Quantized Hall Resistance Research Articles

Cryogenic current comparator bridge for quantum Hall resistance ratio measurements

A cryogenic current comparator (CCC) bridge for quantum Hall resistance ratio measurement has been constructed. Compared to previous CCC systems at the National Physical Laboratory, UK, the new system differs in two aspects. Firstly, it uses a type-II CCC, i.e. the ratio windings are on the outside and the detection winding is on the inside. This has the advantage that the CCC can be made very compact and fits into a standard storage Dewar. Secondly, the bridge electronics uses a digital servo and the SQUID feedback loop is disabled during current reversals. The overall relative measurement uncertainty of the system is of the order of 10−9.

Comparison of resistance standards between the National Institute of Metrology (China) and the Electrotechnical Laboratory (Japan)

The resistance standard maintained at the Electrotechnical Laboratory (ETL, Japan) is based on the resistance of the second plateau of the quantized Hall resistance, RH(2). A resistance ratio bridge with a cryogenic current comparator (CCC) is used for the measurements. The typical relative standard uncertainty in measuring a 1 Ω resistor is estimated to be about 4 × 10-9. The resistance standard maintained at the National Institute of Metrology (NIM, China) is based on the average value of six wire-wound 1 Ω resistors. It was monitored using the ETL quantum Hall effect (QHE) resistance standard in 1992, 1996 and 2000 by bringing 1 Ω resistors from the NIM to the ETL or from the ETL to the NIM. The drift rate of the standard was measured to be -0.024 µΩ/year. The NIM has developed a CCC bridge. The typical relative standard uncertainty in measuring a 1 Ω resistor using this CCC bridge and the QHE system of the NIM is estimated to be about 7 × 10-9. The NIM QHE system was compared with the ETL QHE resistance standard by bringing three 1 Ω resistors from the ETL to the NIM. Differences in the measurements were (+3.9 ± 8.9) nΩ, (+1.0 ± 9.9) nΩ and (-0.9 ± 9.1) nΩ, respectively.

AC behaviour and loss phenomena in quantum Hall samples

The ac quantum Hall resistance of several GaAs-based samples has been investigated. The influence of temperature, current and frequency was measured for the plateau i = 2. Some measurements were performed for the plateau i = 4 in order to determine the scaling behaviour with respect to i. The plateau edge is shown to depend on the electronic temperature and the current at the plateau edge is distributed over the whole width of the sample. At the plateau centre, edge-current effects become apparent which depend on how close the filling factor is to an integer value. The losses of these edge currents cause the ac quantum Hall resistance to differ from the dc quantum Hall resistance.

Adjusting the losses in an ac quantum Hall sample

The ac quantum Hall resistance measured with frequencies in the range of a few kilohertz shows characteristic deviations from the dc quantum Hall resistance. These deviations indicate ac losses which increase linearly with frequency. To investigate these losses, a Hall bar with an inner and an outer "window" has been tested. When external voltages are supplied to the windows, the ac losses can be adjusted to zero. This is explained by a phenomenological model for the current distribution in the Hall bar and leads to a model for the ac losses.

Realizing the ITS-90 below 4.2 K at the National Research Council of Canada

The International Temperature Scale of 1990 (ITS-90) has only recently been realized below 4.2 K at the National Research Council of Canada (NRC). As the NRC Thermometry Group lacked a cryostat capable of reaching 0.65 K, the helium vapour-pressure thermometer was designed to fit the demanding geometry of a top-loading 3He cryostat insert routinely used by the Electrical Standards Group to realize the resistance unit by means of the quantized Hall resistance. The vapour-pressure apparatus has been operated successfully from 0.7 K to 4 K in the 3He cryostat and from 2.3 K to 4.2 K in a 4He cryostat. The resistance-temperature data pairs obtained for the RhFe thermometers over the 0.7 K to 4.2 K range, using the temperature derived from vapour-pressure measurements for both 3He and 4He, were fitted to sixth-degree polynomials. The residuals from the fits were within ±0.3 mK for both thermometers.

Improved Quantum Hall Standard of Resistance at Electrotechnical Laboratory

We improved the quantum Hall standard of resistance at the Electrotechnical Laboratory to measure 1 Ω, 100 Ω and 10 kΩ resistors. It is composed of an 11 T superconducting magnet system with a 3He insert, a resistance ratio bridge using a cryogenic current comparator (CCC bridge) and a 100 Ω transfer resistor. The 100 Ω transfer resistor is directly compared to the second or fourth plateau of the quantized Hall resistance using the CCC bridge, whose combined uncertainty is estimated to be about 4 ×10-9. The 1 Ω, 100 Ω and 10 kΩ resistors are compared to the 100 Ω transfer resistor using the same CCC bridge with different settings, whose combined uncertainty is estimated to be about 3 ×10-9 or less. Total uncertainty of measuring the resistor is given as the root sum squares of these combined uncertainties and estimated to be about 5 ×10-9, because these two comparisons are independent of each other. This is the first report of the procedure for resistance measurement and its uncertainty.

