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.

Experimental observation of the quantum Hall effect and Berry's phase in graphene

Abstract

When electrons are confined in two-dimensional materials, quantum-mechanically enhanced transport phenomena such as the quantum Hall effect can be observed. Graphene, consisting of an isolated single atomic layer of graphite, is an ideal realization of such a two-dimensional system. However, its behaviour is expected to differ markedly from the well-studied case of quantum wells in conventional semiconductor interfaces. This difference arises from the unique electronic properties of graphene, which exhibits electron–hole degeneracy and vanishing carrier mass near the point of charge neutrality1,2. Indeed, a distinctive half-integer quantum Hall effect has been predicted3,4,5 theoretically, as has the existence of a non-zero Berry's phase (a geometric quantum phase) of the electron wavefunction—a consequence of the exceptional topology of the graphene band structure6,7. Recent advances in micromechanical extraction and fabrication techniques for graphite structures8,9,10,11,12 now permit such exotic two-dimensional electron systems to be probed experimentally. Here we report an experimental investigation of magneto-transport in a high-mobility single layer of graphene. Adjusting the chemical potential with the use of the electric field effect, we observe an unusual half-integer quantum Hall effect for both electron and hole carriers in graphene. The relevance of Berry's phase to these experiments is confirmed by magneto-oscillations. In addition to their purely scientific interest, these unusual quantum transport phenomena may lead to new applications in carbon-based electronic and magneto-electronic devices.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Figure 1: Resistance, carrier density, and mobility of graphene measured at 1.7 K at different gate voltages.
Figure 2: Quantized magnetoresistance and Hall resistance of a graphene device.
Figure 3: Temperature dependence and gate-voltage dependence of the SdH oscillations in graphene.

References

  1. 1

    Semenoff, G. W. Condensed-matter simulation of a three-dimensional anomaly. Phys. Rev. Lett. 53, 2449–2452 (1984)

    ADS  Article  Google Scholar 

  2. 2

    Haldane, F. D. M. Model for a quantum hall effect without Landau levels: condensed-matter realization of the “parity anomaly”. Phys. Rev. Lett. 61, 2015–2018 (1988)

    ADS  MathSciNet  CAS  Article  Google Scholar 

  3. 3

    Zheng, Y. & Ando, T. Hall conductivity of a two-dimensional graphite system. Phys. Rev. B 65, 245420 (2002)

    ADS  Article  Google Scholar 

  4. 4

    Gusynin, V. P. & Sharapov, S. G. Unconventional integer quantum Hall effect in graphene. Preprint at http://xxx.lanl.gov/abs/cond-mat/0506575 (2005).

  5. 5

    Peres, N. M. R., Guinea, F. & Neto, A. H. C. Electronic properties of two-dimensional carbon. Preprint at http://xxx.lanl.gov/abs/cond-mat/0506709 (2005).

  6. 6

    Ando, T., Nakaishi, T. & Saito, R. Berry's phase and absence of back scattering in carbon nanotubes. J. Phys. Soc. Jpn. 67, 2857–2862 (1998)

    ADS  CAS  Article  Google Scholar 

  7. 7

    Mikitik, G. P. & Sharlai, Y. V. Manifestation of Berry's phase in metal physics. Phys. Rev. Lett. 82, 2147–2150 (1999)

    ADS  CAS  Article  Google Scholar 

  8. 8

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

    ADS  CAS  Article  Google Scholar 

  9. 9

    Berger, C. et al. Ultrathin epitaxial graphite: 2D electron gas properties and a route toward graphene-based nanoelectronics. J. Phys. Chem. B 108, 19912–19916 (2004)

    CAS  Article  Google Scholar 

  10. 10

    Zhang, Y., Small, J. P., Pontius, W. V. & Kim, P. Fabrication and electric-field-dependent transport measurements of mesoscopic graphite devices. Appl. Phys. Lett. 86, 073104 (2005)

    ADS  Article  Google Scholar 

  11. 11

    Zhang, Y., Small, J. P., Amori, E. S. & Kim, P. Electric field modulation of galvanomagnetic properties of mesoscopic graphite. Phys. Rev. Lett. 94, 176803 (2005)

    ADS  Article  Google Scholar 

  12. 12

    Bunch, J. S., Yaish, Y., Brink, M., Bolotin, K. & McEuen, P. L. Coulomb oscillations and Hall effect in quasi-2D graphite quantum dots. Nano Lett. 5, 287–290 (2005)

    ADS  CAS  Article  Google Scholar 

  13. 13

    Roukes, M. L., Scherer, A. & Van der Gaag, B. P. Are transport anomalies in ‘electron waveguides’ classical? Phys. Rev. Lett. 64, 1154–1157 (1990)

    ADS  CAS  Article  Google Scholar 

  14. 14

    Fang, Z. et al. The anomalous Hall effect and magnetic monopoles in momentum space. Science 302, 92–95 (2003)

    ADS  CAS  Article  Google Scholar 

  15. 15

    McEuen, P. L., Bockrath, M., Cobden, D. H., Yoon, Y. & Louie, S. G. Disorder, pseudospins, and backscattering in carbon nanotubes. Phys. Rev. Lett. 83, 5098–5101 (1999)

    ADS  CAS  Article  Google Scholar 

  16. 16

    Sharapov, S. G., Gusynin, V. P. & Beck, H. Magnetic oscillations in planar systems with the Dirac-like spectrum of quasiparticle excitations. Phys. Rev. B 69, 075104 (2004)

    ADS  Article  Google Scholar 

  17. 17

    Luk'yanchuk, I. A. & Kopelevich, Y. Phase analysis of quantum oscillations in graphite. Phys. Rev. Lett. 93, 166402 (2004)

    ADS  Article  Google Scholar 

  18. 18

    Morozov, S. V. et al. Two dimensional electron and hole gases at the surface of graphite. Preprint at http://xxx.lanl.gov/abs/cond-mat/0505319 (2005).

  19. 19

    Shoenberg, D. Magnetic Oscillation in Metals (Cambridge Univ. Press, Cambridge, 1984)

    Google Scholar 

  20. 20

    Kane, C. L & Mele, E. J. Quantum spin Hall effect in graphene. Preprint at http://xxx.lanl.gov/abs/cond-mat/0411737 (2005).

Download references

Acknowledgements

We thank I. Aleiner, A. Millis, T. F. Heinz, A. Mitra, J. Small and A. Geim for discussions. This research was supported by the NSF Nanoscale Science and Engineering Center at Columbia University, New York State Office of Science (NYSTAR) and the Department of Energy (DOE).

Author information

Affiliations

Authors

Corresponding author

Correspondence to Philip Kim.

Ethics declarations

Competing interests

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

Supplementary information

Supplementary Discussion

This pdf formatted file contains detailed discussions of sample preparation method, cross-correlation of optical microscope and AFM images of single layer and few layer graphene samples, and electrical characterization of double layer graphene samples. (PDF 203 kb)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Zhang, Y., Tan, YW., Stormer, H. et al. Experimental observation of the quantum Hall effect and Berry's phase in graphene. Nature 438, 201–204 (2005). https://doi.org/10.1038/nature04235

Download citation

Further reading

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

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