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.     

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.     

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.     

石墨烯在量子霍尔电阻中的应用

基于砷化镓的量子霍尔电阻自然基准需要在约1.5K的温度条件下运行,存在成本高和操作复杂等诸多问题。随着石墨烯材料独特电性能的发现,因其可以在约4.2K的温度复现量子霍尔效应而成为制作量子霍尔电阻的理想材料。各国专家围绕石墨烯在电学计量领域的应用开展了大量的工作,取得了可喜的进展。对当前石墨烯在量子霍尔电阻中应用的进展和存在的问题进行了总结,并对未来的发展进行了展望。     

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.     

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.     

Observation of Quantum Anomalous Hall Effect and Exchange Interaction in Topological Insulator/Antiferromagnet Heterostructure

Integration of a quantum anomalous Hall insulator with a magnetically ordered material provides an additional degree of freedom through which the resulting exotic quantum states can be controlled. Here, an experimental observation is reported of the quantum anomalous Hall effect in a magnetically-doped topological insulator grown on the antiferromagnetic insulator Cr₂O₃. The exchange coupling between the two materials is investigated using field-cooling-dependent magnetometry and polarized neutron reflectometry. Both techniques reveal strong interfacial interaction between the antiferromagnetic order of the Cr₂O₃ and the magnetic topological insulator, manifested as an exchange bias when the sample is field-cooled under an out-of-plane magnetic field, and an exchange spring-like magnetic depth profile when the system is magnetized within the film plane. These results identify antiferromagnetic insulators as suitable candidates for the manipulation of magnetic and topological order in topological insulator films.     

Temperature Dependence of the Hall and Longitudinal Resistances in a Quantum Hall Resistance Standard

We present detailed measurements of the temperature dependence of the Hall and longitudinal resistances on a quantum Hall device [(GaAs(7)] which has been used as a resistance standard at NIST. We find a simple power law relationship between the change in Hall resistance and the longitudinal resistance as the temperature is varied between 1.4 K and 36 K. This power law holds over seven orders of magnitude change in the Hall resistance. We fit the temperature dependence above about 4 K to thermal activation, and extract the energy gap and the effective g-factor.     

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.     

Quantum‐Hall to Insulator Transition in Ultra‐Low‐Carrier‐Density Topological Insulator Films and a Hidden Phase of the Zeroth Landau Level

A key feature of the topological surface state under a magnetic field is the presence of the zeroth Landau level at the zero energy. Nonetheless, it is challenging to probe the zeroth Landau level due to large electron–hole puddles smearing its energy landscape. Here, by developing ultra‐low‐carrier density topological insulator Sb₂Te₃ films, an extreme quantum limit of the topological surface state is reached and a hidden phase at the zeroth Landau level is uncovered. First, an unexpected quantum‐Hall‐to‐insulator‐transition near the zeroth Landau level is discovered. Then, through a detailed scaling analysis, it is found that this quantum‐Hall‐to‐insulator‐transition belongs to a new universality class, implying that the insulating phase discovered here has a fundamentally different origin from those in nontopological systems.     

Enhancing the Quantum Anomalous Hall Effect by Magnetic Codoping in a Topological Insulator

The quantum anomalous Hall (QAH) effect, which has been realized in magnetic topological insulators (TIs), is the key to applications of dissipationless quantum Hall edge states in electronic devices. However, investigations and utilizations of the QAH effect are limited by the ultralow temperatures needed to reach full quantization—usually below 100 mK in either Cr‐ or V‐doped (Bi,Sb)₂Te₃ of the two experimentally confirmed QAH materials. Here it is shown that by codoping Cr and V magnetic elements in (Bi,Sb)₂Te₃ TI, the temperature of the QAH effect can be significantly increased such that full quantization is achieved at 300 mK, and zero‐field Hall resistance of 0.97 h/e² is observed at 1.5 K. A systematic transport study of the codoped (Bi,Sb)₂Te₃ films with varied Cr/V ratios reveals that magnetic codoping improves the homogeneity of ferromagnetism and modulates the surface band structure. This work demonstrates magnetic codoping to be an effective strategy for achieving high‐temperature QAH effect in TIs.     

