Accurate AC Measurements of the Quantized Hall Resistance from 1 Hz to 1,6 kHz

Delahaye, F.

doi:10.1088/0026-1394/31/5/004

Cited by 90 publications

(61 citation statements)

References 9 publications

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“…Here, the graphene device was connected according to the triple-series connection scheme [22,23] (Fig. 1b), in which the respective equipotential terminals (contacts 1, 7, 8 and contacts 3, 4, 5) are connected outside of the cryostat to the nodes A and B, respectively.…”

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confidence: 99%

Towards a graphene-based quantum impedance standard

Kalmbach

Schurr

Ahlers

et al. 2014

Applied Physics Letters

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Precision measurements of the quantum Hall resistance with alternating current (ac) in the kHz range were performed on epitaxial graphene in order to assess its suitability as a quantum standard of impedance. The quantum Hall plateaus measured with alternating current were found to be flat within one part in 10 7 . This is much better than for plain GaAs quantum Hall devices and shows that the magnetic-fluxdependent capacitive ac losses of the graphene device are less critical. The observed frequency dependence of about -8×10 -8 /kHz is comparable in absolute value to the positive frequency dependence of plain GaAs devices, but the negative sign is attributed to stray capacitances which we believe can be minimized by a careful design of the graphene device. Further improvements thus may lead to a simpler and more user-friendly quantum standard for both resistance and impedance.Graphene is probably the most fascinating electronic material discovered in the last decades [1][2][3]. Among its various unique properties, an anomalous 'half-integer' quantum Hall effect (QHE) is most interesting for metrology, where the fact that the Hall resistance is quantized and depends only on fundamental constants is utilized for the representation and maintenance of the resistance unit, the ohm. Typically, twodimensional electron systems (2DES) realized in GaAs/AlGaAs heterostructures [4] are used for this purpose. The required relative measurement uncertainty of better than 1 part in 10 8 is, however, only obtained at strong magnetic fields around 10 tesla and at temperatures of 1.4 kelvin and below. In contrast, in graphene the cyclotron energy splitting between the Landau levels (which is the main factor determining the robustness of the quantized Hall resistance (QHR)) is so large that fingerprints of the QHE are even observed at room temperature [5]. Thus, with graphene a highly precise QHR standard working at low magnetic fields and temperatures above 4 kelvin is conceivable, which would be an enormous advantage for practical metrology. In fact, when measuring with direct current (dc), it has been demonstrated already that the precision of the QHE in high quality graphene devices matches that of GaAs devices [6][7][8][9]. However, in the forthcoming fundamental constant-based redefinition of the Système International d'Unités (SI) [10], also the impedance units (capacitance and inductance) will be traced to fundamental constants [11]. The most direct way to represent the impedance units is to use a quantum Hall resistance measured with alternating current (ac QHR). This has two advantages. Firstly, deriving the resistance and impedance units from the same quantum effect improves the consistency of the SI. And secondly, using the same QHE device at dc and at ac in one and the same cryomagnetic system would constitute a practical and economical advantage. Therefore, the question naturally arises whether graphene can replace GaAs also in the realm of impedance units, leading to an at least equally precise, but more userfriendl...

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confidence: 99%

Towards a graphene-based quantum impedance standard

Kalmbach

Schurr

Ahlers

et al. 2014

Applied Physics Letters

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“…8 for the low frequency range ( f Ӷ f p ), where Z 13 can be approximated to first order in , 8 for the low frequency range ( f Ӷ f p ), where Z 13 can be approximated to first order in ,…”

Section: B Model Of the Loaded Qhe Devicementioning

confidence: 99%

Electronic simulation of a multiterminal quantum Hall effect device

Sosso

Capra

1999

Review of Scientific Instruments

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A circuit with only resistors and unity gain amplifiers can be proven to be equivalent to the Ricketts and Kemeny electrical model of multiterminal quantum Hall effect (QHE) devices. By means of the new equivalent circuit, commercial software for electronic circuit analysis can be used to study a QHE measurement system. Moreover, it can be easily implemented, and we were able to build a circuit that simulates the electrical behavior of a QHE device. Particular care was taken in the design to reduce the effect of parasitic capacitances, which act as loads connected to the device terminals. Bootstrap buffers have been adopted to significantly reduce the capacitance of input stage. The small residual loading effect can be calculated and eliminated, allowing simulation of a QHE device with good accuracy. (C) 1999 American Institute of Physics. [S0034-6748(99)03004-X]

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“…The quantum Hall effect (QHE) is widely used by national laboratories thanks to its great stability in dc [1,2]. The accuracy of measurements has allowed establishment of the international standard for the electrical resistance unit (Ohm).…”

Section: Introductionmentioning

confidence: 99%

AC-magnetotransport of a 2DEG in the quantum Hall regime

Herńandez¹,

Chaubet²

2014

AIP Conference Proceedings

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Magnetotransport in two-dimensional n -In Ga As ∕ Ga As double-quantum-well structures near the transition from the insulator to the quantum Hall effect regime Low Temp.Abstract. In this paper we present an ac-magneto-transport study of a two-dimensional electron gas (2DEG) in the quantum Hall effect (QHE) regime, for frequencies in the range [100Hz, 1MHz]. We present a new approach to understand admittance measurements based in the Landauer-Buttiker formalism for QHE edge channels and taking into account the capacitance and the topology of the cables connected to the contacts used in the measurements. Our model predicts an universal behavior with the a-dimensional parameter RC where R is the 2 wires resistance of the 2DEG, C the capacitance cables and the angular frequency, in agreement with experiments.

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Accurate AC Measurements of the Quantized Hall Resistance from 1 Hz to 1,6 kHz

Cited by 90 publications

References 9 publications

Towards a graphene-based quantum impedance standard

Towards a graphene-based quantum impedance standard

Electronic simulation of a multiterminal quantum Hall effect device

AC-magnetotransport of a 2DEG in the quantum Hall regime

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