Pseudofractal Networks Enhance Quantized Resistance Outputs in Quantum Hall Devices

The pursuit of exceptionally precise electrical resistance standards drives innovation in metrology, and a new approach to graphene-based quantum Hall arrays promises to significantly expand the accessible range of resistance values. Researchers led by N. T. M. Tran from the National Institute of Standards and Technology, M. Musso from Politecnico di Torino, and D. S. Scaletta from Mount San Jacinto College, demonstrate a novel cross-square network configuration for quantum Hall array resistance standards (QHARS). This design departs from traditional wye-delta arrangements and incorporates a pseudofractal-like recursion, enabling the creation of devices with dramatically higher effective resistance outputs than previously possible. The team achieves resistances of 55. 81 MΩ and 27. 61 GΩ in initial configurations, with theoretical projections reaching 317. 95 TΩ, ultimately pushing the boundaries of high-value quantum resistance standards and revealing limitations in current cryogenic measurement techniques.

In electrical metrology, the quantum Hall effect is accessed at specific conditions to define and disseminate the unit of electrical resistance, the ohm. The robustness of this effect is limited to certain conditions, which constrains the range of accessible resistance values when constructing resistance standards. This motivates research into alternative quantum Hall plateaus that could broaden this range and improve the precision of resistance standards. Investigations therefore focus on enhancing the stability and reproducibility of these alternative quantum Hall states to realise their potential for practical resistance metrology.

Graphene Quantum Hall Resistance Standard Development

Researchers are developing highly accurate, stable, and scalable resistance standards based on the quantum Hall effect in graphene. The goal is to move beyond traditional standards and create a new generation capable of meeting the demands of precision measurement, specifically achieving resistance values in the gigohm range and beyond with extremely low uncertainty. Graphene, a single-layer sheet of carbon atoms, is an ideal material due to its high carrier mobility and potential for large-area fabrication. A crucial technique involves implementing star-mesh networks, connecting multiple graphene-based quantum Hall devices in a specific configuration to achieve higher resistance values while maintaining accuracy.

Researchers are exploring recursive star-mesh designs to achieve even higher resistance values, optimizing these complex designs with pseudofractal analysis and accurate SPICE models to simulate and refine designs before fabrication. Uniformly doped graphene is essential for achieving stable and reproducible quantum Hall effect measurements. The star-mesh approach is designed to be scalable, allowing for the creation of even higher resistance standards. Improving the long-term stability of these standards is a key focus, alongside creating versatile standards for both tabletop measurements and high-current applications.

Successful fabrication and characterization of graphene-based star-mesh networks demonstrate progress towards these goals, utilizing epitaxial graphene grown on silicon carbide with chromium tricarbonyl functionalization to tune carrier density. Challenges remain in optimizing network geometry, minimizing contact resistance, and improving stability. Pushing the limits of resistance by creating even more complex recursive networks and integrating these standards into existing metrological infrastructure are ongoing areas of focus. This research represents a significant step towards a new generation of high-resistance standards based on the quantum Hall effect in graphene, holding the promise of unprecedented levels of accuracy and stability in resistance metrology.

Fractal Network Boosts Resistance Standards Terahertz Range

Researchers have developed a new approach to creating highly accurate electrical resistance standards, extending the boundaries of quantum metrology into the teraohm range and beyond. This work utilizes a cross-square network configuration, inspired by fractal geometry, to dramatically increase the effective resistance output, achieving standards with resistances of 55. 81 megaohms and 27. 61 gigohms. The team’s approach not only increases resistance but also demonstrates the potential to reach even higher values, with theoretical projections reaching 317.
Measurements revealed limitations imposed by resistance leakage within conventional cryogenic setups, highlighting the need for custom probes with exceptional electrical insulation. Despite these limitations, the devices successfully withstood prolonged exposure to high voltages, including 500 volts, demonstrating their robustness and reliability. This new design, utilizing a maximum of 94 elements, offers a substantial improvement over traditional methods that require hundreds of Hall elements in series to achieve comparable resistances. By employing a pseudofractal-like recursion, the team has established a framework for accessing extremely high quantized resistances, paving the way for more accurate and reliable electrical measurements in a variety of scientific and industrial applications.

High-Value Resistance via Quantum Hall Arrays

This research demonstrates a significant advancement in the realization of high-value quantum resistance standards, achieving effective resistances of 55. 81 megaohms and 27. 61 gigohms using quantum Hall array resistance standards. The team employed a cross-square network configuration, building upon existing designs and incorporating a pseudofractal-like recursion to amplify resistance outputs, successfully overcoming limitations associated with conventional series or parallel Hall element arrangements. The study highlights the potential for even higher resistances, hypothetically projecting values up to 317.
Measurements also revealed practical limitations imposed by conventional cryogenic systems due to resistance leakage, indicating areas for future technological development. This research contributes to the ongoing effort to redefine electrical units within the International System of Units.