Academic Background and Problem Statement

In metrology, the quantum Hall effect (QHE) and the Josephson effect respectively provide quantum standards for electrical resistance (ohm) and voltage (volt). However, conventional quantum Hall resistance standards (QHRs) rely on strong external magnetic fields (typically requiring superconducting magnets generating fields above 10 tesla), limiting their practical applicability— especially when integrated with Josephson voltage standards (JVS), which cannot operate under magnetic fields. Therefore, achieving a high-precision quantum resistance standard under zero external magnetic field has become a critical research direction.

The discovery of the quantum anomalous Hall effect (QAHE) provides a potential solution to this issue. QAHE enables the quantization of Hall resistance in magnetic topological insulators (TIs) without the need for external magnetic fields. However, realizing QAHE imposes stringent conditions, typically requiring ultra-low temperatures (below 50 millikelvin) and very low bias currents (below 1 microampere). Additionally, insufficient insulation of the bulk and surface states of materials may limit the accuracy of quantization. Consequently, developing high-precision QAHE-based quantum resistance standards under zero external magnetic fields remains an important challenge in the field.

Paper Source and Author Information

This study, authored by D. K. Patel, K. M. Fijalkowski, M. Kruskopf, and others from the Physikalisch-Technische Bundesanstalt (PTB) in Germany and Universität Würzburg, was published in Nature Electronics in December 2024 under the title “A zero external magnetic field quantum standard of resistance at the 10⁻⁹ level.”

Research Methodology and Experimental Process

1. Device Preparation and Characterization

The research team first grew a 9-nanometer-thick layer of V-doped (Bi,Sb)₂Te₃, a magnetic topological insulator, on a hydrogen-passivated Si(111) substrate using molecular beam epitaxy (MBE). A 10-nanometer-thick protective layer of insulating Te was subsequently deposited. Standard photolithography was employed to fabricate a Hall bar device with a width of 200 micrometers and a length of 730 micrometers. The device consisted of nine electrodes, including a source, a drain, an electrostatic gate, and three pairs of Hall voltage contacts. To ensure ohmic contacts, the Te layer was locally removed via Ar ion milling, followed by electron-beam deposition of a metallic AuGe/Ti/Au layer stack. The top of the device was then coated with a dielectric layer (20 nanometers of AlOx/HfOx) and a 100-nanometer-thick Ti/Au gate layer.

2. Characterization of the Quantum Anomalous Hall Effect

To measure the quantization of Hall resistance under zero external magnetic fields, the team performed experiments in a dilution refrigerator at a base temperature of 34 millikelvin with a gate voltage of 5.8 volts. Using lock-in amplifier techniques, they measured the Hall resistance (Rxy) as a function of an applied perpendicular magnetic field. The measurements exhibited a characteristic ferromagnetic hysteresis loop, with Hall resistance switching between +h/e² and -h/e² depending on the magnetic orientation in the film (where h is Planck’s constant, and e is the elementary charge). Unlike traditional QHRs devices, this device required only a temporary magnetic field of approximately 1 tesla for initializing magnetization before measurements, which were then conducted in a zero-field environment.

3. Precision Measurements

To enhance measurement accuracy, the team employed a cryogenic current comparator (CCC)-based resistance bridge. The 14-bit CCC used in the experiments provided higher precision compared to earlier 12-bit CCC systems. A stable, calibrated 100-ohm resistor served as the reference. By employing a superconducting quantum interference device (SQUID) in combination with the CCC, the net magnetic flux from the measurement setup was detected and balanced to determine the QAHE device resistance with high precision.

Major Results and Data Analysis

1. Accuracy of Hall Resistance Quantization

The results revealed that, when extrapolated to zero measurement current, the deviation of the measured Hall resistance from the von Klitzing constant (RK = h/e²) was (4.4 ± 8.7) nΩ/Ω. When extrapolated to zero longitudinal resistivity (indicative of zero dissipation), the deviation was (8.6 ± 6.7) nΩ/Ω. This precision—achieving a 10⁻⁹ level of relative uncertainty—meets the requirements for metrological applications.

2. Current-Dependent Measurements

The study observed a significant drop in the accuracy of Hall resistance quantization and a sharp increase in longitudinal resistivity when the applied current exceeded 160 nanoamperes. This suggests the onset of current-induced breakdown in the QAHE. The longitudinal resistivity was found to follow an exponential relationship with the applied current, further supporting this observation.

3. Extrapolation Analysis of Quantization Accuracy

To minimize the impact of dissipation on quantization accuracy, the team analyzed the relationship between Hall resistance deviations and longitudinal resistivity. When extrapolated to zero longitudinal resistivity, the deviation in Hall resistance was (8.6 ± 6.7) nΩ/Ω. Similarly, when extrapolated to zero current, the deviation was (4.4 ± 8.7) nΩ/Ω. These results improve the precision of QAHE quantization under zero external magnetic fields by approximately two orders of magnitude compared to previous studies.

Conclusions and Significance

This study demonstrates a zero external magnetic field quantum resistance standard achieving a 10⁻⁹ level of precision using a V-doped (Bi,Sb)₂Te₃ magnetic topological insulator device. The results lay the groundwork for establishing a zero-field quantum resistance standard and suggest the potential for integration with Josephson voltage standards to create a universal quantum electrical reference standard. This study not only advances the fundamental understanding of QAHE but also holds significant implications for future metrology applications.

Research Highlights

1. High-Precision Quantization: Achieved a 10⁻⁹ level of precision in Hall resistance quantization under zero external magnetic field, meeting the criteria for metrological applications.
2. Zero-Field Operation: Successfully eliminated the need for external magnetic fields, addressing a key limitation of traditional QHRs devices.
3. Integration Potential: The device is poised to enable the integration of quantum resistance and voltage standards into a unified universal reference.

Additional Valuable Information

The paper includes comprehensive details on the fabrication process and experimental methodologies. All supporting data are publicly available via PTB’s open-access repository, offering valuable resources for further research in this area.