is also puzzling. On the one hand, graphene appears to be a strictly two-dimensional material, exhibiting such a high crystal quality that electrons can travel submicrometre distances without scattering. On the other hand, perfect two-dimensional crystals cannot exist in the free state, according to both theory and experiment4,5,6,7,8,9. This incompatibility can be avoided by arguing that all the graphene structures studied so far were an integral part of larger three-dimensional structures, either supported by a bulk substrate or embedded in a three-dimensional matrix1,2,3,9,10,11,12. Here we report on individual graphene sheets freely suspended on a microfabricated scaffold in vacuum or air. These membranes are only one atom thick, yet they still display long-range crystalline order. However, our studies by transmission electron microscopy also reveal that these suspended graphene sheets are not perfectly flat: they exhibit intrinsic microscopic roughening such that the surface normal varies by several degrees and out-of-plane deformations reach 1 nm. The atomically thin single-crystal membranes offer ample scope for fundamental research and new technologies, whereas the observed corrugations in the third dimension may provide subtle reasons for the stability of two-dimensional crystals13,14,15.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Suspended graphene membrane.
Figure 2: Transmission electron microscopy of graphene.
Figure 3: Microscopically corrugated graphene.
Figure 4: Atomic resolution imaging of graphene membranes.

Similar content being viewed by others

References

  1. Novoselov, K. S. et al. Electric field effect in atomically thin carbon films. Science 306, 666–669 (2004)

    Article  ADS  CAS  Google Scholar 

  2. Novoselov, K. S. et al. Two-dimensional gas of massless Dirac fermions in graphene. Nature 438, 197–200 (2005)

    Article  ADS  CAS  Google Scholar 

  3. Zhang, Y., Tan, J. W., Stormer, H. L. & Kim, P. Experimental observation of the quantum Hall effect and Berry's phase in graphene. Nature 438, 201–204 (2005)

    Article  ADS  CAS  Google Scholar 

  4. Peierls, R. E. Bemerkungen über Umwandlungstemperaturen. Helv. Phys. Acta 7, 81–83 (1934)

    CAS  Google Scholar 

  5. Peierls, R. E. Quelques proprietes typiques des corpses solides. Ann. Inst. Henri Poincare 5, 177–222 (1935)

    MathSciNet  MATH  Google Scholar 

  6. Landau, L. D. Zur Theorie der Phasenumwandlungen II. Phys. Z. Sowjetunion 11, 26–35 (1937)

    CAS  MATH  Google Scholar 

  7. Landau, L. D. & Lifshitz, E. M. Statistical Physics Part I, Sections 137 and 138 (Pergamon, Oxford, 1980)

  8. Mermin, N. D. Crystalline order in two dimensions. Phys. Rev. 176, 250–254 (1968)

    Article  ADS  Google Scholar 

  9. Novoselov, K. S. et al. Two-dimensional atomic crystals. Proc. Natl Acad. Sci. USA 102, 10451–10453 (2005)

    Article  ADS  CAS  Google Scholar 

  10. Berger, C. et al. Electronic confinement and coherence in patterned epitaxial graphene. Science 312, 1191–1196 (2006)

    Article  ADS  CAS  Google Scholar 

  11. Ohta, T., Bostwick, A., Seyller, T., Horn, K. & Rotenberg, E. Controlling the electronic structure of bilayer graphene. Science 313, 951–954 (2006)

    Article  ADS  CAS  Google Scholar 

  12. Stankovich, S. et al. Graphene-based composite materials. Nature 442, 282–286 (2006)

    Article  ADS  CAS  Google Scholar 

  13. Nelson, D. R. & Peliti, L. Fluctuations in membranes with crystalline and hexatic order. J. Phys. 48, 1085–1092 (1987)

    Article  CAS  Google Scholar 

  14. Radzihovsky, L. & Le Doussal, P. Self-consistent theory of polymerized membranes. Phys. Rev. Lett. 69, 1209–1212 (1992)

