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.     

Derivation of an electronic equivalent of QHE devices

Models of quantum Hall effect (QHE) devices described by an equivalent circuit are used both to analyze measurement systems and to study QHE physics. Although the most widely used equivalent is the one proposed by Ricketts and Kemeny, various other circuits have been published to suit to different needs in QHE analysis, including a network with only resistors and unity-gain amplifiers. In the following we discuss a general approach to the analysis of the electrical behavior of QHE devices, and show that they can be classified as gyrators. Gyrators are nonreciprocal network elements whose properties are well known from the theory of electrical network. They can be regarded as generalized equivalents of Hall effect devices, thus setting a general framework for the study of the electrical behavior of QHE and the derivation of equivalent circuits. Through the application of this technique, an electronic circuit capable of simulating a QHE device with nonnull longitudinal resistance is derived     

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     

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.     

The Material Efforts for Quantized Hall Devices Based on Topological Insulators

A topological insulator (TI) is a kind of novel material hosting a topological band structure and plenty of exotic topological quantum effects. Achieving quantized electrical transport, including the quantum Hall effect (QHE) and the quantum anomalous Hall effect (QAHE), is an important aspect of realizing quantum devices based on TI materials. Intense efforts are made in this field, in which the most essential research is based on the optimization of realistic TI materials. Herein, the TI material development process is reviewed, focusing on the realization of quantized transport. Especially, for QHE, the strategies to increase the surface transport ratio and decrease the threshold magnetic field of QHE are examined. For QAHE, the evolution history of magnetic TIs is introduced, and the recently discovered magnetic TI candidates with intrinsic magnetizations are discussed in detail. Moreover, future research perspectives on these novel topological quantum effects are also evaluated.     

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.     

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     

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.     

A Problem in AC Quantized Hall Resistance Measurements and a Proposed Solution

In all experiments reported to date the measured values of the ac quantized Hall resistances R_H varied with the frequency of the applied current, and differed significantly from the dc values of R_H, making it difficult to use the ac quantum Hall effect as an absolute impedance standard. We analyze the effects due to the large capacitances-to-shields existing in the sample probes on measurements of R_H to see if this is the source of the problem. Equivalent electrical circuits are utilized; they contain capacitances and leakage resistances to the sample probe shields, longitudinal resistances within the quantized Hall effect devices, and multiple connections to the devices. The algebraic solutions for the R_H values in these circuits reveal large out-of-phase contributions to the quantized Hall voltages V_H that would make it difficult to do accurate measurements with high precision ac bridges. These large out-of-phase contributions could introduce the linear frequency dependences observed in previous R_H measurements. We predict, however, that quadruple-series connections to the quantum Hall devices yield only small out-of-phase contributions to V_H which may allow accurate measurements of the quantity R_H − R_x, where R_x is the longitudinal resistance along the device.     

Possible Mechanism of a New Type of Three-Dimensional Quantized Hall Effect in Layered Semiconductors Bi2−xSnxTe3

We have found a new type of three-dimensional quantized Hall effect (QHE) in layered semiconductors Bi₂–xSn_xTe₃ (x0.0125) single crystals. The Hall resistivity is not expressed in a universal relation applicable for a conventional QHE and depends appreciably on the doped Sn concentration x. The flat Hall plateaus are visible at higher Landau levels but are rather suppressed at lower regions. The calculated Landau levels of the upper valence band (UVB) with the best-fit band parameters are in excellent agreement with the experiments, including spin splitting. For Bi₂–xSn_xTe₃, the Sn-originated impurity band (IB) has resonant nature and enhances the density of states at the Fermi level of UVB. The charge transfer occurs between the quantized UVB and the resonant IB or the lower valence band (LVB) for Bi₂–xSn_xTe₃ or Bi₂Te₃, respectively, and the Landau levels are enhanced appreciably. We have revealed that the quasi-localized states are formed in quantized three-dimensional density of state spectra. We have proposed a possible model for the present QHE, which is a modification of Mani's model, where the quasi-localized state is formed at the disorder-originated tail of each Landau level. In the quasi-localized regime, the IB or LVB are responsible for the carrier reservoir to regulate the Hall resistivity.     

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.     

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.     

