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.     

Temperature-dependent Hall analysis of carbon-doped GaAs

The temperature dependence of the electrical properties, such as hole concentration, Hall mobility and resistivity of carbon-doped GaAs epilayers over a wide range of doping levels has been investigated. The carbon-doped GaAs epilayers have been grown by low pressure metalorganic chemical vapor deposition. The electrical properties have been obtained by Hall measurements. Experimental data on the carrier mobility, Hall effect, and resistivity over a wide temperature range have been analyzed and possible scattering mechanisms have been explained. Our experimental data show that the ionized impurity scattering tend to be dominant at temperatures below 100 K, while the lattice scattering as well as the ionized impurity scattering plays an important role at temperatures above 100 K. The dependence of the electrical on the doping levels has also been studied. In the case of heavily C-doped GaAs, the mobility curves are nearly flat at temperatures below 100 K and the mobility decreases as temperature increases above 100 K. The reason is that the degenerate conduction occurs at high doping level. The degenerate conduction begins at the hole concentration of about 2 × 10¹⁸ cm⁻³ at 77 K and at room temperature.     

Hall Coefficient of Equilibrium Supercurrents Flowing inside Superconductors

We study augmented quasiclassical equations of superconductivity with the Lorentz force, which is missing from the standard Ginzburg–Landau and Eilenberger equations. It is shown that the magnetic Lorentz force on equilibrium supercurrents induces a finite charge distribution and the resulting electric field to balance the Lorentz force. An analytic expression is obtained for the corresponding Hall coefficient of clean type-II superconductors with simultaneously incorporating the Fermi-surface and gap anisotropies. It has the same sign and magnitude at zero temperature as the normal state for an arbitrary pairing, having no temperature dependence specifically for s-wave pairing. The gap anisotropy may bring about a considerable temperature dependence in the Hall coefficient and can lead to its sign change as a function of temperature, as exemplified for a model d-wave pairing with a two-dimensional Fermi surface. The sign change may be observed in some high-T _c superconductors.     

Longitudinal and Hall Resistivity in Thin Film Superconductor

We associate both the longitudinal and Hall resistivity of a thin film superconductor YBCO near its transition temperature with vortex lattice melting. In a two dimensional Kosterlitz-Thouless transition there are two characteristic properties, the number of free dislocations and the dielectric function for the dislocation pairs. Using these two parameters, we are able to fit both the longitudinal and Hall resistivity as a function of temperature and magnetic field.     

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。     

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.     

Hall coefficient in vacuum-deposited copper films

The dependence of the Hall coefficient R_H of vacuum-deposited copper films of thickness, temperature and time was investigated by in situ observation. R_H values were found to be larger than the bulk value and a thickness dependence could hardly be observed down to 100 Å. The temperature dependence was appreciably larger than for bulk material, indicating the existence of the size effect predicted by Sondheimer. R_H for very thin films (below 100 Å) left in the vacuum system at 295°K changed with time, and the change was ascribed to the annihilation of lattice defects in the films.     

The Infrared Hall Effect in YBCO: Temperature and Frequency Dependence of Hall Scattering

We measure the Hall angle, _H , in YBCO films in the far- and mid-infrared to determine the temperature and frequency dependence of the Hall scattering. Using novel modulation techniques we measure both the Faraday rotation and ellipticity induced by these films in high magnetic fields to deduce the complex conductivity tensor. We observe a strong temperature dependence of the mid-infrared Hall conductivity in sharp contrast to the weak dependence of the longitudinal conductivity. By fitting the frequency dependent normal state Hall angle to a Lorentzian _H () = _H /( _H – i) we find the Hall frequency, _H , is nearly independent of temperature. The Hall scattering rate, _H , is consistent with _H T ² up to 200 K and is remarkably independent of IR frequency suggesting non-Fermi liquid behavior.     

