Quantum Hall Devices Research Articles

Non-Hermitian topology in a multi-terminal quantum Hall device

Quantum devices characterized by non-Hermitian topology are predicted to show highly robust and potentially useful properties for precision sensing and signal amplification. However, realizing them has remained a daunting experimental task, as non-Hermiticity is often associated with gain and loss, which would require precise tailoring to produce the signatures of non-trivial topology. Here, instead of gain and loss, we use the non-reciprocity of quantum Hall edge states to directly observe non-Hermitian topology in a multi-terminal quantum Hall ring. Our transport measurements evidence a robust, non-Hermitian skin effect, characterized by currents and voltages showing an exponential profile that persists across Hall plateau transitions away from the regime of maximum non-reciprocity. Our observation of non-Hermitian topology in a quantum device introduces a scalable experimental approach to construct and investigate generic non-Hermitian systems.

Performance and Stability Assessment of Graphene-Based Quantum Hall Devices for Resistance Metrology

For more than three decades, GaAs/AlGaAs quantum Hall (QH) devices are being used as standards for the realization of the dc resistance unit ohm. Recently, the outstanding performance of graphene-based quantum Hall resistance (QHR) devices signifies an immense potential for a transition from GaAs to graphene-based devices in the field of resistance and also impedance metrology, with equally good accuracy. The recent developments in epitaxial graphene (EG) quality and fabrication of EG-based doped QHR devices and their improved performance tested in several national metrology institutes (NMIs) all over the world have demonstrated a more user-friendly dissemination of the unit ohm since they can be operated at relatively low magnetic fields and higher temperatures in comparison to existing GaAs-based devices. In this work, we have extensively tested the temporal stability of the magneto-transport properties of our graphene QH devices fabricated in the PTB and the resistance quantization performance by means of repeated high-accuracy cryogenic current comparator (CCC) measurements with several devices. Together with interlaboratory comparisons between NMI’s, the performance and stability assessment demonstrate the readiness of the technology for calibration purposes in resistance metrology.

Tailoring Permanent Charge Carrier Densities in Epitaxial Graphene on SiC by Functionalization with F4‐TCNQ

AbstractThe outstanding properties and the potential for large‐scale fabrication open a wide field for electronic applications of epitaxial graphene on silicon carbide substrates. However, reliable doping methods to permanently control and tailor the carrier concentration to the desired value without applying an electrostatic gate are challenging and still under investigation. In this study, a post‐growth molecular doping technique is investigated that compensates for the high electron density of pristine epitaxial graphene by using the acceptor F4‐TCNQ. By precise adjustment of the dopant concentration, the carrier density can be tuned in a wide range from intrinsic n‐ to the p‐type regime. The fabricated quantum Hall devices are ready‐to‐use, and no further treatments are required. High‐precision resistance measurements of graphene‐based devices with different doping levels show a quantization accuracy of 10−9 that underlines the high quality of the fabricated devices and the suitability of this method for device applications. The experimentally observed correlation between the carrier density and the onset of the quantum Hall plateau gives a reliable criterion for the choice of devices in quantum resistance metrology.

Metrological Assessment of Quantum Anomalous Hall Properties

Efforts to make the International System of Units (SI) more accessible have been growing since the global redefinition of the SI in 2019. Presently, the ohm is defined through the quantum Hall effect (QHE). However, quantum Hall devices require strong magnetic fields for a robust expression of the QHE. Magnetically doped topological insulators offer an opportunity to circumvent this limitation, as they require no magnetic field to provide a quantized resistance plateau via the quantum anomalous Hall effect (QAHE). Here, we detail experimental methodology and noise-analysis techniques for high-precision measurements of QAHE devices.

Pressure-Induced Superconductivity in HgTe Single-Crystal Film.

