The quantum Hall effect1 allows the international standard for resistance to be defined in terms of the electron charge and Planck's constant alone. The effect comprises the quantization of the Hall resistance in two-dimensional electron systems in rational fractions of RK = h/e2 = 25 812.807 557(18) Ω, the resistance quantum2. Despite 30 years of research into the quantum Hall effect, the level of precision necessary for metrology—a few parts per billion—has been achieved only in silicon and iii–v heterostructure devices3,4,5. Graphene should, in principle, be an ideal material for a quantum resistance standard6, because it is inherently two-dimensional and its discrete electron energy levels in a magnetic field (the Landau levels7) are widely spaced. However, the precisions demonstrated so far have been lower than one part per million8. Here, we report a quantum Hall resistance quantization accuracy of three parts per billion in monolayer epitaxial graphene at 300 mK, four orders of magnitude better than previously reported. Moreover, by demonstrating the structural integrity and uniformity of graphene over hundreds of micrometres, as well as reproducible mobility and carrier concentrations across a half-centimetre wafer, these results boost the prospects of using epitaxial graphene in applications beyond quantum metrology.
Subscribe to Journal
Get full journal access for 1 year
only $4.92 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Tax calculation will be finalised during checkout.
Rent or Buy article
Get time limited or full article access on ReadCube.
All prices are NET prices.
von Klitzing, K., Dorda, G. & Pepper, M. New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance. Phys. Rev. Lett. 45, 494–497 (1980).
Mohr, P. J., Taylor, B. N. & Newell, D. B. CODATA recommended values of the fundamental physical constants: 2006. Rev. Mod. Phys. 80, 633–730 (2008).
Jeckelmann, B. & Jeanneret, B. The quantum Hall effect as an electrical resistance standard. Rep. Progr. Phys. 64, 1603–1655 (2001).
Delahaye, F. et al. Precise quantized Hall resistance measurements in GaAs/AlxGa1−xAs and InxGa1−xAs/InP heterostructures. Metrologia 22, 103–110 (1986).
Piquemal, F. et al. Report on a joint BIPM-EUROMET project for the fabrication of QHE samples by the LEP. IEEE Trans. Instrum. 42, 264–268 (1993).
Poirier, W. & Schopfer, F. Resistance metrology based on the quantum Hall effect. Eur. Phys. J. Spec. Top. 172, 207–245 (2009).
Landau, L. D. Diamagnetismus der Metalle. Z. Phys. 64, 629–637 (1930).
Giesbers, A. J. M. et al. Quantum resistance metrology in graphene. Appl. Phys. Lett. 93, 222109 (2008).
Novoselov, K. S. et al. Two-dimensional gas of massless Dirac fermions in graphene. Nature 438, 197–200 (2005).
Zhang, Y. B. et al. Experimental observation of the quantum Hall effect and Berry's phase in graphene. Nature 438, 201–204 (2005).
Novoselov, K. S. et al. Unconventional quantum Hall effect and Berry's phase of 2π in bilayer graphene. Nature Phys. 2, 177–180 (2006).
McCann, E. & Fal'ko, V. I. Landau-level degeneracy and quantum Hall effect in a graphite bilayer. Phys. Rev. Lett. 96, 086805 (2006).
Neto, A. H. C. et al. The electronic properties of graphene. Rev. Mod. Phys. 81, 109–162 (2009).
Geim, A. K. Graphene: status and prospects. Science 324, 1530–1534 (2009).
Novoselov, K. S. et al. Room-temperature quantum Hall effect in graphene. Science 315, 1379–1379 (2007).
Virojanadara, C. et al. Homogeneous large-area graphene layer growth on 6H-SiC(0001). Phys. Rev. B 78, 245403 (2008).
Bostwick, A. et al. Quasiparticle dynamics in graphene. Nature Phys. 3, 36–40 (2007).
Miller, D. L. et al. Observing the quantization of zero mass carriers in graphene. Science 324, 924–927 (2009).
Darancet, P. et al. Quenching of the quantum Hall effect in multilayered epitaxial graphene: the role of undoped planes. Phys. Rev. Lett. 101, 116806 (2008).
McCann, E. et al. Weak-localization magnetoresistance and valley symmetry in graphene. Phys. Rev. Lett. 97, 146805 (2006).
Kleinschmidt, P., Williams, J. M., Fletcher, N. E. & Janssen, T. Cryogenic current comparator bridge for quantum Hall resistance ratio measurements. IEE Proc. Sci. Meas. Technol. 149, 302–304 (2002).
Allan, D. W. Should the classical variance be used as a basic measure in standards metrology? IEEE Trans. Instrum. Meas. 36, 646–654 (1987).
Emtsev, K. V. et al. Towards wafer-size graphene layers by atmospheric pressure graphitization of silicon carbide. Nature Mater. 8, 203–207 (2009).
The authors would like to thank L. Walldén, T. Löfwander, F. Lombardi, J. Gallop and T. Claeson for stimulating discussions and S. Giblin and J. Williams for help with experiments. We are grateful to the NPL Strategic research programme, Swedish Research Council and Foundation for Strategic Research, European Union FP7 SINGLE, UK Engineering and Physical Sciences Research Council grant no. EP/G041954 and the Science & Innovation Award EP/G014787 for financial support.
The authors declare no competing financial interests.
About this article
Cite this article
Tzalenchuk, A., Lara-Avila, S., Kalaboukhov, A. et al. Towards a quantum resistance standard based on epitaxial graphene. Nature Nanotech 5, 186–189 (2010). https://doi.org/10.1038/nnano.2009.474
Clustering and Morphology Evolution of Gold on Nanostructured Surfaces of Silicon Carbide: Implications for Catalysis and Sensing
ACS Applied Nano Materials (2021)
Izmeritel`naya Tekhnika (2021)
Advanced Materials (2021)
Measurement Science and Technology (2021)
Physical Review B (2021)