Quantum Hall Effect Devices Research Articles

Graphene Quantum Hall Effect Devices for AC and DC Electrical Metrology.

A new type of graphene-based quantum Hall standards is tested for electrical quantum metrology applications at alternating current (ac) and direct current (dc). The devices are functionalized with Cr(CO)3 to control the charge carrier density and have branched Hall contacts based on NbTiN superconducting material. The work is an in-depth study about the characteristic capacitances and related losses in the ac regime of the devices and about their performance during precision resistance measurements at dc and ac.

Transmission lines and resonators based on quantum Hall plasmonics: Electromagnetic field, attenuation, and coupling to qubits

Quantum Hall edge states have some characteristic features that can prove useful to measure and control solid state qubits. For example, their high voltage to current ratio and their dissipationless nature can be exploited to manufacture low-loss microwave transmission lines and resonators with a characteristic impedance of the order of the quantum of resistance $h/e^2\sim 25\mathrm{k\Omega}$. The high value of the impedance guarantees that the voltage per photon is high and for this reason high impedance resonators can be exploited to obtain larger values of coupling to systems with a small charge dipole, e.g. spin qubits. In this paper, we provide a microscopic analysis of the physics of quantum Hall effect devices capacitively coupled to external electrodes. The electrical current in these devices is carried by edge magnetoplasmonic excitations and by using a semiclassical model, valid for a wide range of quantum Hall materials, we discuss the spatial profile of the electromagnetic field in a variety of situations of interest. Also, we perform a numerical analysis to estimate the lifetime of these excitations and, from the numerics, we extrapolate a simple fitting formula which quantifies the $Q$ factor in quantum Hall resonators. We then explore the possibility of reaching the strong photon-qubit coupling regime, where the strength of the interaction is higher than the losses in the system. We compute the Coulomb coupling strength between the edge magnetoplasmons and singlet-triplet qubits, and we obtain values of the coupling parameter of the order $100\mathrm{MHz}$; comparing these values to the estimated attenuation in the resonator, we find that for realistic qubit designs the coupling can indeed be strong.

Magnetocapacitance and dissipation factor of epitaxial graphene-based quantum Hall effect devices

We investigate the properties of the magnetocapacitance and dissipation factor of epitaxial graphene Hall bars with different electrode configurations to gain insight into the underlying physical mechanisms. The dependence of magnetocapacitance and dissipation factor on the magnetic field shows how the screening ability of the two-dimensional electron gas (2DEG) changes at the transition from the nonquantized to the quantized state. Both magnetocapacitance and dissipation factor exhibit a characteristic and correlated voltage dependence, which is attributed to the alternating contraction and expansion of the nonscreening 2DEG regions due to the alternating local electric field. Two regimes with seemingly different voltage dependencies are explained as the limiting cases of weak and strong electric fields of the same general voltage dependence. Electric fields in the plane of the 2DEG are found to cause about three orders of magnitude more ac dissipation than perpendicular electric fields. This strong directionality is attributed to the fact that the electrons are mobile in the plane of the 2DEG but are confined in the third dimension. In the quantized state, not only the screening edge of the 2DEG but also compressible puddles embedded in the bulk cause ac dissipation, as follows from the measured frequency dependence. Finally, characteristic parameters like the width of the screening edge, the threshold voltage, and the charging time of the compressible puddles are determined.

Cooling of chiral heat transport in the quantum Hall effect regime of graphene

In the quantum Hall effect (QHE) regime, heat is carried by electrons in the edge states of Landau levels. Here, we study cooling of hot electrons propagating along the edge of graphene at the filling factor $\nu=\pm2$, mediated by acoustic phonons. We determine the temperature profile extended from a hot spot, where the Hall current is injected into graphene from a metallic contact, taking into account specifics of boundary conditions for lattice displacements in graphene in a van der Waals heterostructure with an insulating substrate. Our calculations, performed using generic boundary conditions for Dirac electrons, show that emission of phonons can explain a short cooling length observed in graphene-based QHE devices by Nahm, Hwang and Lee [PRL 110, 226801 (2013)].