Shifting the quantum Hall plateau level in a double layer electron system

We study the plateaux of the integer quantum Hall resistance in a bilayer electron system in tilted magnetic fields. In a narrow range of tilt angles and at certain magnetic fields, the plateau level deviates appreciably from the quantized value with no dissipative transport emerging. A qualitative account of the effect is given in terms of decoupling of the edge states corresponding to different electron layers/Landau levels.

200 kΩ ac resistance transfer standard

A resistance standard, comprising three 200 k resistors mounted in a temperature-controlled enclosure, has been constructed from commercial high-precision metal-foil resistors. The standard is intended for transfer of resistance value between a multifrequency resistance-capacitance (R-C) bridge and an ac quantum Hall resistance (QHR) bridge. The three resistors were fully characterized for their voltage dependence.

A bridge for the comparison of resistance with capacitance at frequencies from 200 Hz to 2 kHz

A bridge for the comparison of resistance with capacitance has been designed and constructed. It is a six-arm generalization of the quad bridge and, while retaining the accuracy of a passive-component bridge, makes extensive use of high-precision amplifiers in both source and detector circuits. It will provide a link between the calculable capacitor and the ac quantum Hall resistance (QHR).

Measurement of frequency dependence of standard capacitors based on the QHR in the range between 1 kHz and 1.592 kHz

A quantized Hall resistance (QHR)-based capacitance measurement chain has been developed. The chain comprises an AC resistance bridge together with an AC-DC calculable resistor, a multifrequency quadrature bridge, and a capacitance bridge. The use of the multifrequency quadrature bridge enables the measurement of the frequency dependence of capacitors in the range between 1-1.592 kHz. The results demonstrate that the frequency dependence of 10-pF standard capacitors can be measured based on the QHR with a relative standard uncertainty of 3/spl times/10/sup -8/.

Optimization of QHE-devices for metrological applications

In the framework of an European project aiming at the realization of a system for the calibration of capacitance standards based on the quantum Hall effect (QHE), optimized QHE devices for the metrological application as dc as well as ac standards of resistance are developed. The present paper describes the dc characterization of a large number of devices with different layouts, contact configurations, carrier concentrations, and mobilities. The results demonstrate the influence of the device parameters on the critical current, the width of the quantized plateaus, the longitudinal voltages along the device and the quantized Hall resistance. Recommendations are given for the layout and mobility of QHE devices in view of their use as dc standards of resistance.

Transport behavior of commercially available 100-Ω standard resistors

Several types of commercial 100-/spl Omega/ resistors can be used with the cryogenic current comparator to maintain the resistance unit, derived from the quantized Hall effect (QHE), and to disseminate this unit to laboratory resistance standards. Up until now, the transport behavior of these resistors has not been investigated. Such an investigation is of importance for carrying out comparisons that are close to the level of a direct comparison of two QHE apparatuses. A set of five 100-/spl Omega/ resistors from three different manufacturers has been sent to 11 participating national metrological institutes. All laboratories but one have measured the resistors based on their laboratory's quantized Hall resistance measurements. A constant drift model has been applied, and the results are evaluated in such a way that the transport properties of these resistors are treated independently for the different types of resistor. Under certain conditions, these resistors allow comparisons with uncertainties better than 1 part in 10/sup 8/.

Resistance bridge based on the cryogenic current comparator in a transport dewar

An optimized resistance bridge based on the Cryogenic Current Comparator (CCC) with SQUID readout has been developed. The bridge can be used for routine secondary resistance calibrations as well as for the traceability of 100 /spl Omega/ to the quantum Hall resistance. The CCC-SQUID, shielding and wiring are mounted in a telescopic insert, fitted in a low-evaporation rate, transportable liquid He dewar, with an autonomy of around 1 month. A difference compensator method is used to balance the bridge. A new, more reliable and self-standing bridge electronics has been fabricated and tested. An uncertainty in the comparison of resistors at least one order of magnitude better than room temperature CCs is expected.