Practical and Fundamental Impact of Epitaxial Graphene on Quantum Metrology

The discovery 8 years ago of the quantum Hall effect (QHE) in graphene sparked an immediate interest in the metrological community. Here was a material which was completely different from commonly used semiconductor systems and which seemed to have some uniques properties which could make it ideally suited for high-precision resistance metrology. However, measuring the QHE in graphene turned out to be not so simple as first thought. In particular the small size of exfoliated graphene samples made precision measurements difficult. This dramatically changed with the development of large-area graphene grown on SiC and in this short review paper we discuss the journey from first observation to the highest-ever precision comparison of the QHE.     

Precision Tests of a Quantum Hall Effect Device DC Equivalent Circuit Using Double-Series and Triple-Series Connections

Precision tests verify the dc equivalent circuit used by Ricketts and Kemeny to describe a quantum Hall effect device in terms of electrical circuit elements. The tests employ the use of cryogenic current comparators and the double-series and triple-series connection techniques of Delahaye. Verification of the dc equivalent circuit in double-series and triple-series connections is a necessary step in developing the ac quantum Hall effect as an intrinsic standard of resistance.     

Degradation of GaAs/AlGaAs Quantized Hall Resistors With Alloyed AuGe/Ni Contacts

Careful testing over a period of 6 years of a number of GaAs/AlGaAs quantized Hall resistors (QHR) made with alloyed AuGe/Ni contacts, both with and without passivating silicon nitride coatings, has resulted in the identification of important mechanisms responsible for degradation in the performance of the devices as resistance standards. Covering the contacts with a film, such as a low-temperature silicon nitride, that is impervious to humidity and other contaminants in the atmosphere prevents the contacts from degrading. The devices coated with silicon nitride used in this study, however, showed the effects of a conducting path in parallel with the 2-dimensional electron gas (2-DEG) at temperatures above 1.1 K which interferes with their use as resistance standards. Several possible causes of this parallel conduction are evaluated. On the basis of this work, two methods are proposed for protecting QHR devices with alloyed AuGe/Ni contacts from degradation: the heterostructure can be left unpassivated, but the alloyed contacts can be completely covered with a very thick (> 3 μm) coating of gold; or the GaAs cap layer can be carefully etched away after alloying the contacts and prior to depositing a passivating silicon nitride coating over the entire sample. Of the two, the latter is more challenging to effect, but preferable because both the contacts and the heterostructure are protected from corrosion and oxidation.     

Atoms in precision electromagnetic measurements

Past, present, and future roles of atoms in precision electromagnetic measurements are discussed. In particular, atomic frequency standards, the current definition of the meter, the Josephson voltage, and the quantized Hall resistance are reviewed. Laser cooling and trapping of atoms are discussed with emphasis on a proposal of further cooling the atoms to a temperature of microkelvins and nanokelvins by utilizing the dipole force rather than the scattering force     

Quantized dissipation of the quantum Hall effect at high currents

Quantized dissipative voltage states are observed when large currents are passed through a high-quality quantized Hall resistance device. These dissipative states are interpreted as occurring when electrons are excited to higher Landau levels and then return to the original Landau level. The author shows that the quantization is more complicated than previously thought. For example, the quantization can be a function of magnetic field. Therefore, the dissipative voltage quantization can, in general, be difficult to verify and determine     

Comparison of the quantized Hall resistance and ohm NRC

A report is given of the progress towards the establishment of a quantized Hall resistance (QHR) measurement system suitable for maintaining the NRC (National Research Center of Canada) representation of the ohm. A system using a cryogenic current comparator bridge is described and compared to the previously reported 15 T, 20-mK potentiometric system. General problems concerning the use of the quantized Hall resistance to realize a representation of the ohm are discussed     

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.     

Giant Piezospintronic Effect in a Noncollinear Antiferromagnetic Metal

One of the main bottleneck issues for room-temperature antiferromagnetic spintronic devices is the small signal read-out owing to the limited anisotropic magnetoresistance in antiferromagnets. However, this could be overcome by either utilizing the Berry-curvature-induced anomalous Hall resistance in noncollinear antiferromagnets or establishing tunnel-junction devices based on effective manipulation of antiferromagnetic spins. In this work, the giant piezoelectric strain modulation of the spin structure and the anomalous Hall resistance in a noncollinear antiferromagnetic metal—D0₁₉ hexagonal Mn₃Ga—is demonstrated. Furthermore, tunnel-junction devices are built with a diameter of 200 nm to amplify the maximum tunneling resistance ratio to more than 10% at room-temperature, which thus implies significant potential of noncollinear antiferromagnets for large signal-output and high-density antiferromagnetic spintronic device applications.