Mini array of quantum Hall devices based on epitaxial graphene

Series connection of four quantum Hall effect (QHE) devices based on epitaxial graphene films was studied for realization of a quantum resistance standard with an up-scaled value. The tested devices showed quantum Hall plateaux RH,2 at a filling factor v = 2 starting from a relatively low magnetic field (between 4 T and 5 T) when the temperature was 1.5 K. The precision measurements of quantized Hall resistance of four QHE devices connected by triple series connections and external bonding wires were done at B = 7 T and T = 1.5 K using a commercial precision resistance bridge with 50 μA current through the QHE device. The results showed that the deviation of the quantized Hall resistance of the series connection of four graphene-based QHE devices from the expected value of 4×RH,2 = 2 h/e2 was smaller than the relative standard uncertainty of the measurement (<1 × 10−7) limited by the used resistance bridge.

A 1 k standardresistor device based on quantum Hall array

Quantum metrological standards based on the fundamental physical constants are the trend of modern metrology because of their attributes such as high accuracy, high stability, and good reproducibility. The quantum Hall effect (QHE), which refers to the electronic charge e and the Planck constant h, is used to define the quantum resistance standard. The quantum Hall resistance (RH) of h/2e2 at the filling factori=2 is used as the standard. It is obvious that the RH is non-integral. However the resistors that need to be calibrated each have a decimal value, such as 1 k, 10 k, 100 k, etc. The calibration chain from the non-integral RH to the real resistor is long. The quantum Hall array resistance standards (QHARSs) are invented to solve this problem. The QHARS which are based on the decimal resistance values can shorten the calibration chain, improve the resistance transfer accuracy, and finally realize the quantization of the whole resistance calibration chain. The QHARS can also replace the traditional physical transfer standard resistor and realize the quantization of the transfer standard resistor. The decimal QHARS devices can be realized by connecting single QHE devices in series or parallel with the multiple link technology. In this paper we report the design, fabrication and characterization of a 1 k QHARS device based on the GaAs/AlxGa1-xAs heterostructures. In our design, the 1 k array device consists of only 29 Hall bars. The nominal value of the device is 999.9999658 with a relative deviation of -3.4210-8 from 1 k. The ratio between the maximum and minimum current flowing through the Hall bars is as small as 14.5. The 1 k QHARS devices are measured in the national resistance standard system at a temperature of 1.5 K. The measurement is taken at the central magnetic field of the 2nd quantum Hall plateau. We compare our 1 k QHARS resistor with a 1 k transfer standard resistor using the direct current comparator. The 1 k transfer standard resistor has already been calibrated in advance with our single QHR standard by cryogenic current comparator. Therefore the resistance of our 1 k QHARS resistor can be obtained. The relative deviation between the measured resistance value and the designed value is -1.9610-7with a standard uncertainty of 2.0710-7. The results show that we have realized the 1 k quantum Hall resistance standard device which can be used for the resistance calibration.

Circuit models and SPICE macro-models for quantum Hall effect devices

Precise electrical measurement technology based on the quantum Hall effect is one of the pillars of modern quantum electrical metrology. Electrical networks including one or more QHE elements can be used as quantum resistance and impedance standards. The analysis of these networks allows metrologists to evaluate the effect of the inevitable parasitic parameters on their performance as standards. This paper presents a concise review of the various circuit models for QHE elements proposed in the literature, and the development of a new model. This last model is particularly suited to be employed with the analogue electronic circuit simulator SPICE. The SPICE macro-model and examples of SPICE simulations, validated by comparison with the corresponding analytical solution and/or experimental data, are provided.

Fabrication and Study of Large-Area QHE Devices Based on Epitaxial Graphene

Quantum Hall effect (QHE) devices based on epitaxial graphene films grown on SiC were fabricated and studied for development of the QHE resistance standard. The graphene-metal contacting area in the Hall devices has been improved and fabricated using a double metallization process. The tested devices had an initial carrier concentration of (0.6-10) · ~10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">11</sup> cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> and showed half-integer QHE at a relatively low (3 T) magnetic field. The application of the photochemical gating method and annealing of the sample provides a convenient way for tuning the carrier density to the optimum value. Precision measurements of the quantum Hall resistance in graphene and GaAs devices at moderate magnetic field strengths (≤7 T) showed a relative agreement within ·10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-9</sup> .