    Article  ADS  Google Scholar 

  15. Nelson, D. R., Piran, T. & Weinberg, S. Statistical Mechanics of Membranes and Surfaces (World Scientific, Singapore, 2004)

    Book  Google Scholar 

  16. Born, M. & Huang, K. Dynamical Theory of Crystal Lattices (Clarendon, Oxford, 1954)

    MATH  Google Scholar 

  17. Mermin, N. D. & Wagner, H. Absence of ferromagnetism or antiferromagnetism in one- or two-dimensional isotropic Heisenberg models. Phys. Rev. Lett. 17, 1133–1136 (1966)

    Article  ADS  CAS  Google Scholar 

  18. Venables, J. A., Spiller, G. D. T. & Hanbucken, M. Nucleation and growth of thin-films. Rep. Prog. Phys. 47, 399–459 (1984)

    Article  ADS  Google Scholar 

  19. Zinkeallmang, M., Feldman, L. C. & Grabow, M. H. Clustering on surfaces. Surf. Sci. Rep. 16, 377–463 (1992)

    Article  ADS  CAS  Google Scholar 

  20. Evans, J. W., Thiel, P. A. & Bartelt, M. C. Morphological evolution during epitaxial thin film growth: Formation of 2D islands and 3D mounds. Surf. Sci. Rep. 61, 1–128 (2006)

    Article  ADS  CAS  Google Scholar 

  21. Horiuchi, S. et al. Carbon nanofilm with a new structure and property. Jpn. J. Appl. Phys. 42, L1073–L1076 (2003)

    Article  ADS  CAS  Google Scholar 

  22. Buseck, P. R., Cowley, J. M. & Eyring, L. High-Resolution Transmission Electron Microscopy (Oxford Univ. Press, Oxford, 1988)

    Google Scholar 

  23. Spence, J. C. H. High-Resolution Electron Microscopy (Oxford Univ. Press, Oxford, 2003)

    Google Scholar 

  24. Peng, L. M. Electron atomic scattering factors and scattering potentials of crystals. Micron 30, 625–648 (1999)

    Article  CAS  Google Scholar 

  25. Yu, M. F., Files, B. S., Arepalli, S. & Ruoff, R. S. Tensile loading of ropes of single wall carbon nanotubes and their mechanical properties. Phys. Rev. Lett. 84, 5552–5555 (2000)

    Article  ADS  CAS  Google Scholar 

  26. Zhao, Q., Nardelli, M. B. & Bernholc, J. Ultimate strength of carbon nanotubes: a theoretical study. Phys. Rev. B 65, 144105 (2002)

    Article  ADS  Google Scholar 

  27. Huang, J. Y. et al. Superplastic carbon nanotubes. Nature 439, 281 (2006)

    Article  ADS  CAS  Google Scholar 

  28. Morozov, S. V. et al. Strong suppression of weak localization in graphene. Phys. Rev. Lett. 97, 016801 (2006)

    Article  ADS  CAS  Google Scholar 

  29. Doyle, P. A. & Turner, P. S. Relativistic Hartree-Fock x-ray and electron scattering factors. Acta Crystallogr. A 24, 390–397 (1968)

    Article  ADS  CAS  Google Scholar 

Download references

Acknowledgements

We thank B. Freitag and D. Beamer of FEI for providing access to their in-house TEM Titan. This work was supported by the EU project CANAPE, the EPSRC (UK) and the Royal Society. M.I.K. acknowledges financial support from FOM (Netherlands).

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Jannik C. Meyer or A. K. Geim.

Ethics declarations

Competing interests

Reprints and permissions information is available at www.nature.com/reprints. The authors declare no competing financial interests.

Supplementary information

Supplementary Information

This file contains Supplementary Notes and Supplementary Figures S1-S5 with Legends (PDF 5004 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Meyer, J., Geim, A., Katsnelson, M. et al. The structure of suspended graphene sheets. Nature 446, 60–63 (2007). https://doi.org/10.1038/nature05545

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature05545

This article is cited by

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing