• Mills, I. M., Mohr, P. J., Quinn, T. J., Taylor, B. N. & Williams, E. R. Redefinition of the kilogram: a decision whose time has come. Metrologia 42, 71–80 (2005).


    Google Scholar
     

  • Milton, M. J., Davis, R. & Fletcher, N. Towards a new SI: a review of progress made since 2011. Metrologia 51, R21 (2014).


    Google Scholar
     

  • Davis, R. An introduction to the revised international system of units (si). IEEE Instrum. Meas. Mag. 22, 4–8 (2019).


    Google Scholar
     

  • Poirier, W., Djordjevic, S., Schopfer, F. & Thévenot, O. The ampere and the electrical units in the quantum era. C. R. Phys. 20, 92–128 (2019).


    Google Scholar
     

  • Taylor, B. & Witt, T. New international electrical reference standards based on the Josephson and quantum Hall effects. Metrologia 26, 47–62 (1989).


    Google Scholar
     

  • Jeckelmann, B. & Jeanneret, B. The quantum Hall effect as an electrical resistance standard. Rep. Prog. Phys. 64, 1603–1655 (2001).


    Google Scholar
     

  • Tzalenchuk, A. et al. Towards a quantum resistance standard based on epitaxial graphene. Nat. Nanotechnol. 5, 186–189 (2010).


    Google Scholar
     

  • Schopfer, F. & Poirier, W. Quantum resistance standard accuracy close to the zero-dissipation state. J. Appl. Phys. 114, 064508 (2013).


    Google Scholar
     

  • Ribeiro-Palau, R. et al. Quantum hall resistance standard in graphene devices under relaxed experimental conditions. Nat. Nanotechnol. 10, 965–971 (2015).


    Google Scholar
     

  • Rigosi, A. F. & Elmquist, R. E. The quantum Hall effect in the era of the new SI. Semicond. Sci. Technol. 34, 093004 (2019).


    Google Scholar
     

  • Bloch, F. Josephson effect in a superconducting ring. Phys. Rev. B 2, 109–121 (1970).


    Google Scholar
     

  • Fulton, T. A. Implications of solid-state corrections to the Josephson voltage-frequency relation. Phys. Rev. B 7, 981–982 (1973).


    Google Scholar
     

  • Clothier, W., Sloggett, G., Bairnsfather, H., Currey, M. & Benjamin, D. A determination of the volt. Metrologia 26, 9–46 (1989).


    Google Scholar
     

  • Tiesinga, E., Mohr, P. J., Newell, D. B. & Taylor, B. N. CODATA recommended values of the fundamental physical constants: 2018. Rev. Mod. Phys. 93, 025010 (2021).


    Google Scholar
     

  • Keller, M. W. Current status of the quantum metrology triangle. Metrologia 45, 102–109 (2008).

    MathSciNet 

    Google Scholar
     

  • Scherer, H. & Camarota, B. Quantum metrology triangle experiments: a status review. Meas. Sci. Technol. 23, 124010 (2012).


    Google Scholar
     

  • Hohls, F. et al. Semiconductor quantized voltage source. Phys. Rev. Lett. 109, 056802 (2012).


    Google Scholar
     

  • Brun-Picard, J., Djordjevic, S., Leprat, D., Schopfer, F. & Poirier, W. Practical quantum realization of the ampere from the elementary charge. Phys. Rev. X 6, 041051 (2016).


    Google Scholar
     

  • Djordjevic, S., Behr, R. & Poirier, W. A primary quantum current standard based on the Josephson and the quantum Hall effects. Nat. Commun. 16, 1447 (2025).


    Google Scholar
     

  • Sullivan, D. & Dziuba, R. F. Low temperature direct current comparators. Rev. Sci. Instrum. 45, 517–519 (1974).


    Google Scholar
     

  • Williams, J. Cryogenic current comparators and their application to electrical metrology. IET Sci. Meas. Technol. 5, 211–224 (2011).


    Google Scholar
     

  • Chae, D.-H., Kim, M.-S., Kim, W.-S., Oe, T. & Kaneko, N.-H. Quantum mechanical current-to-voltage conversion with quantum Hall resistance array. Metrologia 57, 025004 (2020).


    Google Scholar
     

  • Chae, D.-H., Kim, M.-S., Oe, T. & Kaneko, N.-H. Series connection of quantum Hall resistance array and programmable Josephson voltage standard for current generation at one microampere. Metrologia 59, 065011 (2022).


    Google Scholar
     

  • Chen, Y. et al. Massive Dirac fermion on the surface of a magnetically doped topological insulator. Science 329, 659–662 (2010).


    Google Scholar
     

  • Yu, R. et al. Quantized anomalous Hall effect in magnetic topological insulators. Science 329, 61–64 (2010).


    Google Scholar
     

  • Checkelsky, J. G., Ye, J., Onose, Y., Iwasa, Y. & Tokura, Y. Dirac-fermion-mediated ferromagnetism in a topological insulator. Nat. Phys. 8, 729–733 (2012).


    Google Scholar
     

  • Fox, E. J. et al. Part-per-million quantization and current-induced breakdown of the quantum anomalous Hall effect. Phys. Rev. B 98, 075145 (2018).


    Google Scholar
     

  • Götz, M. et al. Precision measurement of the quantized anomalous Hall resistance at zero magnetic field. Appl. Phys. Lett. 112, 072102 (2018).


    Google Scholar
     

  • Rodenbach, L. K. et al. Metrological assessment of quantum anomalous Hall properties. Phys. Rev. Appl. 18, 034008 (2022).