Magnetocapacitance and loss factor of GaAs quantum Hall effect devices

We present a simple and accurate coaxial bridge capable of measuring the magnetocapacitance and the associated loss factor of a quantum Hall effect device, with and without an external Hall current—a situation where commercial instruments are limited. We interpret the results in terms of the model of compressible and incompressible regions in the two-dimensional electron gas and we deduce a novel empirical relation between the loss factor and the voltage dependence of the magnetocapacitance. This highlights the reason for the linear voltage dependence of the loss factor whose elimination is the basis for all metrological applications of the quantum Hall resistance at alternating current.

Structured epitaxial graphene: growth and properties

Graphene is generally considered to be a strong candidate to succeed silicon as an electronic material. However, to date, it actually has not yet demonstrated capabilities that exceed standard semiconducting materials. Currently demonstrated viable graphene devices are essentially limited to micrometre-sized ultrahigh-frequency analogue field effect transistors and quantum Hall effect devices for metrology. Nanoscopically patterned graphene tends to have disordered edges that severely reduce mobilities thereby obviating its advantage over other materials. Here we show that graphene grown on structured silicon carbide surfaces overcomes the edge roughness and promises to provide an inroad into nanoscale patterning of graphene. We show that high-quality ribbons and rings can be made using this technique. We also report on the progress towards high-mobility graphene monolayers on silicon carbide for device applications.

Matrix method analysis of quantum Hall effect device connections

The modelling of electrical connections of single, or several, multiterminal quantum Hall effect (QHE) devices is relevant for electrical metrology: it is known, in fact, that certain particular connections allow (i) the realization of multiples or fractions of the quantized resistance, or (ii) the rejection of stray impedances, so that the configuration maintains the status of quantum standard. Ricketts–Kemeny and Delahaye equivalent circuits are known to be accurate models of the QHE: however, the numerical or analytical solution of electrical networks including these equivalent circuits can be difficult. In this paper, we introduce a method of analysis based on the representation of a QHE device by means of the indefinite admittance matrix: external connections are then represented with another matrix, easily written by inspection. Some examples, including the solution of double- and triple-series connections, are shown.

Imaging by terahertz photon counting

Abstract Photon counting method is indispensable in visible/near-infrared optical measurements for detecting extremely weak radiation. The method, however, has been inaccessible in terahertz region, where the photon energies are more than 100 times smaller and catching individual photons is difficult. Here we review photon counting measurements of terahertz waves, by incorporating a semiconductor quantum-dot terahertz-photon detector into a scanning terahertz microscope. By using a quantum Hall effect detector as well, measurements cover the intensity dynamic range more than six orders of magnitude. Applying the measurement system to the study of semiconductor quantum Hall effect devices, we image extremely weak cyclotron radiation emitted by nonequilibrium electrons. Owing to the unprecedented sensitivity, a variety of new features of electron kinetics are unveiled. Besides semiconductor electric devices studied here, the experimental method will find application in diverse areas of molecular dynamics, microthermography, and cell activities.

Single Photon Counting and Passive Microscopy of Terahertz Radiation

Photon counting method is indispensable in visible/near-infrared optical measurements for detecting extremely weak radiation. The method, however, has been inaccessible in terahertz region, where the photon energies are more than 100 times smaller and catching individual photons is difficult. Here we review recent development of single terahertz photon detectors and passive sensing systems to locally pick up spontaneous emission in an object. Applying a passive terahertz microscope with quantum-dot single photon detectors, we image extremely weak cyclotron radiation emitted from quantum Hall effect devices. Owing to the unprecedented sensitivity, a variety of new features of electron kinetics are unveiled. Besides semiconductor electric devices studied here, the experimental method will find application in diverse areas of molecular dynamics, microthermography, and cell calorimetry.

Manipulating terahertz photons on a quantum Hall effect device

An on-chip terahertz measurement has been performed to investigate photon generation due to electrons injected by quantum Hall edge channels. In this device configuration, terahertz waves emitted from a quantum Hall effect device are transmitted to a quantum-dot single photon detector (fabricated on the same chip) via a coplanar waveguide. Photon generation is found on the confluence of unequally populated edge channels when the source–drain voltage reaches a level of Landau-level energy spacing.

