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.     

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.     

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.     

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。     

Observation of the fractional quantum Hall effect in an oxide

The quantum Hall effect arises from the cyclotron motion of charge carriers in two-dimensional systems. However, the ground states related to the integer and fractional quantum Hall effect, respectively, are of entirely different origin. The former can be explained within a single-particle picture; the latter arises from electron correlation effects governed by Coulomb interaction. The prerequisite for the observation of these effects is extremely smooth interfaces of the thin film layers to which the charge carriers are confined. So far, experimental observations of such quantum transport phenomena have been limited to a few material systems based on silicon, III-V compounds and graphene. In ionic materials, the correlation between electrons is expected to be more pronounced than in the conventional heterostructures, owing to a large effective mass of charge carriers. Here we report the observation of the fractional quantum Hall effect in MgZnO/ZnO heterostructures grown by molecular-beam epitaxy, in which the electron mobility exceeds 180,000 cm(2) V(-1) s(-1). Fractional states such as ν = 4/3, 5/3 and 8/3 clearly emerge, and the appearance of the ν = 2/5 state is indicated. The present study represents a technological advance in oxide electronics that provides opportunities to explore strongly correlated phenomena in quantum transport of dilute carriers.     

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     

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.     

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.     

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.     

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     

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     

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.     

High-Field Electronic Properties of Graphene

We have measured the energy gaps in single-layer and bilayer graphene by means of temperature dependent transport experiments in high magnetic fields up to 33 T. They follow the expected Landau level splitting when a finite level width is taken into account. The quantum Hall effect, hitherto only observed up to 30 K, remains visible up to 200 K in bilayers and even up to room temperature in single-layer graphene. Our experiments in single-layer graphene show that the lowest Landau level, shared equally between electrons and holes at zero energy, becomes extremely narrow in high magnetic fields. It is this narrowing, together with the large Landau level splitting in graphene that leads to an extremely robust localization and makes the quantum Hall effect visible up to room temperature. In high magnetic fields (B>20 T) we observe a strongly increasing resistance with decreasing temperature. These results are explained with field dependent splitting of the lowest Landau level of the order of a few Kelvin, as extracted from activated transport measurements.     

Emergent phenomena at oxide interfaces

Recent technical advances in the atomic-scale synthesis of oxide heterostructures have provided a fertile new ground for creating novel states at their interfaces. Different symmetry constraints can be used to design structures exhibiting phenomena not found in the bulk constituents. A characteristic feature is the reconstruction of the charge, spin and orbital states at interfaces on the nanometre scale. Examples such as interface superconductivity, magneto-electric coupling, and the quantum Hall effect in oxide heterostructures are representative of the scientific and technological opportunities in this rapidly emerging field.     

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     

Limiting bound (minimal and maximum) values of the effective conductivity under the quantum Hall effect conditions

The percolation of current in inhomogeneous media under conditions of the quantum Hall effect has been considered. The lower and upper bound values for the effective Hall conductivity are established, the values of which differ from the minimum and maximum values for the metallic conductivity.     

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.     

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.     

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.     

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.