Quantized Hall Resistance Research Articles

Feasibility of the Josephson voltage and current standards on a single chip

The quantum Josephson voltage standard is well established across the metrology community for many years. It relies on the synchronization of the flux tunneling in the S/I/S Josephson junctions (JJ) with the microwave radiation (MW) of frequency f such that V=Φ0fm, where m = 0, 1, 2, …. The phenomenon is called the Shapiro steps. Together with the quantum Hall resistance standard, the voltage standard forms the foundation of electrostatic metrology. The current is then defined as the ratio of the voltage and resistance. Realization of the quantum current standard would close the electrostatic metrological triangle of voltage–resistance–current. The current quantization I=2efm, the inverse Shapiro steps, was recently shown using the superconducting nanowires and small JJ. The effect is a synchronization of the MW with the Cooper pair tunneling. This paves the way to combine the JJ voltage and current standards on the same chip and demonstrate feasibility of the multi-standard operation. We show the voltage and current quantization on the same chip up to frequency of 10 GHz, corresponding to the amplitudes ∼ 20.67 μV and ∼ 3.2 nA, respectively. The accuracy of the voltage and current quantization, however, is relatively low, 35 and 100 ppk, respectively. We discuss measures to optimize the JJs, circuit, and environment to boost the amplitude and accuracy of the standards.

Quantum Hall resistance standards based on epitaxial graphene with p-type conductivity

In the last decade, quantum resistance metrology has benefited from the application of graphene as the base material for the fabrication of quantum Hall (QH) resistance standards since it allows for the realization of the resistance unit ohm in the revised International System of Units under relaxed experimental conditions. Here, we present a detailed magnetotransport investigation of p-type epitaxial graphene, which was doped by the molecular acceptor F4-TCNQ. High-accuracy measurements of the QH resistance show an excellent quantization and a reproduction of the nominal value, the half of the von Klitzing constant RK/2, within 2 nΩ/Ω. It underlines the universality of the QH effect and shows that p-type epitaxial graphene can also serve as the basis for future resistance standards for operation at relaxed experimental conditions. For the p-type devices, the onset of the QH plateau is observed at about 1 T higher magnetic fields, which can be attributed to an additional disorder or a non-symmetric charge transfer mechanism in the QH regime.

Testing the Renormalization of the von Klitzing Constant by Cavity Vacuum Fields

The value of fundamental physical constants is affected by the coupling of matter to the electromagnetic vacuum state, as predicted and explained by quantum electrodynamics. In this work, we present a millikelvin magnetotransport experiment in the quantum Hall regime that assesses the possibility of the von Klitzing constant being modified by strong cavity vacuum fields. By employing a Wheatstone bridge, we measure the difference between the quantized Hall resistance of a cavity-embedded Hall bar and the resistance standard, achieving an accuracy down to one part in 105 for the lowest Landau level. While our results do not suggest any deviation that could imply a modified Hall resistance, our work represents pioneering efforts in exploring the fundamental implications of vacuum fields in solid-state systems. Published by the American Physical Society 2024

Large quantum anomalous Hall effect in spin-orbit proximitized rhombohedral graphene

The quantum anomalous Hall effect (QAHE) is a robust topological phenomenon that features quantized Hall resistance at zero magnetic field. We report the QAHE in a rhombohedral pentalayer graphene-monolayer tungsten disulfide (WS 2 ) heterostructure. Distinct from other experimentally confirmed QAHE systems, this system has neither magnetic element nor moiré superlattice effect. The QAH states emerge at charge neutrality and feature Chern numbers C = ±5 at temperatures of up to about 1.5 kelvin. This large QAHE arises from the synergy of the electron correlation in intrinsic flat bands of pentalayer graphene, the gate-tuning effect, and the proximity-induced Ising spin-orbit coupling. Our experiment demonstrates the potential of crystalline two-dimensional materials for intertwined electron correlation and band topology physics and may enable a route for engineering chiral Majorana edge states.