ELECTRON SPIN IMAGING IN QUANTUM HALL DEVICES BY KERR ROTATION MEASUREMENT

The electron spin polarization images in a single layer GaAs / AlGaAs quantum well in the quantum Hall effect (QHE) regime have been observed by using an optical fiber-based high sensitive Kerr rotation microscope. The observed Kerr signal image at the Landau level filling factor ν = 1 reveals the small electron density fluctuation less than 1% through the degree of electron spin polarization. We have also observed the Kerr rotation images in the current flowing QHE devices. At ν = 1 QHE plateau, the winding strip of just ν = 1 incompressible state, which contributes the dissipationless electron transport, has been clearly observed in the bulk region of the devices. The highly current dependent Kerr images have valuable information for studying current density distribution and the distribution of spin polarization in the QHE regime. The experimental results and techniques of the Kerr imaging in the QHE regime have been reported in detail.

Magnetic field dependence of the photoresponse time of GaAs/AlGaAs quantum Hall effect device

The characteristic time of far IR response of a quantum Hall effect (QHE) detector in a GaAs/AlGaAs heterostructure has been investigated versus the magnetic field around the even values of the Landau level filling factor ν = 2, 4. The response time is shown to have a dip minimum in the center of a QHE plateau and two sharp maxima at either side of the plateau. Outside the QHE plateau the response time drop seems to result from the rise of the equilibrium population of Landau level over/below the Fermi energy with electrons/holes which increases the probability of photoexcited carrier recombination. The minimum at the QHE plateau center is due to the vanishing of screening of the random potential. The length scale of the potential fluctuations has been estimated.

Spatial imaging of noise voltages by a quantum Hall scanning electrometer

We present a new application of the quantum Hall effect (QHE): a scanning sensor for imaging the spatial distributions of noise voltages. This technique is based on a scanning electrometer employing a QHE device, which utilizes capacitive coupling between electrometer and sample. By measuring local voltage fluctuations with the QHE electrometer, we have been able to produce the first image of a noise-voltage distribution in a QHE sample. We found that a high noise level occurs in the lower magnetic field region of a QHE plateau of Landau-level-filling factor 2, and that it is concentrated in a high-potential edge region of the Hall bar sample. These results show that our noise-imaging system serves as a useful tool for probing edge-state electrons in QHE systems.

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.

Quantum Hall effect devices based on AlGaAs/GaAs structures studied by photoreflectance spectroscopy

The optical properties of MBE-grown quantum Hall effect devices have been studied by photoreflectance spectroscopy (PR) at different temperatures. The room temperature PR spectra show two typical signals around 1.42 and 1.85eV attributed to the energy band edges of GaAs and AlGaAs, respectively. Between the former band edge transitions broad oscillations (BO) are observed. 15K PR spectra from samples and photoluminescence spectroscopy reveal that a component of the BO is originated from the surface quantum well (SQW) created by the AlGaAs–GaAs–vacuum discontinuity. This signal experience a blue shift when the GaAs is gradually etched-off in good agreement with the PR spectra behavior from SQWs previously reported. Besides, PR measurements were performed at low temperatures. In this process, the near-surface band bending of the structures is virtually flattened during the cooling procedure. We observed a signal whose intensity decreased as the temperature is lowered. Therefore, the former results suggest that BO consist in two superimposed signals coming from the SQW and the electric field cap region.

Behavior of the contacts of quantum Hall effect devices at high currents

We have analyzed the behavior of contacts of quantum Hall effect devices while increasing the current through the sample. Experiments have been performed in the i=2 plateau, which is used in all metrological measurements of the von Klitzing constant RK, before the onset of dissipation. Using only electrical measurements, we show that a high electric field zone appears in the vicinity of the current contact which injects the electrons in the two-dimensional electron gas, when the current is increased. This heating phenomenon develops in the region close to the source, increases the electronic temperature in the sample, and limits the precision in the measurement of RK. We have studied several samples of different width, using a well-defined configuration for the measurements. It is observed that the threshold current for the onset of the voltage drop across the contact increases with the width of the Hall bar. Consequences for high precision measurements are discussed in terms of experimental protocol and of contact’s geometry.