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     

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.     

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     

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.     

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     

Electronic properties and the quantum Hall effect in bilayer graphene

In this paper, I review the quantum Hall effect (QHE) and far-infra red (FIR) absorption properties of bilayer graphene in a strong magnetic field. This includes a derivation of the effective low-energy Hamiltonian for this system and the consequences of this Hamiltonian for the sequencing of the Landau levels in the material: the form of this effective Hamiltonian gives rise to the presence of a level with doubled degeneracy at zero energy. The effect of a potential difference between the layer of a bilayer is also investigated. It is found that there is a density-dependent gap near the K points in the band structure. The consequences of this gap on the QHE are then described. Also, the magneto-absorption spectrum is investigated and an experiment proposed to distinguish between model groundstates of the bilayer QHE system based on the different absorption characteristics of right- and left-handed polarization of FIR light. Finally, the effects of trigonal warping are taken into account in the absorption picture.     

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.     

Metrology and microscopic picture of the integer quantum Hall effect

Since 1990, the integer quantum Hall effect has provided the electrical resistance standard, and there has been a firm belief that the measured quantum Hall resistances are described only by fundamental physical constants--the elementary charge e and the Planck constant h. The metrological application seems not to rely on detailed knowledge of the microscopic picture of the quantum Hall effect; however, technical guidelines are recommended to confirm the quality of the sample to confirm the exactness of the measured resistance value. In this paper, we give our present understanding of the microscopic picture, derived from systematic scanning force microscopy investigations on GaAs/(AlGa)As quantum Hall samples, and relate these to the technical guidelines.     

Current Distributions in Quantum Hall Effect Devices

This paper addresses the question of how current is distributed within quantum Hall effect devices. Three types of flow patterns most often mentioned in the literature are considered. They are: (1) skipping orbits along the device periphery (which arise from elastic collisions off hard-walled potentials); (2) narrow conducting channels along the device sides (which are presumed to be generated from confining potentials); and (3) currents distributed throughout the device (which are assumed to arise from a combination of confining and charge-redistribution potentials). The major conclusions are that skipping orbits do not occur in quantum Hall effect devices, and that nearly all of the externally applied current is located within the device interior rather than along the device edges.     

Cryogenic Current Comparators for the Realisation of Electrical Quantum Standards

The cryogenic current comparator has played a central role in the realisation of electrical quantum standards over the last 40 years. It is the method of choice for National Measurement Laboratories in realising a quantum Hall effect primary standard of resistance. Single electron transport devices are expected to provide a primary standard of current within the next few years and this paper considers how they will be integrated into electrical metrology.     

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.     

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.     

当代计量科学发展的新趋势

回顾了计量科学在日常生活和科学研究方面的重要性,指出以实物计量基准建立的计量单位制存在的问题.分析了以基本物理常数(真空光速值c0,元电荷e,普朗克常数h,波尔兹曼常数kB和阿伏加德罗常数NA)和原子的物理特性(约瑟夫森效应和量子霍尔效应)进行计量基本单位量子化研究的重要性和紧迫性.介绍了长度、质量、电学量、温度和时间等计量基本单位量子化研究的新趋势.简单介绍了欧盟计量科学研究计划新动向.     

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.     

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.     

Hall conductivity of a moving magnetic-field-induced spin-density wave

The influence of the motion of a magnetic-field-induced spin-density-wave (FISDW) on the quantum Hall effect in a quasi-one-dimensional conductor is studied theoretically. In the ideal case, when the pinning and the damping of the FISDW can be neglected, it is found that the counterflow of the FISDW precisely cancels the quantum Hall current, so that the resultant Hall conductivity is zero. In real systems, the Hall conductivity should vanish at the high frequencies where the dynamics of the FISDW is dominated by inertia, and the pinning and the damping can be neglected.This work was partially supported by the NSF Grant No. DMR 89-06958.     

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.     

Loss phenomena in the AC quantum Hall effect

We investigated the ac quantum Hall effect of several GaAs-based samples. The influence of temperature, current, and frequency was measured for the plateaux i=2. Some measurements of the plateaux i=4 were performed to determine the scaling behavior with respect to i. The observed relations can be described by simple formulas which provide some insight into the ac quantum Hall effect     

Near room-temperature formation of a skyrmion crystal in thin-films of the helimagnet FeGe

The skyrmion, a vortex-like spin-swirling object, is anticipated to play a vital role in quantum magneto-transport processes such as the quantum Hall and topological Hall effects. The existence of the magnetic skyrmion crystal (SkX) state was recently verified experimentally for MnSi and Fe(0.5)Co(0.5)Si by means of small-angle neutron scattering and Lorentz transmission electron microscopy. However, to enable the application of such a SkX for spintronic function, materials problems such as a low crystallization temperature and low stability of SkX have to be overcome. Here we report the formation of SkX close to room temperature in thin-films of the helimagnet FeGe. In addition to the magnetic twin structure, we found a magnetic chirality inversion of the SkX across lattice twin boundaries. Furthermore, for thin crystal plates with thicknesses much smaller than the SkX lattice constant (as) the two-dimensional SkX is quite stable over a wide range of temperatures and magnetic fields, whereas for quasi-three-dimensional films with thicknesses over as the SkX is relatively unstable and observed only around the helical transition temperature. The room-temperature stable SkX state as promised by this study will pave a new path to designing quantum-effect devices based on the controllable skyrmion dynamics.