Quantum resistance metrology in Graphene

The Hall resistance in two-dimensional electron systems (2DESs) is quantized in terms of natural constants only, RH = h/ie2 with i an integer number. Due to its high accuracy and reproducibility this quantized Hall resistance in conventional 2DESs is nowadays used as a universal resistance standard.
Graphene, the purely two-dimensional form of carbon, is a system fundamentally different from conventional 2DESs displaying a novel type of half-integer quantum Hall effect which remains visible up to room-temperature. This makes graphene a promising candidate for a high-temperature quantum resistance standard and may give further evidence that the quantum Hall resistance is indeed given by the relation h/ie2.
In close collaboration with the NMi van Swinden Laboratory and the University of Manchester, we have performed the first metrological characterization of the quantum Hall resistance in an only 1 μm wide graphene Hall-bar. The quantization of the Hall plateaus is within (-5 ± 15) ppm equal to that in conventional semiconductors, RH = (12,906.34 ± 0.20) Ω.
The principal limitation of the present experiments is the relatively high contact resistances in the quantum Hall regime, inducing measurement noise and local heating. Extrapolating our results to samples with lower resistance contacts for both electrons and holes and using wider samples with high breakdown currents, would most probably allow precision measurements of the quantum Hall effect in graphene with accuracies in the ppb range.

Figure: (left) Hall resistivity (red) and longitudinal resistivity (blue) in graphene at 14 Tesla and 0.4 Kelvin showing the exact quantization of the ν = ±2 Hall-plateaus and the accompaniing zero minimas in the longitudinal resistivity. The inset show a false color scanning electron image of the graphene Hall-barr sample. (right) Presision measurements in the middel of the ν = 2 plateaus for different contacts and their average, displaying the Hall-resistivity equal to conventional semiconductors within (-5 ± 15) ppm leading to RH = (12,906.34 ± 0.20)Ω.

This work was published in:

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, 222109 (2008).

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