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.

  • Article
  • Published:

Evolution of microscopic localization in graphene in a magnetic field from scattering resonances to quantum dots

Nature Physics volume 7, pages 245–251 (2011)Cite this article

Abstract

Graphene exhibits rich new physics and great promise for applications in electronics. The half-integer quantum Hall effect and high carrier mobility are critically dependent on interactions with impurities/substrates and localization of Dirac fermions in realistic devices. We microscopically study these interactions using scanning tunnelling spectroscopy (STS) of exfoliated graphene on a SiO2 substrate in an applied magnetic field. The magnetic field strongly affects the electronic behaviour of the graphene; the states condense into well-defined Landau levels with a dramatic change in the character of localization. In zero magnetic field, weakly localized states are created by the substrate induced disorder potential. In strong magnetic fields, the two-dimensional electron gas breaks into a network of interacting quantum dots formed at the potential hills and valleys of the disorder potential. Our results demonstrate how graphene properties are perturbed by the disorder potential; a finding essential for the physics and applications of graphene.

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

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

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

Figure 1: STM topography and STS dI/dV measurements at zero magnetic field.
Figure 2: Gate and magnetic-field dependence of STS dI/dV spectra.
Figure 3: dI/dV gate maps around the Dirac point in the quantum Hall regime.
Figure 4: Formation of graphene QDs in the quantum Hall regime.

Similar content being viewed by others

References

  1. Castro Neto, A. H., Guinea, F., Peres, N. M. R., Novoselov, K. S. & Geim, A. K. The electronic properties of graphene. Rev. Mod. Phys. 81, 109–162 (2009).

    Article  ADS  Google Scholar 

  2. Geim, A. K. & Novoselov, K. S. The rise of graphene. Nature Mater. 6, 183–191 (2007).

    Article  ADS  Google Scholar 

  3. de Heer, W. A. et al. Epitaxial graphene. Solid State Commun. 143, 92–100 (2007).

    Article  ADS  Google Scholar 

  4. Zhang, Y., Brar, V. W., Girit, C., Zettl, A. & Crommie, M. F. Origin of spatial charge inhomogeneity in graphene. Nature Phys. 5, 722–726 (2009).

    Article  ADS  Google Scholar 

  5. Rutter, G. M. et al. Scattering and interference in epitaxial graphene. Science 317, 219–222 (2007).

    Article  ADS  Google Scholar 

  6. Martin, J. et al. Observation of electron–hole puddles in graphene using a scanning single-electron transistor. Nature Phys. 4, 144–148 (2008).

    Article  ADS  Google Scholar 

  7. Martin, J. et al. The nature of localization in graphene under quantum Hall conditions. Nature Phys. 5, 669–674 (2009).

    Article  ADS  Google Scholar 

  8. Miller, D. L. et al. Observing the quantization of zero mass carriers in graphene. Science 324, 924–927 (2009).

    Article  ADS  Google Scholar 

  9. Song, Y. J. et al. High resolution tunnelling spectroscopy of a graphene quartet. Nature 467, 185–189 (2010).

    Article  ADS  Google Scholar 

  10. Li, G. & Andrei, E. Y. Observation of Landau levels of Dirac fermions in graphite. Nature Phys. 3, 623–627 (2007).

    Article  ADS  Google Scholar 

  11. Li, G., Luican, A. & Andrei, E. Scanning tunnelling spectroscopy of graphene on graphite. Phys. Rev. Lett. 102, 176804 (2009).

    Article  ADS  Google Scholar 

  12. Miller, D. L. et al. Structural analysis of multilayer graphene via atomic moiré interferometry. Phys. Rev. B 81, 125427 (2010).

    Article  ADS  Google Scholar 

  13. Miller, D. L. et al. Real-space mapping of magnetically quantized graphene states. Nature Phys. 6, 811–817 (2010).

    Article  ADS  Google Scholar 

  14. Zhang, Y. et al. Giant phonon-induced conductance in scanning tunnelling spectroscopy of gate-tunable graphene. Nature Phys. 4, 627–630 (2008).

    Article  ADS  Google Scholar 

  15. Kouwenhoven, L. et al. Electron transport in quantum dots. Mesoscopic Electron Transport 345, 105–214 (1997).

    Google Scholar 

  16. Ilani, S. et al. The microscopic nature of localization in the quantum Hall effect. Nature 427, 328–332 (2004).

    Article  ADS  Google Scholar 

  17. Ishigami, M., Chen, J. H., Cullen, W. G., Fuhrer, M. S. & Williams, E. D. Atomic structure of graphene on SiO2 . Nano Lett. 7, 1643–1648 (2007).

