Skip to main content
Log in

Practical and Fundamental Impact of Epitaxial Graphene on Quantum Metrology

  • Review Paper
  • Published:
MAPAN Aims and scope Submit manuscript

Abstract

The discovery 8 years ago of the quantum Hall effect (QHE) in graphene sparked an immediate interest in the metrological community. Here was a material which was completely different from commonly used semiconductor systems and which seemed to have some uniques properties which could make it ideally suited for high-precision resistance metrology. However, measuring the QHE in graphene turned out to be not so simple as first thought. In particular the small size of exfoliated graphene samples made precision measurements difficult. This dramatically changed with the development of large-area graphene grown on SiC and in this short review paper we discuss the journey from first observation to the highest-ever precision comparison of the QHE.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

Similar content being viewed by others

References

  1. K.V. Klitzing, G. Dorda and M. Pepper, New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance, Phys. Rev. Lett., 45 (1980) 4.

    Article  Google Scholar 

  2. B. Jeckelmann and B. Jeanneret, The quantum Hall effect as an electrical resistance standard, Rep. Prog. Phys., 64 (2001) 1603–1655.

    Article  ADS  Google Scholar 

  3. A.K. Geim, Graphene: status and prospects, Science, 324 (2009) 1530–1534.

    Article  ADS  Google Scholar 

  4. K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, M.I. Katsnelson, I.V. Grigorieva, S.V. Dubonos and A.A. Firsov, Two-dimensional gas of massless Dirac fermions in graphene, Nature, 438 (2005) 197–200.

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  6. K.S. Novoselov, Z. Jiang, Y. Zhang, S.V. Morozov, H.L. Stormer, U. Zeitler, J.C. Maan, G.S. Boebinger, P. Kim and A.K. Geim, Room-temperature quantum Hall effect in graphene, Science, 315 (2007) 1379–1379.

    Article  ADS  Google Scholar 

  7. T.J.B.M. Janssen, A. Tzalenchuk, S. Lara-Avila, S. Kubatkin and V.I. Fal’ko, Rep. Prog. Phys., (2013, in press).

  8. I.M. Mills, P.J. Mohr, T.J. Quinn, B.N. Taylor and E.R. Williams, Redefinition of the kilogram, ampere, kelvin and mole: a proposed approach to implementing CIPM recommendation 1 (CI-2005), Metrologia, 43 (2006) 227–246.

    Article  ADS  Google Scholar 

  9. A.J.M. Giesbers, G. Rietveld, E. Houtzager, U. Zeitler, R. Yang, K.S. Novoselov, A.K. Geim and J.C. Maan, Quantum resistance metrology in graphene, Appl. Phys. Lett., 93 (2008) 222109–222112.

    Article  ADS  Google Scholar 

  10. T. Shen, J.J. Gu, M. Xu, Y.Q. Wu, M.L. Bolen, M.A. Capano, L.W. Engel and P.D. Ye, Observation of quantum-hall effect in gated epitaxial graphene grown on SiC (0001), Appl. Phys. Lett., 95 (2009) 3.

    Google Scholar 

  11. X.S. Wu, Y.K. Hu, M. Ruan, N.K. Madiomanana, J. Hankinson, M. Sprinkle, C. Berger and W.A. de Heer, Half integer quantum Hall effect in high mobility single layer epitaxial graphene, Appl. Phys. Lett., 95 (2009) 3.

    Google Scholar 

  12. A. Tzalenchuk, S. Lara-Avila, A. Kalaboukhov, S. Paolillo, M. Syvajarvi, R. Yakimova, O. Kazakova, T.J.B. M. Janssen, V. Fal’ko and S. Kubatkin, Towards a quantum resistance standard based on epitaxial graphene, Nat. Nanotechnol., 5 (2010) 186–189.

    Article  ADS  Google Scholar 

  13. J. Jobst, D. Waldmann, F. Speck, R. Hirner, D.K. Maude, T. Seyller and H.B. Weber, Quantum oscillations and quantum Hall effect in epitaxial graphene, Phys. Rev. B, 81 (2010) 6.

    Article  Google Scholar 

  14. S. Tanabe, Y. Sekine, H. Kageshima, M. Nagase and H. Hibino, Half-integer quantum Hall effect in gate-controlled epitaxial graphene devices, Appl. Phys. Express, 3 (2010) 3.

    Article  Google Scholar 

  15. J.M. Williams, T.J.B.M. Janssen, G. Rietveld and E. Houtzager, An automated cryogenic current comparator resistance ratio bridge for routine resistance measurements, Metrologia, 47 (2010) 167–174.

    Article  ADS  Google Scholar 

  16. S. Kopylov, A. Tzalenchuk, S. Kubatkin and V.I. Fal’ko, Charge transfer between epitaxial graphene and silicon carbide, Appl. Phys. Lett., 97 (2010) 3.

