Letter | Published:

Controlling charge quantization with quantum fluctuations

Nature volume 536, pages 5862 (04 August 2016) | Download Citation

Abstract

In 1909, Millikan showed that the charge of electrically isolated systems is quantized in units of the elementary electron charge e. Today, the persistence of charge quantization in small, weakly connected conductors allows for circuits in which single electrons are manipulated, with applications in, for example, metrology, detectors and thermometry1,2,3,4,5. However, as the connection strength is increased, the discreteness of charge is progressively reduced by quantum fluctuations. Here we report the full quantum control and characterization of charge quantization. By using semiconductor-based tunable elemental conduction channels to connect a micrometre-scale metallic island to a circuit, we explore the complete evolution of charge quantization while scanning the entire range of connection strengths, from a very weak (tunnel) to a perfect (ballistic) contact. We observe, when approaching the ballistic limit, that charge quantization is destroyed by quantum fluctuations, and scales as the square root of the residual probability for an electron to be reflected across the quantum channel; this scaling also applies beyond the different regimes of connection strength currently accessible to theory6,7,8. At increased temperatures, the thermal fluctuations result in an exponential suppression of charge quantization and in a universal square-root scaling, valid for all connection strengths, in agreement with expectations8. Besides being pertinent for the improvement of single-electron circuits and their applications, and for the metal–semiconductor hybrids relevant to topological quantum computing9, knowledge of the quantum laws of electricity will be essential for the quantum engineering of future nanoelectronic devices.

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Acknowledgements

This work was supported by the European Research Council (ERC-2010-StG-20091028, no. 259033), the French RENATECH network, the national French programme ‘Investissements d’Avenir’ (Labex NanoSaclay, ANR-10-LABX-0035), the US Department of Energy (DE-FG02-08ER46482) and the Swiss National Science Foundation.

Author information

Author notes

    • S. Jezouin
    •  & Z. Iftikhar

    These authors contributed equally to this work.

Affiliations

  1. Centre de Nanosciences et de Nanotechnologies (C2N), CNRS, Université Paris Sud–Université Paris-Saclay, Université Paris Diderot-Sorbonne Paris Cité, 91120 Palaiseau, France

    • S. Jezouin
    • , Z. Iftikhar
    • , A. Anthore
    • , F. D. Parmentier
    • , U. Gennser
    • , A. Cavanna
    • , A. Ouerghi
    •  & F. Pierre
  2. Institute for Theoretical Physics, ETH Zurich, CH-8093 Zurich, Switzerland

    • I. P. Levkivskyi
  3. Département de Physique Théorique, Université de Genève, CH-1211 Genève, Switzerland

    • E. Idrisov
    •  & E. V. Sukhorukov
  4. Department of Physics, Yale University, New Haven, Connecticut 06520, USA

    • L. I. Glazman

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Contributions

S.J. and Z.I. performed the experiment with inputs from A.A. and F.P.; S.J., Z.I., A.A. and F.P. analysed the data; F.D.P. fabricated the sample and contributed to a preliminary experiment; U.G., A.C. and A.O. grew the 2DEG; I.P.L., E.I., E.V.S. and L.I.G. developed the strong thermal fluctuations theory; F.P. led the project and wrote the manuscript with inputs from all authors.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to F. Pierre.

Reviewer Information Nature thanks Y. Nazarov and the other anonymous reviewer(s) for their contribution to the peer review of this work.

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DOI

https://doi.org/10.1038/nature19072

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