HgTe film is widely used for quantum Hall well studies and devices, as it has unique properties, like band gap inversion, carrier‐type switch, and topological evolution depending on the film thickness modulation near the so‐called critical thickness (63.5 Å), while its counterpart bulk materials do not hold these nontrivial properties at ambient pressure. Here, much richer transport properties emerging in bulk HgTe crystal through pressure‐tuning are reported. Not only the above‐mentioned abnormal properties can be realized in a 400 nm thick bulk HgTe single crystal, but superconductivity is also discovered in a series of high‐pressure phases. Combining crystal structure, electrical transport, and Hall coefficient measurements, a p‐n carrier type switching is observed in the first high‐pressure cinnabar phase. Superconductivity emerges after the semiconductor‐to‐metal transition at 3.9 GPa and persists up to 54 GPa, crossing four high‐pressure phases with an increased upper critical field. Density functional theory calculations confirm that a surface‐dominated topologic band structure contributes these exotic properties under high pressure. This discovery presents broad and efficient tuning effects by pressure on the lattice structure and electronic modulations compared to the thickness‐dependent critical properties in 2D and 3D topologic insulators and semimetals.

Onsager-Casimir frustration from resistance anisotropy in graphene quantum Hall devices.

We report on nonreciprocity observations in several configurations of graphene-based quantum Hall devices. Two distinct measurement configurations were adopted to verify the universality of the observations (i.e., two-terminal arrays and four-terminal devices). Our findings determine the extent to which epitaxial graphene anisotropies contribute to the observed asymmetric Hall responses. The presence of backscattering induces a device-dependent asymmetry rendering the Onsager-Casimir relations limited in their capacity to describe the behavior of such devices, except in the low-field classical regime and the fully quantized Hall state. The improved understanding of this quantum electrical process broadly limits the applicability of the reciprocity principle in the presence of quantum phase transitions and for anisotropic two-dimensional materials.

Suppression of the radiation squeezing in interacting quantum Hall edge channels

We study the quantum fluctuations of the two quadratures of the emitted electromagnetic radiation generated by a quantum Hall device in a quantum point contact geometry. In particular, we focus our attention on the role played by the unavoidable electron–electron interactions between the two edge channels at filling factor two. We investigate quantum features of the emitted microwave radiation, such as squeezing, by studying the current fluctuations at finite frequency, accessible through a two-filters set-up placed just after the quantum point contact. We compare two different drives, respectively a cosine and a train of Lorentzian pulses, used for the injection of the excitations into the system. In both cases quantum features are reduced due to the interactions, however the Lorentzian drive is still characterized by a robust squeezing effect which can have important application on quantum information.

Enhancing spin–orbit coupling in high-mobility graphene by introducing chiral space curvature

Graphene is an excellent two-dimensional materials with high-mobility and relativistic electronic linear dispersion. Its rich physical properties such as half-integer quantum Hall effect and device application potential have been continuously attracting great attention. However, light carbon atoms also imply negligible intrinsic spin–orbit coupling (SOC) strength which hinders its spintronic application. To enhance the SOC effect, we introduce a special deformation vector with chiral curvature, borrowed from the Einstein theory of general relativity, to mimic space warping and twisting. The derived Rashba type pseudospin–spin coupling locks the spin orientation of an electron with respect to its pseudospin. Combined with the original Dirac type Hamiltonian specifying the pseudospin orientation of an electron with respect to its wavevector, it lifts the spin degeneracy and paves the way for graphene-based spintronic devices. An estimate suggests that a Rashba type pseudospin–spin coupling of the order of 5 meV can be achieved in tens nanometer samples.

A four-terminal-pair Josephson impedance bridge combined with a graphene-quantized Hall resistance

This paper introduces a four-terminal-pair impedance bridge based on pulse-driven Josephson junctions arrays which is designed to link any kind of impedance to the quantized Hall resistance. The unique features of the quantized Hall resistance in a multiple series connection allows to dispense a combining network and leads to a compact and simple design of the whole setup. Moreover, the low noise of a quantized Hall resistance reduces the measurement time compared to resistance standards at room temperature which is essential for the characterization of quantum Hall devices in the AC regime. A first measurement campaign confirmed the expected low noise of 1.82 for a link to a 10 nF capacitance standard. The repeatability of the bridge was found to be few parts in 108. Capacitance and resistance standards were measured at 1233.15 Hz against graphene based quantum Hall resistance devices.