    Article  Google Scholar 

  17. T.J.B.M. Janssen, A. Tzalenchuk, R. Yakimova, S. Kubatkin, S. Lara-Avila, S. Kopylov and V.I. Fal’ko, Anomalously strong pinning of the filling factor ν = 2 in epitaxial graphene, Phys. Rev. B, 83 (2011) 4.

    Article  Google Scholar 

  18. S. Lara-Avila, K. Moth-Poulsen, R. Yakimova, T. Bjornholm, V. Fal’ko, A. Tzalenchuk and S. Kubatkin, Non-volatile photochemical gating of an epitaxial graphene/polymer heterostructure, Adv. Mater., 23 (2011) 5.

    Article  Google Scholar 

  19. T.J.B.M. Janssen, N.E. Fletcher, R. Goebel, J.M. Williams, A. Tzalenchuk, R. Yakimova, S. Lara-Avila, S. Kubatkin and V.I. Fal’ko, Graphene, universality of the quantum Hall effect and redefinition of the SI system, New J. Phys., 13 (2011) 6.

    Article  Google Scholar 

  20. C. Virojanadara, C. Virojanadara, M. Syvajarvi, R. Yakimova, L.I. Johansson, A.A. Zakharov and T. Balasubramanian, Homogeneous large-area graphene layer growth on 6H-SiC(0001), Phys. Rev. B, 78 (2008) 6.

    Article  Google Scholar 

  21. S. Lara-Avila, A. Tzalenchuk, S. Kubatkin, R. Yakimova, T.J.B.M. Janssen, K. Cedergren, T. Bergsten and V.I. Fal’ko, Phys. Rev. Lett., (2011, in press).

  22. A. van Bommel, J. Crombeen and A. van Tooren, LEED and auger electron observations of the SiC(0001) surface, Surf. Sci., 48 (1975) 463–472.

    Article  ADS  Google Scholar 

  23. C. Riedl, U. Starke, J. Bernhardt, M. Franke and K. Heinz, Structural properties of the graphene-SiC(0001) interface as a key for the preparation of homogeneous large-terrace graphene surfaces, Phys. Rev. B, 76 (2007) 8.

    Article  Google Scholar 

  24. F. Varchon, R. Feng, J. Hass, X. Li, B.N. Nguyen, C. Naud, P. Mallet, J.Y. Veuillen, C. Berger, E.H. Conrad and L. Magaud, Electronic structure of epitaxial graphene layers on SiC: effect of the substrate, Phys. Rev. Lett., 99 (2007) 4.

    Article  Google Scholar 

  25. A. Mattausch and O. Pankratov, Ab initio study of graphene on SiC, Phys. Rev. Lett., 99 (2007) 4.

    Article  Google Scholar 

  26. K.V. Emtsev, F. Speck, T. Seyller, L. Ley and J.D. Riley, Interaction, growth, and ordering of epitaxial graphene on SiC0001 surfaces: a comparative photoelectron spectroscopy study, Phys. Rev. B, 77 (2008) 10.

    Article  Google Scholar 

  27. Y. Qi, S.H. Rhim, G.F. Sun, M. Weinert and L. Li, Epitaxial graphene on SiC(0001): more than just honeycombs, Phys. Rev. Lett., 105 (2010) 4.

    Google Scholar 

  28. K.V. Emtsev, A. Bostwick, K. Horn, J. Jobst, G.L. Kellogg, L. Ley, J.L. McChesney, T. Ohta, S.A. Reshanov, J. Rohrl, E. Rotenberg, A.K. Schmid, D. Waldmann, H.B. Weber and T. Seyller, Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide, Nat. Mater., 8 (2009) 5.

    Article  Google Scholar 

  29. C. Coletti, C. Riedl, D.S. Lee, B. Krauss, L. Patthey, K. von Klitzing, J.H. Smet and U. Starke, Charge neutrality and band-gap tuning of epitaxial graphene on SiC by molecular doping, Phys. Rev. B, 81 (2010) 8.

    Article  Google Scholar 

  30. D. Waldmann, J. Jobst, F. Speck, T. Seyller, M. Krieger and H.B. Weber, Bottom-gated epitaxial graphene, Nat. Mater., 10 (2011) 357–360.

    Article  ADS  Google Scholar 

  31. F. Schwierz, Graphene transistors, Nat. Nanotechnol., 5 (2010) 487–496.

    Article  ADS  Google Scholar 

  32. S. Luryi, Quantum capacitance devices, Appl. Phys. Lett., 52 (1988) 501.

    Article  ADS  Google Scholar 

  33. J.P. Eisenstein, L.N. Pfeiffer and K.W. West, Compressibility of the 2-dimensional electron-gas—measurements of the zero-field exchange energy and fractional quantum Hall gap, Phys. Rev. B, 50 (1994) 1760–1778.

    Article  ADS  Google Scholar 

  34. D.L. John, L.C. Castro and D.L. Pulfrey, Quantum capacitance in nanoscale device modeling, J. Appl. Phys., 96 (2004) 5180–5184.