A balanced quantum Hall resistor

The quantum anomalous Hall effect in magnetic topological insulators has potential for use in quantum resistance metrology applications. Electronic conductance is quantized to e2/h (where e is the elementary charge and h is the Planck constant) due to the effect, which persists down to zero external magnetic field and is compatible with the quantum standard of voltage. However, metrological applications of the quantum anomalous Hall effect are currently restricted by the need for low measurement currents and low temperatures. Here we report a measurement scheme that increases the robustness of a zero-magnetic-field quantum anomalous Hall resistor and extends its operating range to higher currents. In the scheme, we simultaneously inject current into two disconnected perimeters of a multi-terminal Corbino device, which is based on V0.1(Bi0.2Sb0.8)1.9Te3, to balance the electrochemical potential between the edges. This screens the electric field that drives backscattering through the bulk and thus improves the stability of the quantization at increased currents. Our approach could also be applied to existing quantum resistance standards that rely on the integer quantum Hall effect.

Fractional quantum anomalous Hall effect in multilayer graphene.

The fractional quantum anomalous Hall effect (FQAHE), the analogue of the fractional quantum Hall effect1 at zero magnetic field, is predicted to exist in topological flat bands under spontaneous time-reversal-symmetry breaking2-6. The demonstration of FQAHE could lead to non-Abelian anyons that form the basis of topological quantum computation7-9. So far, FQAHE has been observed only in twisted MoTe2 at a moiré filling factor v > 1/2 (refs. 10-13). Graphene-based moiré superlattices are believed to host FQAHE with the potential advantage of superior material quality and higher electron mobility. Here we report the observation of integer and fractional QAH effects in a rhombohedral pentalayer graphene-hBN moiré superlattice. At zero magnetic field, we observed plateaus of quantized Hall resistance [Formula: see text] at v = 1, 2/3, 3/5, 4/7, 4/9, 3/7 and 2/5 of the moiré superlattice, respectively, accompanied by clear dips in the longitudinal resistance Rxx. Rxy equals [Formula: see text] at v = 1/2 and varies linearly with v, similar to the composite Fermi liquid in the half-filled lowest Landau level at high magnetic fields14-16. By tuning the gate-displacement field D and v, we observed phase transitions from composite Fermi liquid and FQAH states to other correlated electron states. Our system provides an ideal platform for exploring charge fractionalization and (non-Abelian) anyonic braiding at zero magnetic field7-9,17-19, especially considering a lateral junction between FQAHE and superconducting regions in the same device20-22.

Development and implementation of an automated four-terminal-pair Josephson impedance bridge

The four-terminal-pair impedance bridge using pulse-driven Josephson voltage standards at PTB has been fully automated. The same bridge configuration was employed to determine R:R and C:C ratios over the frequency range between 53 Hz to 50 kHz. Only minor changes are needed to cover this large frequency range: amplifiers to increase the sensitivity of the current detections for low frequencies and signal generators with higher resolution at high frequencies to reach 50 kHz. Furthermore, the bridge can be operated for quadrature R:(1/ωC) measurements. The combined standard uncertainties (k = 1) for the new bridge were evaluated for all operating frequencies. They reach 2 nF F−1 and 4 nΩ Ω−1 at 1233.15 Hz. At this frequency, the 10 nF:10 nF ratio matched the ratio of PTB’s bridge employing inductive voltage dividers within 1 nF F−1 ± 3 nF F−1 (k = 1). Over 45 days, the 10 nF:10 nF ratio deviated less than −2 nF F−1 ± 3 nF F−1 (k = 1). The 12.9 kΩ:10 kΩ ratio at 53 Hz differed −2 nΩ Ω−1 ± 5 nΩ Ω−1 (k = 1) from the DC ratio measured by the PTB’s cryogenic current comparator bridge. Using a 12.9 kΩ resistance standard and a graphene AC quantum Hall resistance, the 10 nF:10 nF ratios derived from quadrature measurements agreed with the PTB’s inductive voltage divider bridge better than 9 nF F−1 ± 13 nF F−1 (k = 1).

