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  • Letter
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An electron turnstile for frequency-to-power conversion

Nature Nanotechnology volume 17, pages 239–243 (2022)Cite this article

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Abstract

Single-electron transport relates an operation frequency f to the emitted current I through the electron charge e as I = ef (refs. 1,2,3,4,5). Similarly, direct frequency-to-power conversion (FPC) links both quantities through a known energy. FPC is a natural candidate for a power standard resorting to the most basic definition of the watt: energy emitted per unit of time. The energy is traceable to Planck’s constant and the time is in turn traceable to the unperturbed ground state hyperfine transition frequency of the caesium 133 atom. Hence, FPC comprises a simple and elegant way to realize the watt6. In this spirit, single-photon emission7,8 and detection9 at known rates have been proposed as radiometric standards and experimentally realized10,11,12,13,14. However, power standards are so far only traceable to electrical units, that is, to the volt and the ohm6,15,16,17. In this Letter, we demonstrate an alternative proposal based on solid-state direct FPC using a hybrid single-electron transistor (SET). The SET injects n (integer) quasi-particles (QPs) per cycle into the two superconducting leads with discrete energies close to their superconducting gap Δ, even at zero source-drain voltage. Furthermore, the application of a bias voltage can vary the distribution of the power among the two leads, allowing for an almost equal power injection nΔf into the two. While in single-electron transport current is related to a fixed universal constant (e), in our approach Δ is a material-dependent quantity. We estimate that under optimized conditions errors can be well below 1%.

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Fig. 1: Single-electron turnstile for frequency-to-power conversion.
Fig. 2: Power injection at zero bias.
Fig. 3: Power injection and dynamical behaviour of the device at zero bias.
Fig. 4: Power injection at non-zero bias.

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Data availability

Data supporting the manuscript and supplementary figures as well as further findings are available at https://doi.org/10.5281/zenodo.5727157 (ref. 34). Source data are provided with this paper.

Code availability

The codes for generating the measured manuscript and supplementary figures are available at https://doi.org/10.5281/zenodo.5727157 (ref. 34). Algorithms for generating calculated curves are available from the corresponding author upon reasonable request.

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Acknowledgements

We acknowledge O. Maillet and E. T. Mannila for useful discussions. This research made use of the Otaniemi Research Infrastructure for Micro and Nanotechnologies (OtaNano) and its Low Temperature Laboratory. We are grateful for funding from the Academy of Finland through grant 312057. M.M.-S. and J.P.P. acknowledge support from the European Union’s Horizon 2020 research and innovation programme under the European Research Council (ERC) programme (grant agreement 742559). J.P.P. acknowledges funding from the Russian Science Foundation (grant No. 20-62-46026).

Author information

Authors and Affiliations

  1. Pico group, QTF Centre of Excellence, School of Science, Department of Applied Physics, Aalto University, Aalto, Finland

    Marco Marín-Suárez, Joonas T. Peltonen, Dmitry S. Golubev & Jukka P. Pekola

  2. Moscow Institute of Physics and Technology, Dolgoprudny, Russia

    Jukka P. Pekola

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  1. Marco Marín-Suárez
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  3. Dmitry S. Golubev
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  4. Jukka P. Pekola
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Contributions

M.M.-S. made part of the fabrication, carried out the measurements, performed simulations and analysed the data with important input from J.P.P. and D.S.G. Most parts of the devices were fabricated by J.T.P who also prepared the measurement instruments. D.S.G. and J.P.P. estimated the heat losses along the system. The idea was conceived by M.M.-S. and J.P.P. The manuscript was prepared by M.M-S. with important input from J.P.P., J.T.P. and D.S.G.

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Correspondence to Marco Marín-Suárez.

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The authors declare no competing interests.

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Nature Nanotechnology thanks Vyacheslavs Kashcheyevs and Masaya Kataoka for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Current and injected power at f = 20 MHz.

Extension of Fig. 4a. a, Measured (dots) and simulated (lines) pumped current, colors correspond to the legend of panel (b). Data for Vb = 240 μV has been included for completeness. b, As in (a) for the power injected to the left lead. c, As in (b) for the right lead.

Source data

Extended Data Fig. 2 Current and injected power at f = 60 MHz.

Extension of Fig. 4b. a, Measured (dots) and simulated (lines) pumped current, colors correspond to the legend of panel (b). Data for Vb = 160 μV has been included for completeness. b, As in (a) for the power injected to the left lead. c, As in (b) for the right lead. Observe how power is more equally distributed as back-tunnelling disappears at Vb = 320 μV. This makes the power transmitted through the most transparent junction to decrease with bias voltage.

Source data

Extended Data Fig. 3 Current and injected power at f = 120 MHz.

a, Measured (dots) and simulated (lines) pumped current, colors correspond to the legend of panel (b). b, As in (a) for the power injected to the left lead. c, As in (b) for the right lead. Here the higher base temperature (Tb = 130 mK) has decreased the bolometers trapping efficiencies and hence the experimental power curves appear systematically below the calculated ones. However, the amount of injected power through the transistor junctions is not expected to vary. Observe how power is more equally distributed as back-tunnelling reduces. This makes the power transmitted through the most transparent junction to decrease with bias voltage.

Source data

Extended Data Fig. 4 Pumped current against bias voltage.

a, Experimental pumped current at constant amplitude with a driving frequency of 30, 60, 80, 160 MHz as blue, red, yellow and purple dots, respectively. Black lines are calculations made with a Markovian equation, the dashed lines designate the ideal pumped current I = ef. b, Differential conductance obtained by numerical differentiation of panel (a) data. Black lines are numerical derivatives of calculations of panel (a). Lower operation frequencies give sharper pumped current and conductance.

Source data

Supplementary information

Supplementary Information

Supplementary Figs. S1–S5, Sections S1–S7 and extra references.

Source data

Source Data Fig. 1

Fig. 1c original SEM image. With no colour and full size.

Source Data Fig. 2

Source data for Fig. 2 with each axis given as a separate sheet.

Source Data Fig. 3

Source data for Fig. 3. Panels separated in different sheets. Measured and calculated curves in different sheets. Figure 3g axes in different sheets.

Source Data Fig. 4

Source data for Fig. 4. Panels separated in different sheets. Measured and calculated curves in different sheets.

Source Data Extended Data Fig. 1

Source data for Extended Data Fig. 1. Panels separated in different sheets. Measured and calculated curves in different sheets.

Source Data Extended Data Fig. 2

Source data for Extended Data Fig. 2. Panels separated in different sheets. Measured and calculated curves in different sheets.

Source Data Extended Data Fig. 3

Source data for Extended Data Fig. 3. Panels separated in different sheets. Measured and calculated curves in different sheets.

Source Data Extended Data Fig. 4

Source data for Extended Data Fig. 4. Panels separated in different sheets. Measured and calculated curves in different sheets.

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Marín-Suárez, M., Peltonen, J.T., Golubev, D.S. et al. An electron turnstile for frequency-to-power conversion. Nat. Nanotechnol. 17, 239–243 (2022). https://doi.org/10.1038/s41565-021-01053-5

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