Microwave cavity perturbation technique for measurements of the quantum Hall effect

A microwave cavity perturbation cryostat was constructed for the measurement of the quantum Hall effect. The conductivity and the dielectricity on the two-dimensional electron system have been measured at low temperature. Rapid changes in the resonant frequency shift and the resonance width were observed with increasing the magnetic field. These changes reflect the dielectric properties of the sample accompanied by the rapid decrease of the conductivity. In higher magnetic field, we observed oscillations of the cavity parameters in accordance with the quantum Hall effect.     

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.     

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.     

Observation and an Explanation of Breakdown of the Quantum Hall Effect

We observe a spatially localized breakdown of the nearly dissipationless quantum Hall effect into a set of discrete dissipative states in wide, high-quality GaAs/AlGaAs samples. The phenomenon can be explained by an extension of the quasi-elastic inter-Landau level scattering model of Eaves and Sheard.     

Comparison of the dimensions of electrical resistance units, supported on the basis of the hall quantum effect, in the All-Russia Research Institute of Metrological Service and the Czech Metrological Institute

VNIIMS (Russia) and CMI (Czech Republic) quantum Hall resistance standards are compared using a VNIIMS portable resistance standard of 1 and 10 kΩ. Conformity is established for the dimensions of units within the limits of relative expanded (k = 2) uncertainty of 10⁻⁷. Translated from Izmeritel’naya Tekhnika, No. 12. pp. 58–61, December, 2008.     

基于霍尔效应的印刷机能耗检测方法研究

目的采用霍尔元件法搭建印刷机群能耗数字化检测平台。方法通过建立印刷机能耗指标模型框架体系,形成以总耗电量指标、均值类指标、耗电比例类指标等为主的印刷机耗电评价标准,完善能耗评价准则。采用灵敏度高、稳定性好的霍尔元件作为能耗检测元件,并分析霍尔效应、磁平衡式电流和电压霍尔传感器的检测电路。采用伏安法功率测量方式分别检测各负载电路的电流与电压,通过A/D转换模块实现检测数据数字化,并通过硬件控制核心对采集的数字信号进行运算、输出和显示,采用CAN总线实现硬件控制系统与上位机之间数字信息交互。结果搭建了印刷机群能耗数字化检测系统平台,实现了外围设备与上位机间的数据交互,实现了印刷机群以数据为核心,通过能耗检测、能效分析、能源成本控制以及能源指标优化,提高了能源利用效率。结论能耗检测的实现既能减少冗余电量损耗,又有利于监测电路稳定性,利用霍尔元件法实现印刷机群能耗检测的方法是可行的。     

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     

Potential and Current Distributions Calculated Across a Quantum Hall Effect Sample at Low and High Currents

The potential and current distributions are calculated across the width of a quantum Hall effect sample for applied currents between 0 μA and 225 μA. For the first time, both a confining potential and a current-induced charge-redistribution potential are used. The confining potential has a parabolic shape, and the charge-redistribution potential is logarithmic. The solution for the sum of the two types of potentials is unique at each current, with no free parameters. For example, the charge-depletion width of the confining potential is determined from a localization experiment by Choi, Tsui, and Alavi, and the spatial extent of the conducting two-dimensional electron gas across the sample width is obtained from the maximum electric field deduced from a high-current breakdown experiment by Cage and Lavine, and from the quantum Hall voltage. The spatial extent has realistic cut-off values at the sample sides; e.g., no current flows within 55 magnetic lengths of the sides for currents less than 215 μA. The calculated potential distributions are in excellent agreement with contactless electro-optic effect laser beam measurements of Fontein et al.