Hall effect in chromium-copper alloy films

Chromium-copper alloy was deposited in thin film form by vapor deposition at room temperature onto well cleaned glass substrates at a pressure of 10⁻⁵ Pa. The polycrystalline alloy thus formed was vacuum annealed up to a temperature of 525 K. Hall coefficient R_H and Hall mobility μ have been measured for annealed polycrystalline chromium-copper alloy films at 300 K. Below 50 nm, a film thickness dependence (size effect) was observed. Data on polycrystalline alloy film agree well with Sondheimer theory for perfect diffuse scattering so that the best fit mean free path value can be calculated. The calculated mean free path value (37 nm) agrees fairly well with the mean free path value reported from electrical resistivity data (37.6 nm) and temperature coefficient of resistivity data (36.3 nm) for perfect diffuse scattering. The decline of the Hall mobility is expected theoretically. The bulk Hall coefficient and bulk mobility of the alloy can be predicted from the experimental data and comes out to be −5.2 × 10⁻⁵ cm³/coulomb and 13.57 cm²/v-sec respectively. The results are discussed.     

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.     

Hall Effect due to channeled pinning potential in Nb thin films

We have studied the Magnetoresistance and Hall Effect in Nb superconducting thin films with triangular arrays of holes. Three different arrays of defects have been prepared with different orientations with respect to the current. Because vortex dynamics in the mixed state in type-II superconductors is strongly influenced by the pinning centers, a channeled pinning landscape is formed by the pinned vortices. It is suggested that the motion of interstitial vortices has great influence by the channel. When vortices propagate through these arrays, both the longitudinal and transversal voltages show cusp-like anomalies at matching fields. Vortices can be guided by the channel formed between pinned vortices. The longitudinal voltages are the same when there is a sign change of magnetic field. The longitudinal and transversal Hall voltages are dependent on the rotating angle of the arrays.     

Electron transport effects in the IR photoconductivity of InGaAs/GaAs structures with quantum dots

We have studied the temperature dependence of the Hall effects in multilayer selectively doped InGaAs/GaAs heterostructures with quantum dots (QDs). It was found that structures possessing photoconductivity in the IR range exhibit a sharp (nearly exponential) growth of the conductivity and Hall mobility in the temperature interval from 8 to 30 K at a virtually constant Hall coefficient and electron density. A new mechanism of the lateral photoconductivity in the structures with QDs is proposed which is related to the change in the electron mobility in the two-dimensional channel as a result of a decrease in the Coulomb scattering on charged QDs.     

The Hall coefficient of Pd and some β-phase PdH alloys

Measurements of the Hall coefficient have been made, from 4.2 to 220 K, for Pd and some -phase PdH alloys. The results for Pd have a temperature dependence of a form which is given quite well by the model of Kimura and Shimizu. The results for the alloys show an anomaly at 50 K, and a time dependence below this temperature, which is similar to that shown by the electrical resistivity.Work supported by the National Research Council of Canada.     

A Sensitive AC System for Measuring Changes in Small Hall Voltages at High Temperatures

A simple ac sysyem which incorprates a phase-sensitive detector for measuring changes in small Hall voltages at high temperatures is described. Under optimum operating conditions, the system has a sensitivity of better than 10-8 V. The apparatus has been used to directly investigate the change of charge carrier concentration with time in very heavily doped semiconductor material while undergoing high-temperature isothermal heat treatment.1 A chart recording of a < 10-7-V change in Hall voltage at a temperature of 1040 K is given as an indication of the system's performance. The results of Hall-voltage measurements on zone levelled n-type Si63.5 Ge36.5 alloy doped with phosphorus to ~1.2 X 1026 m-3 over a range of heat-treatment temperatures and as a function of time are reported. The results indicate that over a certain temperature range, precipitation of phosphorus takes place very rapidly and the rate of change of carrier concentration exhibits a maximum in the temperature range around 750 K.     

