Recent determinations of R/sub H/ in terms of Omega /sub 69-BI/

A system based on a cryogenic current comparator is used to measure the quantized Hall resistance R/sub H/ in terms of Omega /sub 69-BI/, the Bureau International des Poids et Mesures (BIPM) representation of the ohm, with an uncertainty of 1.5*10/sup -8/. This measurement system and the former potentiometric one are in good agreement within their combined uncertainties (5.1*10/sup -8/).<>     

New realization of the ohm and farad using the NBS calculablecapacitor

Results of a realization of the ohm and farad using the US National Bureau of Standards (NBS) calculable capacitor and associated apparatus are reported. The results show that both the NBS representation of the ohm and the NBS representation of the farad are changing with time, Ω_NBS at the rate of -0.054 p.p.m./year and F_NBS at the rate of 0.010 p.p.m./year. The realization of the ohm is of particular significance because of its role in assigning an SI value to the quantized Hall resistance. The estimated uncertainty of the ohm realization is 0.022 p.p.m. (1σ), while the estimated uncertainty of the farad realization is 0.014 p.p.m. (1σ)     

A reevaluation of the NML absolute ohm and quantized Hallresistance determinations

Several electrical and geometrical aspects of the National Measurement Laboratory (NML) calculable capacitor are reexamined for effects of wear and other possible causes of error. A new set of quantized Hall resistance measurements is made and related to the NML realization of the SI ohm based on the calculable capacitor. The results of these measurements may be expressed as R_H=25812.8 (1.000,000,363 (66)) Ω     

Determination of the time-dependence of ΩNBS usingthe quantized Hall resistance

The quantum Hall effect is being used to monitor the US legal representation of the ohm, or as-maintained ohm, Ω_NBS. Measurements have been made on a regular basis since August 1983. Individual transfers between the quantized Hall resistance R _H and the five 1-Ω resistors which comprise Ω_NBS can be made with a total of one standard deviation (1σ) uncertainty of ±0.014 p.p.m. This uncertainty is the root-sum-square of 32 individual components. The time-dependent expression for R_H in terms of Ω_NBS is: R_H=25812.8[1+(1.842±0.012)×10^-6 =(0.0529±0.0040)(t-0.7785)×10^-6 /year] Ω_NBS, where t is measured in years from January 1, 1987. The value of Ω_NBS is, therefore, decreasing at the rate of (0.0529±0.0040) p.p.m./year     

Calculating the Effects of Longitudinal Resistance in Multi-Series-Connected Quantum Hall Effect Devices

Many ac quantized Hall resistance experiments have measured significant values of ac longitudinal resistances under temperature and magnetic field conditions in which the dc longitudinal resistance values were negligible. We investigate the effect of non-vanishing ac longitudinal resistances on measurements of the quantized Hall resistances by analyzing equivalent circuits of quantized Hall effect resistors. These circuits are based on ones reported previously for dc quantized Hall resistors, but use additional resistors to represent longitudinal resistances. For simplification, no capacitances or inductances are included in the circuits. The analysis is performed for many combinations of multi-series connections to quantum Hall effect devices. The exact algebraic solutions for the quantized Hall resistances under these conditions of finite ac longitudinal resistances provide corrections to the measured quantized Hall resistances, but these corrections do not account for the frequency dependences of the ac quantized Hall resistances reported in the literature.     

Evidence for the π-d Interaction Comparing Magnetoresistance in (EDT-DSDTFVO)2 X, X=FeCl4, GaCl4

Hall resistance and magnetic torque measurements have been carried out in the field-induced spin-density-wave (FISDW) phase of deuterated (TMTSF)₂ClO₄ for various cooling rates through the anion ordering temperature. We have found that the Hall resistance in the intermediate cooled state shows a phase transition from the non-quantized Hall phase to the quantized Hall phase (n=1) with hysteresis. We have also found that the magnetic torque in the non-quantized Hall phase rapidly decreases with increasing cooling rate. These results suggest that there is a new phase transition from the non-quantized Hall phase to the quantized Hall phase in (TMTSF)₂ClO₄.     