(Invited) Silicon Quantum Dot Single-Electron Pumps for the Closure of the Quantum Metrology Triangle

Si quantum dot (QD) devices fabricated by MOSFET technology are promising for future and ultimate quantum electronics such as quantum electrical standards and quantum computers. We have developed Si tunable-barrier QD devices with a quasi-gate-all-around (GAA) nanowire [1], which are designed to be used as basic elements such as single-electron (SE) transfer devices and qubits; the precise manipulation of charges and their states are realized in the QDs. The device is especially suitable for high-speed tunable-barrier SE pumps driven at GHz frequencies [2,3] which can generate an electric current via a single QD precisely equal to the elementary charge times the driving frequency and thereby are promising for quantum current standards [4].To achieve a high accuracy using tunable-barrier SE pumps [5-7], proper designs of device structures are required to secure robust charge quantization. The potential shape of the QD and the entrance tunnel barrier [8] are critical parameters to dictate the pump accuracy because they determine the charging energy and energy filtering effect during SE capture into the QD. Furthermore, deep understanding of electron dynamics such as mechanism crossover of the dynamical charge quantization process [9] and quantum nonadiabatic excitation [10]/electron-phonon relaxation inside the QD are important to get optimal accuracy and extend the frequency breakdown of SE pumps. We have recently developed a device simulator of Si GAA-nanowire SE pumps [11], which is a useful tool to find optimal design and control parameters in all the above-mentioned respects.One of the long-desired targets of SE pumps is to close the quantum metrology triangle (QMT) [12] by checking the consistency among three quantum electrical standards: the SE current standard, the quantum Hall resistance standard, and Josephson voltage standard (JVS). The Japanese QMT project [13] has aimed to conduct the QMT experiment with sub-ppm uncertainty in a single dilution refrigerator by placing all the quantum electric standards inside it. Our key approaches are to use quantum Hall array resistance (QHAR) [14] and parallelized Si SE pumps, which provide higher resistance and current respectively, making the generated voltage more easily compared to JVS. In the project we have succeeded in developing a current-reversal technique with electromechanical relays to cancel out the drift and low frequency noise from various sources in the measurement setup, and applying it to high accuracy measurement of current delivered by a Si SE pump [15]. We have also recently performed a comparison measurement of two Si SE pump operated in parallel and thereby have confirmed a sub-ppm level accuracy [16]. All these progresses will lead to a more precise closure of QMT at deep sub-ppm level in the new future. Si MOSFET technology continues to expand its versatility into quantum electronics technology. This work was supported by JSPS KAKENHI Grant Number JP18H05258. A. Fujiwara et al., Appl. Phys. Lett. 84, 1323 (2004); Appl. Phys. Lett. 88 053121 (2006).A. Fujiwara et al., Appl. Phys. Lett. 92, 042102 (2008)G. Yamahata et al., Appl. Phys. Lett. 106, 023112 (2015).N.-H. Kaneko et al., Meas. Sci. Technology 27 032001 (2016).B. Kaestner and V. Kashcheyevs, Rep. Prog. Phys. 78, 103901 (2015).G. Yamahata et al., Appl. Phys. Lett. 109, 013101 (2016).S. P. Giblin et al., Metrologia 56, 044004 (2019).N. Johnson et al., Appl. Phys. Lett. 115, 162103 (2019).G. Yamahata et al., Phys. Rev. B 103, 245306 (2021).G. Yamahata et al., Nat. Nanotechnol. 14, 1019 (2019).A. Fujiwara et al., in the Conference on Precision Electromagnetic Measurements (CPEM 2022).F. Piquemal and G. Genevès, Metrologia 37, 207 (2000).https://www.jsps.go.jp/file/storage/grants/j-grantsinaid/12_kiban/ichiran_30/e-data/h_30_eng_18h05258.pdf; http://www.brl.ntt.co.jp/people/afuji/kakenS/ (only in Japanese).T. Oe et al., IEEE Trans. Instrum. Meas. 66, 1475 (2017).S. Nakamura et al., IEEE Trans. Instrum. Meas, under review.S. Nakamura et al., in preparation.

