Compendium for precise ac measurements of the quantum Hall resistance

Ahlers, F. J.; Jeanneret, B.; Overney, F.; Schurr, J.; Wood, B.M.

doi:10.1088/0026-1394/46/5/r01

Cited by 33 publications

(36 citation statements)

References 26 publications

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“…The understanding of the frequency dependence is beyond the scope of the paper. However, let us just remark that the linear frequency dependent term has a significant amplitude of −3.07 × 10 −7 /kHz in configuration C A that could result from losses in capacitances as was observed at higher frequency (a few kHz) 6 . The extrapolation of (∆R/R) f to f = 0 Hz measured in configurations C A and C B for each current results in ∆R/R CA (I) and ∆R/R CB (I) respectively, the weighted mean value ∆R/R CAB (I) of which can then be calculated.…”

Section: Frequency Dependence Of the Hall Resistance Discrepancymentioning

confidence: 89%

Quantum resistance standard accuracy close to the zero-dissipation state

Schopfer

Poirier

2013

Journal of Applied Physics

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We report on a comparison of four GaAs/AlGaAs-based quantum resistance standards using an original technique adapted from the well-known Wheatstone bridge. This work shows that the quantized Hall resistance at Landau level filling factor $\nu=2$ can be reproducible with a relative uncertainty of $32\times 10^{-12}$ in the dissipationless limit of the quantum Hall effect regime. In the presence of a very small dissipation characterized by a mean macroscopic longitudinal resistivity $\bar{R_{xx}(B)}$ of a few $\mu\Omega$, the discrepancy $\Delta R_{\mathrm{H}}(B)$ measured on the Hall plateau between quantum Hall resistors turns out to follow the so-called resistivity rule $\bar{R_{xx}(B)}=\alpha B\times d(\Delta R_{\mathrm{H}}(B))/dB$. While the dissipation increases with the measurement current value, the coefficient $\alpha$ stays constant in the range investigated ($40-120 \mathrm{\mu A}$). This result enlightens the impact of the dissipation emergence in the two-dimensional electron gas on the Hall resistance quantization, which is of major interest for the resistance metrology. The quantum Hall effect is used to realize a universal resistance standard only linked to the electron charge \emph{e} and the Planck's constant \emph{h} and it is known to play a central role in the upcoming revised \emph{Syst\`eme International} of units. There are therefore fundamental and practical benefits in testing the reproducibility property of the quantum Hall effect with better and better accuracy.Comment: 6 pages, 6 figure

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Section: Frequency Dependence Of the Hall Resistance Discrepancymentioning

confidence: 89%

Quantum resistance standard accuracy close to the zero-dissipation state

Schopfer

Poirier

2013

Journal of Applied Physics

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“…Thereby, the unit ohm can be currently maintained in national metrology institutes (NMIs) with a relative uncertainty of 1 × 10 −9 . The application of the QHE in metrology was more recently enlarged by its implementation in the alternating current (AC) regime 9 and by the development of quantized Hall array resistance standards (QHARS) 5,10 . These successes rely on a technique of multiple connection which cancels the effect of any impedance connected in series to the Hall bar terminals 11 .…”

Section: Introductionmentioning

confidence: 99%

“…The PJAVS maintains the voltage V J between the nodes A and B. The QHR of resistance R H is connected at these nodes using a triple series connection (a similar connection scheme is used in AC regime 9,26 ) with the peculiarity that a CCC winding of number of turns N JK is inserted in each of the three wires connecting the node B to the terminals of the Hall bar. A CCC auxiliary winding of N turns is connected to different external circuits.…”

Section: Introductionmentioning

confidence: 99%

A programmable quantum current standard from the Josephson and the quantum Hall effects

Poirier

Lafont

Djordjevic

et al. 2014

Journal of Applied Physics

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We propose a way to realize a programmable quantum current standard (PQCS) from the Josephson voltage standard and the quantum Hall resistance standard (QHR) exploiting the multiple connection technique provided by the quantum Hall effect (QHE) and the exactness of the cryogenic current comparator. The PQCS could lead to breakthroughs in electrical metrology like the realization of a programmable quantum current source, a quantum ampere-meter and a simplified closure of the quantum metrological triangle. Moreover, very accurate universality tests of the QHE could be performed by comparing PQCS based on different QHRs.

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“…The investigation of the Quantum Hall Effect (QHE) requires the use of coaxial ac bridges to compare the Quantum Hall Resistance (QHR) to calculable resistance standards at audio frequencies [1], [2], [3]. Such dedicated bridges are optimized to give the highest accuracy in impedance comparison [4].…”

Section: Introductionmentioning

confidence: 99%

Digitally assisted coaxial bridge for automatic quantum Hall effect measurements at audio frequencies

Overney

Lüönd

Jeanneret

2014

29th Conference on Precision Electromagnetic Measurements (CPEM 2014)

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This paper describes the principle of a new fully automatic digitally assisted coaxial bridge having a large bandwidth ranging from 100 Hz to 20 kHz. The bridge is characterized by making a 1:1 comparison between calculable ac resistors. The agreement between the calculated and the measured frequency dependence of the resistors is better than 10 −7 over its entire bandwidth. Such a bridge is a perfect tool to start investigating the ac transport properties of graphene in the quantum Hall regime.

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Compendium for precise ac measurements of the quantum Hall resistance

Cited by 33 publications

References 26 publications

Quantum resistance standard accuracy close to the zero-dissipation state

Quantum resistance standard accuracy close to the zero-dissipation state

A programmable quantum current standard from the Josephson and the quantum Hall effects

Digitally assisted coaxial bridge for automatic quantum Hall effect measurements at audio frequencies

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