New international representations of the volt and ohm effectiveJanuary 1, 1990

Starting January 1, 1990, new representations of the volt and ohm based on the Josephson and quantum Hall effects, respectively, are to come into effect worldwide. Their implementation in the US will result in increases in the values of the national representation of the volt and ohm maintained at the National Institute of Standards and Technology (NIST) of 9.264 parts per million (p.p.m.) and 1.69 p.p.m., respectively. The resulting increases in the values of the US representation of the ampere and US electrical representation of the watt will be 7.57 p.p.m. and 16.84 p.p.m., respectively. The reporting of calibration results in terms of the new representations is discussed     

Intrinsic Capacitances and Inductances of Quantum Hall Effect Devices

Analytic solutions are obtained for the internal capacitances, kinetic inductances, and magnetic inductances of quantum Hall effect devices to investigate whether or not the quantized Hall resistance is the only intrinsic impedance of importance in measurements of the ac quantum Hall effect. The internal capacitances and inductances are obtained by using the results of Cage and Lavine, who determined the current and potential distributions across the widths of quantum Hall effect devices. These intrinsic capacitances and inductances produce small out-of-phase impedance corrections to the in-phase quantized Hall resistance and to the in-phase longitudinal resistance.     

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 standardresistors

Several types of commercial 100-Ω 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-Ω 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 ⁸     

Quantized Hall resistance measurements

The quantized Hall resistances, R_H(4), of Si MOSFETs were measured at ≈0.5 K in a magnetic field of 15 T. The value of R_H(4) was determined in terms of the Commonwealth Scientific and Industrial Research Organization (CSIRO) realization of the SI ohm. A weighted mean of three determinations gave a value for the quantity R_H(4) of (6453.203,36(52)) Ω_SI-NML which can also be expressed as 6453.2(1.000,000,52(8)) Ω_SI-NML. This R_H (4) value gives a value for h/e² which is about 0.3 p.p.m. larger than the value for h/e² derived from the anomalous moment of the electron, using the quantum electrodynamics (QED) theory     

An AC-bridge for low-frequency measurements of the quantized Hallresistance

A simple circuit which makes possible the use of a resistance-ratio bridge based on a cryogenic current comparator (CCC) with both AC and DC is described. The different sources of uncertainty associated with the use of AC in a CCC bridge are discussed. It is shown that they should have an effect which does not exceed a few parts in 10 ⁹ of the resistance-ratio being measured, if the frequency is limited to a few hertz. This analysis is confirmed by experimental results of resistance-ratio measurements between the quantized Hall resistance (QHR) and a 100 Ω resistance standard carried out at DC, 1, 2, and 4 Hz. These measurements are, to the author's knowledge, the first accurate DC measurements of the QHR. They demonstrate that the quantization of the Hall resistance, observed with AC and for the frequency range studied here, remains complete to within a few parts in 10⁹ or better     

Developments in the quantum Hall effect

The most important applications of the quantum Hall effect (QHE) are in the field of metrology. The observed quantization of the resistance is primarily used for the reproduction of the SI unit ohm, but is also important for high precision measurements of both the fine structure constant and the Planck constant. Some current QHE research areas include the analysis of new electron-electron correlation phenomena and the development of a more complete microscopic picture of this quantum effect. Recently, scanning force microscopy (SFM) of the potential distribution in QHE devices has been used to enhance the microscopic understanding of current flow in quantum Hall systems. This confirms the importance of the theoretically predicted stripes of compressible and incompressible electronic states close to the boundary of the QHE devices.     

Analyzing the Effects of Capacitances-to-Shield in Sample Probes on AC Quantized Hall Resistance Measurements

We analyze the effects of the large capacitances-to-shields existing in all sample probes on measurements of the ac quantized Hall resistance R_H. The object of this analysis is to investigate how these capacitances affect the observed frequency dependence of R_H. Our goal is to see if there is some way to eliminate or minimize this significant frequency dependence, and thereby realize an intrinsic ac quantized Hall resistance standard. Equivalent electrical circuits are used in this analysis, with circuit components consisting of: capacitances and leakage resistances to the sample probe shields; inductances and resistances of the sample probe leads; quantized Hall resistances, longitudinal resistances, and voltage generators within the quantum Hall effect device; and multiple connections to the device. We derive exact algebraic equations for the measured R_H values expressed in terms of the circuit components. Only two circuits (with single-series “offset” and quadruple-series connections) appear to meet our desired goals of measuring both R_H and the longitudinal resistance R_x in the same cool-down for both ac and dc currents with a one-standard-deviation uncertainty of 10⁻⁸ R_H or less. These two circuits will be further considered in a future paper in which the effects of wire-to-wire capacitances are also included in the analysis.     