Perspectives of the generation and measurement of small electric currents

This paper provides a comprehensive overview of the historical background, current status, and future prospects related to the generation and measurement of small electric currents. It specifically caters to nonprofessional readers, with the aim of making the information comprehensible. A range of technologies are introduced, applicable in both basic research and industrial context. Quantum-mechanical approaches have been the focus of extensive efforts in this field, encompassing various types of single-electron pumps and combinations of two other quantum standards: the Josephson voltage standard and the quantized Hall resistance standard. These methods offer a reliable and precise means of generating and measuring small electric currents, minimizing uncertainties. However, operating complex cryogenic systems requires specialized expertise. Alternatively, conventional room-temperature systems are comparatively easier to handle. They employ low-noise amplifiers in conjunction with stable high-value resistors or capacitors charged with voltage ramps. This paper not only examines the characteristics of the both quantum and classical approaches from multiple perspectives but also outlines current and future applications for the generation and measurement of small electric currents.

Electrical switching of the edge current chirality in quantum anomalous Hall insulators.

A quantum anomalous Hall (QAH) insulator is a topological phase in which the interior is insulating but electrical current flows along the edges of the sample in either a clockwise or counterclockwise direction, as dictated by the spontaneous magnetization orientation. Such a chiral edge current eliminates any backscattering, giving rise to quantized Hall resistance and zero longitudinal resistance. Here we fabricate mesoscopic QAH sandwich Hall bar devices and succeed in switching the edge current chirality through thermally assisted spin-orbit torque (SOT). The well-quantized QAH states before and after SOT switching with opposite edge current chiralities are demonstrated through four- and three-terminal measurements. We show that the SOT responsible for magnetization switching can be generated by both surface and bulk carriers. Our results further our understanding of the interplay between magnetism and topological states and usher in an easy and instantaneous method to manipulate the QAH state.

On the calibration of DC resistance ratio bridges

Current comparator bridges are employed for the realization of the resistance scale from the quantum Hall effect in several National Metrology Institutes and calibration centers. Quantum resistance standards under development, based on novel materials and tabletop dry cryostats, make the more achievable DC current comparator bridges (DCCs) a viable alternative to the more accurate but more expensive cryogenic current comparator bridges (CCCs). A DCC ratios’ calibration against a reference CCC is a straightforward way to improve the DCC’s performances and the resistance scale overall accuracy.The paper reports the calibration results of two DCCs on the ratios employed in a 1Ω to 10kΩ resistance scale traceable to a 12.906kΩ quantized Hall resistance, showing a good reproducibility and stability of the DCC readings over the measurement period and supporting the possibility of a DCC errors’ correction and of a realization of the primary resistance scale at the 10-8 level.

Optimization of graphene-based quantum Hall arrays for recursive star–mesh transformations

A mathematical approach is adopted for optimizing the number of total device elements required for obtaining high effective quantized resistances in graphene-based quantum Hall array devices. This work explores an analytical extension to the use of star–mesh transformations such that fractal-like, or recursive, device designs can yield high enough resistances (like 1 EΩ, arguably the highest resistance with meaningful applicability) while still being feasible to build with modern fabrication techniques. Epitaxial graphene elements are tested, whose quantized Hall resistance at the ν=2 plateau (RH≈ 12 906.4 Ω) becomes the building block for larger effective, quantized resistances. It is demonstrated that, mathematically, one would not need more than 200 elements to achieve the highest pertinent resistances.