    Article  ADS  Google Scholar 

  35. L.A. Ponomarenko, R. Yang, R.V. Gorbachev, P. Blake, A.S. Mayorov, K.S. Novoselov, M.I. Katsnelson and A.K. Geim, Density of states and zero Landau level probed through capacitance of graphene, Phys. Rev. Lett., 105 (2010) 136801.

    Article  ADS  Google Scholar 

  36. Y.J. Song, A.F. Otte, Y. Kuk, Y.K. Hu, D.B. Torrance, P.N. First, W.A. de Heer, H.K. Min, S. Adam, M.D. Stiles, A.H. MacDonald and J.A. Stroscio, High-resolution tunnelling spectroscopy of a graphene quartet, Nature, 467 (2010) 185–189.

    Article  ADS  Google Scholar 

  37. A.J.M. Giesbers, U. Zeitler, M.I. Katsnelson, L.A. Ponomarenko, T.M. Mohiuddin and J.C. Maan, Quantum-hall activation gaps in graphene, Phys. Rev. Lett., 99 (2007) 4.

    Article  Google Scholar 

  38. M. Furlan, Electronic transport and the localization length in the quantum Hall effect, Phys. Rev. B, 57 (1998) 14818–14828.

    Article  ADS  Google Scholar 

  39. A.J.M. Giesbers, U. Zeitler, L.A. Ponomarenko, R. Yang, K.S. Novoselov, A.K. Geim and J.C. Maan, Scaling of the quantum Hall plateau–plateau transition in graphene, Phys. Rev. B, 80 (2009) 4.

    Google Scholar 

  40. K. Bennaceur, P. Jacques, F. Portier, P. Roche and D.C. Glattli, Unveiling quantum Hall transport by Efros-Shklovskii to Mott variable-range hopping transition in graphene, Phys. Rev. B, 86 (2012) 085433.

    Google Scholar 

  41. J.M. Williams, G. Rietveld, E. Houtzager and T.J.B.M. Janssen, Design considerations for a CCC bridge with complete digital control, IEEE Trans. Instrum. Meas., (2011) 1–6.

  42. T.J. Witt and D. Reymann, Using Power Spectra and Allan Variances to Characterise the Noise of Zener-Diode Voltage Standards, IEE Proc. Sci. Meas. Technol., 147 (2000) 177–182.

  43. A. Hartland, K. Jones, J.M. Williams, B.L. Gallagher and T. Galloway, Direct Comparison of the Quantized Hall Resistance in Gallium–Arsenide and Silicon, Phys. Rev. Lett., 66 (1991) 969–973.

    Article  ADS  Google Scholar 

  44. T.J.B.M. Janssen, J.M. Williams, N.E. Fletcher, R. Goebel, A. Tzalenchuk, R. Yakimova, S. Lara-Avila, S. Kubatkin and V.I. Fal’ko, Precision comparison of the quantum Hall effect in graphene and gallium arsenide, Metrologia, 49 (2012) 294–306.

    Article  ADS  Google Scholar 

  45. B. Jeckelmann and B. Jeanneret, High-precision measurements of the quantized Hall resistance: experimental conditions for universality, Phys. Rev. B, 55 (1997) 13124–13134.

    Article  ADS  Google Scholar 

  46. F. Schopfer and W. Poirier, Testing universality of the quantum Hall effect by means of the Wheatstone bridge, J. Appl. Phys., 102 (2007) 9.

    Article  Google Scholar 

  47. W. Poirier and F. Schopfer, Resistance metrology based on the quantum Hall effect, Eur. Phys. J. Special Top., 172 (2009) 207–245.

    Article  ADS  Google Scholar 

  48. D.J. Thouless, Topological interpretations of quantum Hall conductance, J. Math. Phys., 35 (1994) 5362–5372.

    Article  ADS  MATH  MathSciNet  Google Scholar 

  49. H. Bachmair, Determination of the unit of resistance and the Von Klitzing constant R(k) based on a calculable capacitor, Euro. Phys. J. Special Top., 172 (2009) 257–266.

    Article  ADS  Google Scholar 

Download references

Acknowledgements

Many people have contributed to various parts of our research and the authors are grateful to Rositza Yakimova, Sergey Kopylov, Olga Kazakova, Nick Fletcher, Roland Goebel, Jonathan Williams, Dale Henderson, Stephen Giblin, Pravin Patel, Thomas Bjørnholm, Kasper Moth-Poulsen, Karin Cedergren, and Mikael Syväjärvi. This work was supported by the NMS Pathfinder Programme, Swedish Research Council and Foundation for Strategic Research, EU FP7 STREPs ConceptGraphene and SINGLE, EPSRC Grant EP/G041954 and the Science & Innovation Award EP/G014787.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Theodoor Jan B. M. Janssen.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Janssen, T.J.B.M., Tzalenchuk, A., Lara-Avila, S. et al. Practical and Fundamental Impact of Epitaxial Graphene on Quantum Metrology. MAPAN 28, 239–250 (2013). https://doi.org/10.1007/s12647-013-0064-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12647-013-0064-y

Keywords

Navigation