Magnetotransport Anomaly in Room‐Temperature Ferrimagnetic NiCo2O4 Thin Films

The inverse spinel ferrimagnetic NiCo₂O₄ presents a unique model system for studying the competing effects of crystalline fields, magnetic exchange, and various types of chemical and lattice disorder on the electronic and magnetic states. Here, magnetotransport anomalies in high‐quality epitaxial NiCo₂O₄ thin films resulting from the complex energy landscape are reported. A strong out‐of‐plane magnetic anisotropy, linear magnetoresistance, and robust anomalous Hall effect above 300 K are observed in 5–30 unit cell NiCo₂O₄ films. The anomalous Hall resistance exhibits a nonmonotonic temperature dependence that peaks around room temperature, and reverses its sign at low temperature in films thinner than 20 unit cells. The scaling relation between the anomalous Hall conductivity and longitudinal conductivity reveals the intricate interplay between the spin‐dependent impurity scattering, band intrinsic Berry phase effect, and electron correlation. This study provides important insights into the functional design of NiCo₂O₄ for developing spinel‐based spintronic applications.     

Planar Hall effect of indium antimonide thin film on silicon and nickel–zinc ferrite substrates

We have investigated Hall and planar Hall (PH) effect of indium antimonide (InSb) films thermally evaporated on two different substrates including Si and soft magnetic Ni–Zn ferrite. Polycrystalline InSb film with an average grain size of 1.2 μm shows substantial electron mobility of 6,700 cm²/Vs for Si and 5,680 cm²/Vs for Ni–Zn ferrite substrates respectively. Four-point bridge type Hall bar of InSb was fabricated using photolithography followed by chemical wet etch. An abrupt change in PH deviated from a normal PH curve was found on a ferrite substrate within a low field range of −50 to 50 Oe while no change happens on the Si substrate. Sharp PH curve immediately returns to the ordinary PH curve when applied field goes over −50 to 50 Oe without leaving any hysteresis of resistance. This is mainly attributed to the presence of the Bloch wall of Ni–Zn ferrite underneath InSb Hall bar. Intragranular domain wall movement is believed to be a prime source of the anomalous PH behavior in the low field range. The linear field dependence of PH in a resolution of 10 mΩ/Oe is sensitive high enough to be used as low-field magnetic sensors.     

Transport properties of SnTe interpreted by means of a two valence band model

Electrical conductivity, thermoelectric power and Hall coefficient of SnTe have been measured between 300 K and 160 K. The temperature variation of thermoelectric power and the carrier concentration estimated from the Hall coefficient have been explained with a two valence band model. The variation of mobility with temperature has been calculated from the above measurements. The mobility of holes in the upper valence band is found to follow the usual $\text{T}{}^{\mathrm{<mtext>-3</mtext><mtext>2</mtext>}}$ law, whereas the mobility in the lower valence band increases with temperature in a peculiar manner which cannot be explained with the help of a parabolic band.     

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.     

Crystal field effects in the anomalous Hall coefficient

The anomalous Hall coefficient is calculated for rare earth ions in cubic matrices, including crystal field effects and virtual boundd states associated with the rare earth ions. The results suggest that the temperature dependence of the Hall coefficient should follow the ionic susceptibility and thus be sensitive to modifications in temperature dependence of the susceptibility due to crystal field effects. The validity of this result is tested using available results for rare earths in noble metal hosts.Supported by the Ministère de l'Education de Québec and the National Research Council.     

Memory Behavior of the Planar Hall Effect in Ferromagnetic (Ga, Mn)As/GaAs Superlattices

The planar Hall effect (PHE) has been studied in short period (Ga,?Mn)As/GaAs superlattices displaying a ferromagnetic interlayer coupling between the magnetic layers. Complex dependence of the PHE on applied magnetic field is explained by taking into account the magnetocrystalline anisotropy of the (Ga,?Mn)As layers, which results from biaxial compressive strain in the layers epitaxially grown on GaAs. Two-state behavior of the planar Hall resistance at zero magnetic field provides its usefulness for applications in nonvolatile memory devices. In addition, using an appropriate sequence of applied magnetic fields four different states of the planar Hall resistance, suitable for quaternary memory devices, can be realized owing to the formation of a stable multidomain structure in the Hall bar.