(Invited) Silicon Quantum Dot Single-Electron Pumps for the Closure of the Quantum Metrology Triangle

We have developed silicon quantum dot single-electron pumps for the application to quantum electrical standards. High-speed silicon pumps operated at GHz frequencies, generating a large current at a sub-nanoampere level, are promising for the realization of a precise closure of the quantum metrology triangle; it is a consistency check experiment with the quantum Hall resistance standard and Josephson voltage standard. We have found that, to improve the pump accuracy which is governed by the dynamical charge quantization process in a quantum dot, the optimal design and operation of pumps regarding the gate length and cross coupling to the quantum dot is important. The Japanese project, which aims at a precise closure of the quantum metrology triangle, is described with its recent progress.

Long-term stability of molecular doped epigraphene quantum Hall standards: single elements and large arrays (R K/236 ≈ 109 Ω)

In this work we investigate the long-term stability of epitaxial graphene (epigraphene) quantum Hall resistance standards, including single devices and an array device composed of 236 elements providing R K/236 ≈ 109 Ω, with R K the von Klitzing constant. All devices utilize the established technique of chemical doping via molecular dopants to achieve homogenous doping and control over carrier density. However, optimal storage conditions and the long-term stability of molecular dopants for metrological applications have not been widely studied. In this work we aim to identify simple storage techniques that use readily available and cost-effective materials which provide long-term stability for devices without the need for advanced laboratory equipment. The devices are stored in glass bottles with four different environments: ambient, oxygen absorber, silica gel desiccant, and oxygen absorber/desiccant mixture. We have tracked the carrier densities, mobilities, and quantization accuracies of eight different epigraphene quantum Hall chips for over two years. We observe the highest stability (i.e. lowest change in carrier density) for samples stored in oxygen absorber/desiccant mixture, with a relative change in carrier density below 0.01% per day and no discernable degradation of quantization accuracy at the part-per-billion level. This storage technique yields a comparable stability to the currently established best storage method of inert nitrogen atmosphere, but it is much easier to realize in practice. It is possible to further optimize the mixture of oxygen absorber/desiccant for even greater stability performance in the future. We foresee that this technique can allow for simple and stable long-term storage of polymer-encapsulated molecular doped epigraphene quantum Hall standards, removing another barrier for their wide-spread use in practical metrology.

Contrasting Transport Performance of Electron- and Hole-Doped Epitaxial Graphene for Quantum Resistance Metrology

Epitaxial graphene grown on silicon carbide (SiC/graphene) is a promising solution for achieving a high-precision quantum Hall resistance standard. Previous research mainly focused on the quantum resistance metrology of n-type SiC/graphene, while a comprehensive understanding of the quantum resistance metrology behavior of graphene with different doping types is lacking. Here, we fabricated both n- and p-type SiC/graphene devices via polymer-assisted molecular adsorption and conducted systematic magneto-transport measurements in a wide parameter space of carrier density and temperature. It is demonstrated that n-type devices show greater potential for development of quantum resistance metrology compared with p-type devices, as evidenced by their higher carrier mobility, lower critical magnetic field for entering quantized Hall plateaus, and higher robustness of the quantum Hall effect against thermal degeneration. These discrepancies can be reasonably attributed to the weaker scattering from molecular dopants for n-type devices, which is further supported by the analyses on the quantum interference effect in multiple devices. These results enrich our understanding of the charged impurity on electronic transport performance of graphene and, more importantly, provide a useful reference for future development of graphene-based quantum resistance metrology.

Realization of Graphene-based Quantum Hall Resistance Standard

Quantum Hall Resistance (QHR) standard replaced the physical resistance standard as a primary standard. Traditional QHR standard needs liquid helium to operate, which limits the application of the QHR standard. A graphene-based QHR standard with G-M cryocooler is realized, which does not need liquid helium and has been in operation continuously with high performance. It can meet extensive needs of accurate measurement of precision resistors and helps to promote the development of traceability flattening.

Exchange-Biased Quantum Anomalous Hall Effect.