    Google Scholar
     

  • Okazaki, Y. et al. Quantum anomalous Hall effect with a permanent magnet defines a quantum resistance standard. Nat. Phys. 18, 25–29 (2022).


    Google Scholar
     

  • Patel, D. K. et al. A zero external magnetic field quantum standard of resistance at the 10−9 level. Nat. Electron. 7, 1111–1116 (2024).


    Google Scholar
     

  • Stewart, W. Current-voltage characteristics of Josephson junctions. Appl. Phys. Lett. 12, 277–280 (1968).


    Google Scholar
     

  • Kautz, R. L. Design and operation of series-array Josephson voltage standards. In Proc. International School of Physics ‘Enrico Fermi’, Course CX, 27 June–7 July, 1989 (eds Crovini, L. & Quinn, T. J.) 259–296 (Eslevier, 1992).

  • Kautz, R. L. Shapiro steps in large-area metallic-barrier Josephson junctions. J. Appl. Phys. 78, 5811–5819 (1995).


    Google Scholar
     

  • Rosen, I. T. et al. Measured potential profile in a quantum anomalous Hall system suggests bulk-dominated current flow. Phys. Rev. Lett. 129, 246602 (2022).


    Google Scholar
     

  • Lippertz, G. et al. Current-induced breakdown of the quantum anomalous Hall effect. Phys. Rev. B 106, 045419 (2022).


    Google Scholar
     

  • Gotz, M. et al. Improved cryogenic current comparator setup with digital current sources. IEEE Trans. Instrum. Meas. 58, 1176–1182 (2009).


    Google Scholar
     

  • Drung, D. et al. Improving the stability of cryogenic current comparator setups. Supercond. Sci. Technol. 22, 114004 (2009).


    Google Scholar
     

  • Drung, D., Götz, M., Pesel, E., Barthelmess, H. J. & Hinnrichs, C. Aspects of application and calibration of a binary compensation unit for cryogenic current comparator setups. IEEE Trans. Instrum. Meas. 62, 2820–2827 (2013).


    Google Scholar
     

  • Mise en Pratique for the Definition of the Ampere and Other Electrical Units (BIPM, 2019); www.bipm.org/documents/20126/41489676/SI-App2-ampere.pdf/0987a90e-051b-dd7f-827d-3f7b32751a61

  • BIPM et al. Evaluation of Measurement Data—Guide to the Expression of Uncertainty in Measurement. JCGM 100:2008 (JCGM, 2008); www.bipm.org/documents/20126/2071204/JCGM_100_2008_E.pdf

  • Calibration and measurement capabilities electricity and magnetism: DC current (low and intermediate values). BIPM www.bipm.org/kcdb/ (2023).

  • Keller, M. W., Zimmerman, N. M. & Eichenberger, A. L. Uncertainty budget for the NIST electron counting capacitance standard, ECCS-1. Metrologia 44, 505–512 (2007).


    Google Scholar
     

  • Camarota, B. et al. Electron counting capacitance standard with an improved five-junction R-pump. Metrologia 49, 8–14 (2011).


    Google Scholar
     

  • Giblin, S. et al. Towards a quantum representation of the ampere using single electron pumps. Nat. Commun. 3, 930 (2012).


    Google Scholar
     

  • Stein, F. et al. Validation of a quantized-current source with 0.2 ppm uncertainty. Appl. Phys. Lett. 107, 103501 (2015).


    Google Scholar
     

  • Bae, M.-H. et al. Precision measurement of single-electron current with quantized Hall array resistance and Josephson voltage. Metrologia 57, 065025 (2020).


    Google Scholar
     

  • Stein, F. et al. Robustness of single-electron pumps at sub-ppm current accuracy level. Metrologia 54, S1–S8 (2016).


    Google Scholar
     

  • Yamahata, G., Giblin, S. P., Kataoka, M., Karasawa, T. & Fujiwara, A. Gigahertz single-electron pumping in silicon with an accuracy better than 9.2 parts in 107. Appl. Phys. Lett. 109, 013101 (2016).


    Google Scholar
     

  • Zhao, R. et al. Thermal-error regime in high-accuracy gigahertz single-electron pumping. Phys. Rev. Appl. 8, 044021 (2017).


    Google Scholar
     

  • Giblin, S., Yamahata, G., Fujiwara, A. & Kataoka, M. Precision measurement of an electron pump at 2 GHz; the frontier of small DC current metrology. Metrologia 60, 055001 (2023).


    Google Scholar
     

  • Bestwick, A. et al. Precise quantization of the anomalous Hall effect near zero magnetic field. Phys. Rev. Lett. 114, 187201 (2015).


    Google Scholar
     

  • White, M. et al. Direct implementation of a frequency-programmable Josephson voltage standard to provide an SI traceable optical power scale. Metrologia 61, 045002 (2024).


    Google Scholar
     

  • Fox, A. E., Dresselhaus, P. D., Rüfenacht, A., Sanders, A. & Benz, S. P. Junction yield analysis for 10 V programmable Josephson voltage standard devices. IEEE Trans. Appl. Supercond. 25, 1–5 (2014).


    Google Scholar
     

  • Fox, A. E., Butler, G., Thompson, M., Dresselhaus, P. D. & Benz, S. P. Induced current effects in Josephson voltage standard circuits. IEEE Trans. Appl. Supercond. 29, 1–8 (2019).


    Google Scholar
     

  • Rodenbach, L. K. et al. Bulk dissipation in the quantum anomalous Hall effect. APL Mater. 9, 081116 (2021).


    Google Scholar