Controlling ac losses in quantum Hall effect devices

When measured with ac at kilohertz frequencies the quantized Hall resistance (QHR) of a quantum Hall effect (QHE) device is usually found to be current- and frequency-dependent. This is a limitation on its use as a quantum impedance standard. We develop a model for the principal ac losses arising in the QHE device and show how they are responsible for the observed QHR current and frequency coefficients. We believe that losses are mainly caused by dissipative ac charging of the device along its edges. Charging is induced by the passage of the Hall current and by capacitive coupling between an edge and any nearby conductor maintained at an ac potential different to that of the edge, as for example at shield potential. The loss power is proportional to frequency and increases more rapidly than the square of the applied voltage or current. We model losses in terms of in-phase loss currents, which are a function of the amplitude of the ac charge reaching or leaving edges. The QHR frequency coefficient is zero only when the loss current for one portion of the high-potential edge and that for a corresponding portion of the low-potential edge are equal and of opposite sign. We propose a simple method for approaching that balance condition: gates are located under the device edges and their ac potentials adjusted so that the QHR current coefficient, evaluated at a constant frequency, is zero. We report measurements of the residual QHR frequency coefficients obtained after adjustment for GaAs/GaAlAs devices of two different types. For five different devices of the most favourable type, the QHR frequency coefficients do not exceed ±2 parts in 108 per kilohertz.

Why nanovoltmeter offset currents do not explain measured deviations in the quantized Hall resistance

T.P. Chen and H.A. Chua [ibid. vol. 47, pp. 592-594, 1998] have suggested that deviations in the value of resistance in QHR devices with resistive contacts may be attributable to the offset (or bias) current of the nanovoltmeter used to measure the QHR devices. We present two reasons why their explanation is unreasonable.

International comparison of 10 pF and 100 pF capacitance standards: EUROMET Project No. 345

An international comparison of 10 pF and 100 pF capacitance standards has taken place within the framework of EUROMET. The comparison, which was piloted by the National Physical Laboratory (NPL, UK), involved seventeen laboratories, including several which are members of other regional organizations. The agreement demonstrated by the comparison provides confidence in maintaining traceability for the farad, via either a calculable capacitor or a quantum Hall resistance (QHR) standard and the internationally agreed value of RK-90. However, the results appear to show that there are slight but significant differences between the representation of the farad for some laboratories. A full report of the comparison has been published by the NPL.

Bilateral comparison of 1 Ω, 10 kΩ and 100 MΩ resistance standards between the PTB and the UME

In order to evaluate the agreement between the Physikalisch-Technische Bundesanstalt (PTB, Germany) and the Ulusal Metroloji Enstitüsü (TÜBTAK-UME, Turkey) and to establish a firm basis for traceability, a bilateral comparison has been carried out using 1 Ω, 10 kΩ and 100 MΩ resistors. Measurements obtained by the PTB, based on their quantum Hall resistance standard (QHRS), differ from the UME results by 46 nΩ/Ω (standard uncertainty u = 0.19 µΩ/Ω) at the 1 Ω level, and by 3.0 nΩ/Ω (u = 0.25 µΩ/Ω) at the 10 kΩ level. The 100 MΩ resistors were compared using both a UME-constructed Wheatstone bridge and a commercial bridge. Measurement results obtained with the Wheatstone bridge show better agreement with those of the PTB, within 0.34 µΩ/Ω (u = 8.7 µΩ/Ω), than the results obtained with the commercial bridge, within 3.6 µΩ/Ω (u = 5.1 µΩ/Ω).

Calculable coaxial resistors for precision measurements

Coaxial straight-wire resistors have been constructed with the purpose of improving comparisons between resistors, capacitors, and inductors in the audio-frequency range. The design is based on the principle that a coaxial line with a cylindrical shield can be described by relatively simple equations for the real and imaginary parts of the impedance. The resistors, with values at and above 100 /spl Omega/ will be used as transfer standards for characterization of the frequency dependence of standard resistors and of the quantum Hall resistance in the audio frequency range.

Collapse of quantized Hall resistance and breakdown of dissipationless state in the integer quantum Hall effect: filling factor dependence

Magnetic field dependence of critical current for collapse of quantized Hall resistance I cr(collapse) and critical current for breakdown of dissipationless state I cr(breakdown) have been measured near the filling factor ν=4 of Landau levels in a GaAs/AlGaAs heterostructure Hall bar. The difference I cr(breakdown)− I cr(collapse) decreases against the increase and the decrease in ν from 4 and the critical behavior disappears outside of the region 3.85< ν<4.15.

The quantized Hall insulator

The quantized Hall insulator is characterized by vanishing conductivities and a quantized Hall resistance. For low mobility samples, the quantized Hall insulator is obtained when the magnetic field is increased well above the ν = 1 quantum Hall state. For higher mobility samples, a similar quantization is observed when the magnetic field is increased above the ν = 1/3 fractional quantum Hall states. This quantization, throughout the quantum Hall liquid-to-insulator transition, leads to a perfect semicircle relation for the diagonal and Hall conductivities. The measurements were performed in Ge/SiGe quantum Wells and in n-type InP/InGaAs and GaAs/AlGaAs heterostuctures.