    Article  ADS  Google Scholar 

  18. Stolyarova, E. et al. High-resolution scanning tunnelling microscopy imaging of mesoscopic graphene sheets on an insulating surface. Proc. Natl Acad. Sci. USA 104, 9209–9212 (2007).

    Article  ADS  Google Scholar 

  19. Deshpande, A., Bao, W., Miao, F., Lau, C. N. & LeRoy, B. J. Spatially resolved spectroscopy of monolayer graphene on SiO2 . Phys. Rev. B 79, 205411 (2009).

    Article  ADS  Google Scholar 

  20. Sarma, S. D., Adam, S., Hwang, E. H. & Rossi, E. Electronic transport in two dimensional graphene. Rev. Mod. Phys. (2010, in the press).

  21. Efros, A. & Shklovskii, B. Coulomb gap and low temperature conductivity of disordered systems. J. Phys. C 8, L49–L51 (1975).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  23. Zhang, Y., Tan, Y., 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  Google Scholar 

  24. Shytov, A. V., Katsnelson, M. I. & Levitov, L. S. Atomic collapse and Quasi–Rydberg states in graphene. Phys. Rev. Lett. 99, 246802 (2007).

    Article  ADS  Google Scholar 

  25. Shytov, A. V., Katsnelson, M. I. & Levitov, L. S. Vacuum polarization and screening of supercritical impurities in graphene. Phys. Rev. Lett. 99, 236801 (2007).

    Article  ADS  Google Scholar 

  26. Dial, O. E., Ashoori, R. C., Pfeiffer, L. N. & West, K. W. High-resolution spectroscopy of two-dimensional electron systems. Nature 448, 176–179 (2007).

    Article  ADS  Google Scholar 

  27. Dial, O. E., Ashoori, R. C., Pfeiffer, L. N. & West, K. W. Anomalous structure in the single particle spectrum of the fractional quantum Hall effect. Nature 464, 566–570 (2010).

    Article  ADS  Google Scholar 

  28. Efros, A. Non-linear screening and the background density of 2DEG states in magnetic field. Solid State Commun. 67, 1019–1022 (1988).

    Article  ADS  Google Scholar 

  29. LeRoy, B. J., Kong, J., Pahilwani, V. K., Dekker, C. & Lemay, S. G. Three-terminal scanning tunnelling spectroscopy of suspended carbon nanotubes. Phys. Rev. B 72, 075413 (2005).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We would like to acknowledge M. Stiles and S. Adam for fruitful discussions and S. Blankenship, A. Band, and F. Hess for their technical assistance. We thank D. Davidovic and C. E. Malec for informing us of their unpublished work on tunnelling in graphene.

Author information

Author notes

  1. Suyong Jung and Gregory M. Rutter: These authors contributed equally to this work

Authors and Affiliations

  1. Center for Nanoscale Science and Technology, NIST, Gaithersburg, Maryland 20899, USA

    Suyong Jung, Gregory M. Rutter, Nikolai N. Klimov, Nikolai B. Zhitenev & Joseph A. Stroscio

  2. Maryland NanoCenter, University of Maryland, College Park, Maryland 20742, USA

    Suyong Jung & Nikolai N. Klimov

  3. Electronics and Electrical Engineering Laboratory, NIST, Gaithersburg, Maryland 20899, USA

    Nikolai N. Klimov & David B. Newell

  4. Physics Laboratory, NIST, Gaithersburg, Maryland 20899, USA

    Irene Calizo & Angela R. Hight-Walker

Authors
  1. Suyong Jung
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gregory M. Rutter
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Nikolai N. Klimov
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. David B. Newell
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Irene Calizo
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Angela R. Hight-Walker
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Nikolai B. Zhitenev
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Joseph A. Stroscio
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

The graphene sample was fabricated by S.J. and N.N.K. STM/STS measurements were carried out by S.J., G.M.R., N.N.K. and J.A.S. The data analysis and preparation of the manuscript were carried by S.J., G.M.R., J.A.S., D.B.N. and N.B.Z. The Raman spectroscopy measurements to confirm single-layer graphene flakes were carried by I.C. and A.R.H-W.

Corresponding authors

Correspondence to Nikolai B. Zhitenev or Joseph A. Stroscio.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

Supplementary Information (PDF 749 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jung, S., Rutter, G., Klimov, N. et al. Evolution of microscopic localization in graphene in a magnetic field from scattering resonances to quantum dots. Nature Phys 7, 245–251 (2011). https://doi.org/10.1038/nphys1866

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nphys1866

This article is cited by

Search

Advanced 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