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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

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.