The quantum anomalous Hall (QAH) effect is characterized by a dissipationless chiral edge state with a quantized Hall resistance at zero magnetic field. Manipulating the QAH state is of great importance in both the understanding of topological quantum physics and the implementation of dissipationless electronics. Here, the QAH effect is realized in the magnetic topological insulator Cr-doped (Bi,Sb)2 Te3 (CBST) grown on an uncompensated antiferromagnetic insulator Al-doped Cr2 O3 . Through polarized neutron reflectometry (PNR), a strong exchange coupling is found between CBST and Al-Cr2 O3 surface spins fixing interfacial magnetic moments perpendicular to the film plane. The interfacial coupling results in an exchange-biased QAH effect. This study further demonstrates that the magnitude and sign of the exchange bias can be effectively controlled using a field training process to set the magnetization of the Al-Cr2 O3 layer. It demonstrates the use of the exchange bias effect to effectively manipulate the QAH state, opening new possibilities in QAH-based spintronics.

Cryogenic sensor enabling broad-band and traceable power measurements

Recently, great progress has been made in the field of ultrasensitive microwave detectors, reaching even the threshold for utilization in circuit quantum electrodynamics. However, cryogenic sensors lack the compatibility with broad-band metrologically traceable power absorption measurements at ultralow powers, which restricts their range of applications. Here, we demonstrate such measurements using an ultralow-noise nanobolometer, which we extend by an additional direct-current (dc) heater input. The tracing of the absorbed power relies on comparing the response of the bolometer between radio frequency and dc-heating powers traced to the Josephson voltage and quantum Hall resistance. To illustrate this technique, we demonstrate two different methods of dc-substitution to calibrate the power that is delivered to the base temperature stage of a dilution refrigerator using our in situ power sensor. As an example, we demonstrate the ability to accurately measure the attenuation of a coaxial input line between the frequencies of 50MHz and 7GHz with an uncertainty down to 0.1 dB at a typical input power of -114 dBm.

Calibration of 10 nF capacitance standard from DC quantum Hall resistance using a digital impedance bridge

This paper describes the calibration of a 10 nF capacitance standard traced to the DC quantum Hall resistance primary standard using a multi-purpose digital impedance bridge. The bridge can directly compare the unlike impedances in the fully digital (FD) mode, so the capacitance standard can be calibrated by a direct comparison against the AC resistance standard. The measurement ability of the bridge in the FD mode was evaluated in various angles, and the bridge voltage dependencies were improved by selecting appropriate impedances for the high current arms and also by using an additional injection circuit. Thereby, the measurement accuracy could reach up to 10−7 in relative terms. Based on the bridge evaluation, a 10 nF capacitance standard was calibrated against a 10 kΩ resistance standard, and the measurement value agreed with a reference value in the level of 10−7.

Confinement-Induced Chiral Edge Channel Interaction in Quantum Anomalous Hall Insulators.

In quantum anomalous Hall (QAH) insulators, the interior is insulating but electrons can travel with zero resistance along one-dimensional (1D) conducting paths known as chiral edge channels (CECs). These CECs have been predicted to be confined to the 1D edges and exponentially decay in the two-dimensional (2D) bulk. In this Letter, we present the results of a systematic study of QAH devices fashioned in a Hall bar geometry of different widths under gate voltages. At the charge neutral point, the QAH effect persists in a Hall bar device with a width of only ∼72 nm, implying the intrinsic decaying length of CECs is less than ∼36 nm. In the electron-doped regime, we find that the Hall resistance deviates quickly from the quantized value when the sample width is less than 1 μm. Our theoretical calculations suggest that the wave function of CEC first decays exponentially and then shows a long tail due to disorder-induced bulk states. Therefore, the deviation from the quantized Hall resistance in narrow QAH samples originates from the interaction between two opposite CECs mediated by disorder-induced bulk states in QAH insulators, consistent with our experimental observations.