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.     

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.     

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.     

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.     

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。     

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.     

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.     

新型量子霍尔电阻样品计量应用研究

采用AsGa砷化镓系材料研制了多种结构的新型量子霍尔电阻样品,介绍了该样品的特点及应用领域。使用常温电流比较仪和低温电流比较仪,用过渡比对法对新型的量子霍尔电阻与标准量子霍尔电阻样品进行了双重测量比对验证,在实验室内测量结果的相对偏差小于4×10^-8,验证了新型的量子霍尔电阻样品和测量系统的准确度满足当前计量应用需求。     

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。     

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.     

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.     

量子化霍尔电阻国家标准的研究

中国计量科学研究院在2003年建成了量子化霍尔电阻标准装置。成功研制了系统的核心器件—量子化霍尔器件。并通过对低温电流比较仪系统及运行过程的研究,发现了氦气气压波动引起的冻结磁通蠕动导致的附加噪声是限制系统不确定度的主要原因。进而提出了一种新型的气压滤波器,消除了这些干扰因素。还改进了电路动态特性,改善了前馈补偿环节,把匝数比提高了8倍,信噪比也因而提高了8倍。完成的量子化霍尔电阻标准装置的综合不确定度为2.4×10-10(k=1)。     

基于量子化霍尔电阻考核的国家电阻基准的稳定性

报告了自1990年以来通过与量子化霍尔电阻比对考核的国家直流电阻（实物）基准的长期漂移率及偏差。结果表明2001年以来,国家直流电阻（实物）副基准的漂移率为-0．0551μΩ／a,主基准的漂移率为-0．0808μΩ／a;2006年10月25日,国家直流电阻（实物）基准复现的电阻量值较量子化霍尔电阻的相对偏差为＋0．677mm,预计2007年1月1日需要修正-0．69μΩ／a。     

Anomalous Hall and Nernst Effects in Normal State of SC Cuprates

It is demonstrated that scattering of mobile charge carriers by fluctuations of local spin density in the normal state of SC-cuprates results in anomalous contribution to the transport phenomena (Hall and Nernst effects are included). Depending on their sign and magnitude, they can change value and sign of the corresponding effect measured.     

基于交流阻抗的聚乙烯/碳纳米管导电复合材料的室温逾渗性能

聚合物基导电复合材料的室温逾渗机理是其使用和制备的重要基础。为了阐述聚乙烯/碳纳米管导电复合材料的室温逾渗性能,文中基于交流阻抗的分析思路和方法,采用电阻电容的等效电路模拟复合材料中的电学性能。以熔融法制备的高密度聚乙烯(HDPE)/碳纳米管(CNTs)复合材料为研究对象,测试其室温下的电学性能与CNTs含量间的关系,其中交流(AC)阻抗测试频率范围为100Hz到106.5Hz。当碳纳米管质量分数为0.5%时复合材料的电导率升至10~(-6)S/cm,表明复合材料中逾渗网络已初步形成。随频率变化的AC阻抗可清晰地展示HDPE/CNTs中导电网络的形成过程,并表明在导电复合材料的电学逾渗中,复合材料的导电机理逐渐由电容主导向电阻主导变化。     

Quadratic dependence of the spin-induced Hall voltage on longitudinal electric field

The effect of optically induced spins in semiconductors in the low electric field is investigated. Here we report an experiment which investigates the effect of a longitudinal electric field (E) on the spin-polarized carriers generated by a circularly polarized light in semiconductors. Our experiment observes the effect as a spin-induced anomalous Hall voltage (V_AH) resulting from spin-carrier electrons accumulating at the transverse edges of the sample. Unlike the ordinary Hall effect, a quadratic dependence of V_AH on E is observed, which agrees with the results of the recent theoretical investigations. It is also found that V_AH depends on the doping density. The results are discussed.     

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.