AC measurements of the minimum longitudinal resistance of a QHEsample from 10 Hz to 10 kHz

AC measurements of the longitudinal resistance, R_xx, of a quantum Hall effect (QHE) sample have been made in a frequency range from 10 Hz to 10 kHz. The results show no frequency effect on the minimum value of R_xx corresponding to the quantum numbers i=2 and i=4, within the measurement resolution of 0.5 mΩ. Therefore, the influence of frequency on the value of the quantized Hall resistance, R_H, should not exceed a few parts in 10⁹ . Some unwanted effects detected during the development of the resistance bridge have been pointed out     

Dependence of Quantized Hall Effect Breakdown Voltage on Magnetic Field and Current

When large currents are passed through a high-quality quantized Hall resistance device the voltage drop along the device is observed to assume discrete, quantized states if the voltage is plotted versus the magnetic field. These quantized dissipative voltage states are interpreted as occurring when electrons are excited to higher Landau levels and then return to the original Landau level. The quantization is found to be, in general, both a function of magnetic field and current. Consequently, it can be more difficult to verify and determine dissipative voltage quantization than previously suspected.     

Improvement of the superconducting magnetic levitation system forthe determination of the magnetic flux quantum

An improvement of the preliminary superconducting magnetic levitation system for the absolute determination of the magnetic flux quantum is described. This improvement includes the development of the flux-up method to determine the flux in terms of the Josephson voltage. The improvement is essential for the determination of the magnetic flux quantum as well as of the coil current, in terms of the Josephson voltage and quantized Hall resistance     

Equivalent Electrical Circuit Representations of AC Quantized Hall Resistance Standards

We use equivalent electrical circuits to analyze the effects of large parasitic impedances existing in all sample probes on four-terminal-pair measurements of the ac quantized Hall resistance R_H. The circuit components include the externally measurable parasitic capacitances, inductances, lead resistances, and leakage resistances of ac quantized Hall resistance standards, as well as components that represent the electrical characteristics of the quantum Hall effect device (QHE). Two kinds of electrical circuit connections to the QHE are described and considered: single-series “offset” and quadruple-series. (We eliminated other connections in earlier analyses because they did not provide the desired accuracy with all sample probe leads attached at the device.) Exact, but complicated, algebraic equations are derived for the currents and measured quantized Hall voltages for these two circuits. Only the quadruple-series connection circuit meets our desired goal of measuring R_H for both ac and dc currents with a one-standard-deviation uncertainty of 10⁻⁸ R_H or less during the same cool-down with all leads attached at the device. The single-series “offset” connection circuit meets our other desired goal of also measuring the longitudinal resistance R_x for both ac and dc currents during that same cool-down. We will use these predictions to apply small measurable corrections, and uncertainties of the corrections, to ac measurements of R_H in order to realize an intrinsic ac quantized Hall resistance standard of 10⁻⁸ R_H uncertainty or less.     

Comparison of Quantized Hall Resistance with a 1-? Standard

A major step in the precise determination of the quantized Hall resistance is the comparison of a resistor of value nominally 6453.2 ? with a 1-? standard. For this purpose the National Measurement Laboratory will use a build-up resistor comprising 83 resistors each of 80? ?, giving a ratio of 64534/9. An accuracy of better than 1 in 108 is expected.     

Special Report on Electrical Standards: New Internationally Adopted Reference Standards of Voltage and Resistance

This report provides the background for and summarizes the main results of the 18th meeting of the Consultative Committee on Electricity (CCE) of the International Committee of Weights and Measures (CIPM) held in September 1988. Also included are the most important implications of these results. The principal recommendations originating from the meeting, which were subsequently adopted by the CIPM, establish new international reference standards of voltage and resistance based on the Josephson effect and the quantum Hall effect, respectively. The new standards, which are to come into effect starting January 1, 1990, will result in improved uniformity of electrical measurements worldwide and their consistency with the International System of Units or SI. To implement the CIPM recommendations in the U.S. requires that, on January 1, 1990, the value of the U.S. representation of the volt be increased by about 9.26 parts per million (ppm) and the value of the U.S. representation of the ohm be increased by about 1.69 ppm. The resulting increases in the U.S. representations of the ampere and watt will be about 7.57 ppm and 16.84 ppm, respectively. The CCE also recommended a particular method, affirmed by the CIPM, of reporting calibration results obtained with the new reference standards that is to be used by all national standards laboratories.