Frequency Dependent Electrical Transport in the Integer Quantum Hall Effect

Schweitzer, L.

doi:10.1007/978-3-540-45202-7_6

Cited by 2 publications

(4 citation statements)

References 53 publications

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“…It is largest between the plateaux and strongly decreases towards the plateau centres. Theoretical calculations yield a power-law frequency dependence but different powers of 1 and about 2, and without an absolute scale, have been predicted [29,30]. A scale can be estimated from several high-frequency Hall conductivity measurements which have been carried out at frequencies of a few MHz up to 40 GHz, for example [31][32][33].…”

Section: Uncertainty Budget Of Residual Frequency Dependencementioning

confidence: 97%

The quantum Hall impedance standard

et al. 2011

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Alternating current measurements of double-shielded quantum Hall devices have revealed a fascinating property of which only a quantum effect is capable: it can detect its own frequency dependence and convert it to a current dependence which can be used to eliminate both of them. According to an experimentally verified model, the residual frequency dependence is smaller than the measuring uncertainty of 1.3 × 10−9 kHz−1. In this way, a highly precise quantum standard of impedance can be established, without having to correct for any calculated frequency dependence and without the need for any artefact with a calculated frequency dependence. Nothing else like that is known to us and we hope that our results encourage other national metrology institutes to also apply it to impedance metrology and further explore its beautiful properties.

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Section: Uncertainty Budget Of Residual Frequency Dependencementioning

confidence: 97%

The quantum Hall impedance standard

et al. 2011

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“…The localized electrons in the 2DEG are expected to interact with the alternating electrical Hall field and to dissipate energy; this would affect the QHR value and give rise to an intrinsic frequency dependence. Theoretical calculations yield a powerlaw frequency dependence but it is difficult to predict an absolute scale of the effect [95,88]. When the theoretical models are used to scale the experimental high-frequency data to the audio frequency range, an upper limit of the relative intrinsic frequency dependence in the central plateau region of only 2 × 10 −10 kHz −1 is estimated.…”

Section: Intrinsic Frequency Dependence Of the Qhrmentioning

confidence: 99%

“…For magnetic fields corresponding to the central plateau region, the current is believed to flow mainly along conducting edge regions while the rest of the 2DEG behaves like a dielectric (in the sense that electric fields are not shielded) 4 [98,2]. As a result, the capacitance of the 2DEG decreases considerably and exhibits a curved or somehow structured shape when measured in the central plateau region as a function of the magnetic field [20,88,91]. The loss factor of the capacitance between the 2DEG and a parallel gate was measured at the BIPM and PTB by means of a coaxial capacitance bridge as shown in figure 14 [20,85].…”

Section: Magnetocapacitance and Loss Factorsmentioning

confidence: 99%

“…Side-gates also can be made as a 2DEG window around the main 2DEG [74]. In any case, an additional split back-gate at shield potential is required to define and pin the potential distribution in the 2DEG [88]. Then, voltage-controlled side-gates are found to have the same effect as a voltage-controlled split back-gate (without sidegates).…”

Section: Gated Qhr Devicesmentioning

confidence: 99%

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The ac quantum Hall resistance as an electrical impedance standard and its role in the SI

Schurr

Ahlers

Kibble

2012

Meas. Sci. Technol.

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Since 1990, the quantum Hall resistance measured with direct current (dc) has been established to represent and maintain the dc resistance unit and thereby has replaced the former derivation from calculated inductance and capacitance standards. Because of this success, it has been suggested to measure this quantum effect with alternating current (ac) and in this way to derive the units of resistance, capacitance and inductance consistently from the same quantum effect. In this paper, we recall the relations between these units, their role in the determination of the von Klitzing constant and the relations between the fundamental constants involved in the conventional and the quantum approach. Then, we review the first ac measurements of the quantum Hall resistance and show how the difficulties uncovered have been solved by relatively simple means. As a result, the measurement of the ac quantum Hall resistance has become as precise and reliable as its dc counterpart and much more accurate than any conventional impedance artefact.

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Frequency Dependent Electrical Transport in the Integer Quantum Hall Effect

Cited by 2 publications

References 53 publications

The quantum Hall impedance standard

The quantum Hall impedance standard

The ac quantum Hall resistance as an electrical impedance standard and its role in the SI

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