Electrical and magnetic properties of ohmic contacts of the quantum hall resistance devices

Quantum Hall effect is used to realize resistance standard which is in terms of the Planck constant [Formula: see text] and elementary charge [Formula: see text] in metrology. The quantum Hall resistance devices are fabricated based on two-dimensional electron gas formed in [Formula: see text] as heterostructures. Low-resistance Ohmic contact to the 2DEG is crucial in fabricating quantum Hall devices to obtain reproducible and accurate results. Annealed Au/Ge/Ni multilayer is widely used for Ohmic contacts to GaAs. In this paper, electrical and magnetic properties of optimized Ohmic contacts of quantum Hall devices are studied. For the electrical property evaluation, contact resistances are measured by three-terminal method in the quantum Hall [Formula: see text] plateau regime. Most of the contacts were Ohmic with values less than 2.4 [Formula: see text] and a good yield of better than 99% is obtained. In the magnetic property study, the annealed Au/Ge/Ni multilayer shows much smaller magnetization than the as-deposited one. TEM-EDS study shows the pure Ni layer diffused into the GaAs and AlGaAs layer and converts into the compounds closed to Ni2GeAs and NiAs phase. Density functional theory is used to calculate the atomic moments of pure face-centered cubic Ni, hexagonal Ni2GeAs and NiAs. The calculation results explained the magnetization drop of annealed samples well.

Realization of 5he2 with graphene quantum Hall resistance array

We report on the realization of 10 quantum Hall devices in series fabricated using epitaxial graphene on silicon carbide. Precision measurements with a resistance bridge indicate that the quantized Hall resistance across an array at a filling factor of 2 is equivalent to 5he2 within the measurement uncertainty of approximately 4 × 10−8. A quantum Hall phase diagram for the array shows that a metrological quantization of 5he2 can be achieved at the magnetic field of 6 T and a temperature of 4 K. This experiment demonstrates the possibility of timely unchangeable resistance reference in various ranges in relaxed experimental conditions.

Quantum Hall devices for the primary resistance standard based on the GaAs/AlxGa1−x As heterostructure

Quantum Hall devices for primary resistance metrology based on the GaAs/Al[Formula: see text]Ga[Formula: see text]As heterostructure were fabricated and compared with the devices from international metrology organization International Bureau of Weights and Measures (BIPM) by calibrating the same 100 [Formula: see text] transfer standard resistor with a cryogenic current comparator. Relative deviation between NIM-made device NIM-C1 and BIPM-made device BIPM-1 was −4.49 parts in 109 with an uncertainty of 3.63 parts in 109 which indicated NIM-C1 satisfied the requirement for the primary resistance standard.

Many-body wave functions for correlated systems in magnetic fields: Monte Carlo simulations in the lowest Landau level

We put forward possible wave functions for quantum Hall states in the lowest Landau level. These were deduced from the topological approach based on the relation between braid groups and the quantum statistics, as well as the commensurability condition unavoidable for collective states in magnetic fields. In this paper we demonstrate that the -field imposes restrictions on braid trajectories (i.e. elements of the full braid group). This results in the appearance of cyclotron subgroups, instead of the full braid group, for certain filling factors. The fermion representation of cyclotron subgroups defines transformations of wave functions in the quantum Hall regime. Hence, it sets quantum statistics (transformations of under exchanges of arguments), which is unavoidable for collective states (in compliance with the framework of Feynman’s path integrals). Finally, the topological approach allows to define the hierarchy of fillings in the lowest Landau level, which agree with the hierarchy observed in quantum Hall devices (i.e. in transport measurements).The symmetry of a many-body wave function (i.e. quantum statistics) is always determined by a 1D unitary representation of the system’s braid group. Using this topologically-originated property, we demonstrate that many-body wave functions for selected fillings of the lowest Landau level may not be purely antisymmetric. Only systems composed of fermions are investigated.Additionally, we present Monte Carlo calculations in a disc geometry, which remain in a nice agreement with predictions of exact diagonalizations (expected values of potential energy and pair distribution functions are presented). No boundary potential is assumed.

4p-J-10 量子ホール効果デバイスでの雑音測定II

4p-J-10 量子ホール効果デバイスでの雑音測定II

Examining epitaxial graphene surface conductivity and quantum Hall device stability with Parylene passivation

Homogeneous, single-crystal, monolayer epitaxial graphene (EG) is the one of most promising candidates for the advancement of quantized Hall resistance (QHR) standards. A remaining challenge for the electrical characterization of EG-based quantum Hall devices as a useful tool for metrology is that they are electrically unstable when exposed to air due to the adsorption of and interaction with atmospheric molecular dopants. The resulting changes in the charge carrier density become apparent by variations in the surface conductivity, the charge carrier mobility, and may result in a transition from n-type to p-type conductivity. This work evaluates the use of Parylene C and Parylene N as passivation layers for EG. Electronic transport of EG quantum Hall devices and non-contact microwave perturbation measurements of millimeter-sized areas of EG are both performed on bare and Parylene coated samples to test the efficacy of the passivation layers. The reported results, showing a significant improvement in passivation due to Parylene deposition, suggest a method for the mass production of millimeter-scale graphene devices with stable electrical properties.

Nonreciprocal quantum Hall devices with driven edge magnetoplasmons in two-dimensional materials

We develop a theory that describes the response of non-reciprocal devices employing 2-dimensional materials in the quantum Hall regime capacitively coupled to external electrodes. As the conduction in these devices is understood to be associated to the edge magnetoplasmons (EMPs), we first investigate the EMP problem by using the linear response theory in the random phase approximation. Our model can incorporate several cases, that were often treated on different grounds in literature. In particular, we analyze plasmonic excitations supported by smooth and sharp confining potential in 2-dimensional electron gas, and in monolayer graphene, and we point out the similarities and differences in these materials. We also account for a general time-dependent external drive applied to the system. Finally, we describe the behavior of a non-reciprocal quantum Hall device: the response contains additional resonant features, which were not foreseen from previous models.

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.

Towards a graphene-based quantum impedance standard

Precision measurements of the quantum Hall resistance with alternating current (ac) in the kHz range were performed on epitaxial graphene in order to assess its suitability as a quantum standard of impedance. The quantum Hall plateaus measured with alternating current were found to be flat within one part in 107. This is much better than for plain GaAs quantum Hall devices and shows that the magnetic-flux-dependent capacitive ac losses of the graphene device are less critical. The observed frequency dependence of about −8 × 10−8/kHz is comparable in absolute value to the positive frequency dependence of plain GaAs devices, but the negative sign is attributed to stray capacitances which we believe can be minimized by a careful design of the graphene device. Further improvements thus may lead to a simpler and more user-friendly quantum standard for both resistance and impedance.

Distributed-element circuit model of edge magnetoplasmon transport

We report experimental and theoretical studies of edge magnetoplasmon (EMP) transport in quantum Hall (QH) devices. We develop a model that allows us to calculate the transport coefficients of EMPs in QH devices with various geometries. In our model, a QH system is described as a chiral distributed-element (CDE) circuit, where the effects of Coulomb interaction are represented by an electrochemical capacitance distributed along unidirectional transmission lines. We measure the EMP transport coefficients through single- and coupled-edge channels, a quantum point contact, and single- and double-cavity structures. These measured transmission spectra can be reproduced well by simulations using the corresponding CDE circuits. By fitting the experimental results with the simulations, we deduce the circuit parameters that characterize the electrostatic environment around the edge channels in a realistic QH system. The observed gate-voltage dependences of the EMP transport properties in gate-defined structures are explained in terms of the gate tuning of the circuit parameters in CDE circuits.

Noise and Correlation Study of Quantum Hall Devices

We report voltage noise measurements on the cryogenic quantum Hall resistance (QHR) and present two new findings to illustrate the potential of the two-channel instrumentation used. Without applied current, only Johnson-Nyquist noise is present, but at two separate pairs of quantum Hall terminals, it can be cross-correlated via a longitudinal resistance. With applied current, excess noise due to dissipation bursts appears, which increases dramatically with the noninteger fraction of the filling factor.