Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Bipolar thermoelectric Josephson engine

Nature Nanotechnology volume 17, pages 1084–1090 (2022)Cite this article

Subjects

Abstract

Thermoelectric effects in metals are typically small due to the nearly perfect particle–hole symmetry around their Fermi surface. Furthermore, thermo-phase effects and linear thermoelectricity in superconducting systems have been identified only when particle–hole symmetry is explicitly broken, since thermoelectric effects were considered impossible in pristine superconductors. Here, we experimentally demonstrate that superconducting tunnel junctions develop a very large bipolar thermoelectricity in the presence of a sizable thermal gradient thanks to spontaneous particle–hole symmetry breaking. Our junctions show Seebeck coefficients of up to ±300 μV K–1, which is comparable with quantum dots and roughly 105 times larger than the value expected for normal metals at subkelvin temperatures. Moreover, by integrating our junctions into a Josephson interferometer, we realize a bipolar thermoelectric Josephson engine generating phase-tunable electric powers of up to ~140 nW mm–2. Notably, our device implements also the prototype for a persistent thermoelectric memory cell, written or erased by current injection. We expect that our findings will lead to applications in superconducting quantum technologies.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Bipolar thermoelectric Josephson engine.
Fig. 2: Bipolar thermoelectric effect.
Fig. 3: Low temperature behaviour of the BTJE.
Fig. 4: Temperature dependence of the BTJE.

Similar content being viewed by others

Data availability

All data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request.

References

  1. Ashcroft, N. & Mermin, N. Solid State Physics (Holt-Saunders, 1976).

    Google Scholar 

  2. Abrikosov, A. A. Fundamentals of the Theory of Metals (Courier Dover Publications, 2017).

  3. Mott, N. F. & Jones, H. The Theory of the Properties of Metals and Alloys (Dover Publications, 1958).

    Google Scholar 

  4. Mamin, H. J., Clarke, J. & Van Harlingen, D. J. Charge imbalance induced by a temperature gradient in superconducting aluminum. Phys. Rev. B 29, 3881–3890 (1984).

    Article  CAS  Google Scholar 

  5. Meissner, W. Z. Das elektrische verhalten der metalle im temperaturgebiet des flüssigen heliums. Z. Ges. Kälte Industrie 34, 197 (1927).

    Google Scholar 

  6. Ginzburg, V. On the thermoelectric phenomena in superconductors. Zh. Eksp. Teor. Fiz. 14, 134 (1944).

    Google Scholar 

  7. Shelly, C. D., Matrozova, E. A. & Petrashov, V. T. Resolving thermoelectric ‘paradox’ in superconductors. Science 2, e1501250 (2016).

    Google Scholar 

  8. Guttman, G. D., Nathanson, B., Ben-Jacob, E. & Bergman, D. J. Thermoelectric and thermophase effects in Josephson junctions. Phys. Rev. B 55, 12691–12700 (1997).

    Article  CAS  Google Scholar 

  9. Giazotto, F., Heikkilä, T. T. & Bergeret, F. S. Very large thermophase in ferromagnetic Josephson junctions. Phys. Rev. Lett. 114, 067001 (2015).

    Article  CAS  Google Scholar 

  10. Kleeorin, Y., Meir, Y., Giazotto, F. & Dubi, Y. Large tunable thermophase in superconductor – quantum dot – superconductor Josephson junctions. Sci. Rep. 6, 35116 (2016).

    Article  CAS  Google Scholar 

  11. Smith, A. D., Tinkham, M. & Skocpol, W. J. New thermoelectric effect in tunnel junctions. Phys. Rev. B 22, 4346–4354 (1980).

    Article  CAS  Google Scholar 

  12. Machon, P., Eschrig, M. & Belzig, W. Nonlocal thermoelectric effects and nonlocal Onsager relations in a three-terminal proximity-coupled superconductor-ferromagnet device. Phys. Rev. Lett. 110, 047002 (2013).

    Article  CAS  Google Scholar 

  13. Ozaeta, A., Virtanen, P., Bergeret, F. S. & Heikkilä, T. T. Predicted very large thermoelectric effect in ferromagnet-superconductor junctions in the presence of a spin-splitting magnetic field. Phys. Rev. Lett. 112, 057001 (2014).

    Article  CAS  Google Scholar 

  14. Kolenda, S., Wolf, M. J. & Beckmann, D. Observation of thermoelectric currents in high-field superconductor-ferromagnet tunnel junctions. Phys. Rev. Lett. 116, 097001 (2016).

    Article  CAS  Google Scholar 

  15. Bergeret, F. S., Silaev, M., Virtanen, P. & Heikkilä, T. T. Colloquium: nonequilibrium effects in superconductors with a spin-splitting field. Rev. Mod. Phys. 90, 041001 (2018).

    Article  CAS  Google Scholar 

  16. Linder, J. & Robinson, J. W. A. Superconducting spintronics. Nat. Phys. 11, 307–315 (2015).

    Article  CAS  Google Scholar 

  17. Virtanen, P. & Heikkilä, T. T. Thermopower induced by a supercurrent in superconductor–normal-metal structures. Phys. Rev. Lett. 92, 177004 (2004).

    Article  Google Scholar 

  18. Blasi, G., Taddei, F., Arrachea, L., Carrega, M. & Braggio, A. Nonlocal thermoelectricity in a superconductor–topological-insulator–superconductor junction in contact with a normal-metal probe: evidence for helical edge states. Phys. Rev. Lett. 124, 227701 (2020).

    Article  CAS  Google Scholar 

  19. Tan, Z. B. et al. Thermoelectric current in a graphene Cooper pair splitter. Nat. Commun. 12, 138 (2021).

    Article  Google Scholar 

  20. Eom, J., Chien, C.-J. & Chandrasekhar, V. Phase dependent thermopower in Andreev interferometers. Phys. Rev. Lett. 81, 437–440 (1998).

    Article  CAS  Google Scholar 

  21. Jiang, Z. & Chandrasekhar, V. Quantitative measurements of the thermal resistance of Andreev interferometers. Phys. Rev. B 72, 020502(R) (2005).

    Article  Google Scholar 

  22. Hofstetter, L., Csonka, S., Nygård, J. & Schönenberger, C. Cooper pair splitter realized in a two-quantum-dot Y-junction. Nature 461, 960–963 (2009).

    Article  CAS  Google Scholar 

  23. Benenti, G., Casati, G., Saito, K. & Whitney, R. S. Fundamental aspects of steady-state conversion of heat to work at the nanoscale. Phys. Rep. 694, 1–124 (2017).

    Article  CAS  Google Scholar 

  24. Campisi, M., Pekola, J. P. & Fazio, R. Nonequilibrium fluctuations in quantum heat engines: theory, example, and possible solid state experiments. N. J. Phys. 17, 035012 (2015).

    Article  Google Scholar 

  25. Bera, M. L., Lewenstein, M. & Bera, M. N. Attaining Carnot efficiency with quantum and nanoscale heat engines. npj Quantum Inf. 7, 31 (2021).

    Article  Google Scholar 

  26. Josefsson, M. et al. A quantum-dot heat engine operating close to the thermodynamic efficiency limits. Nat. Nanotechnol. 13, 920–924 (2018).

    Article  CAS  Google Scholar 

  27. Dubi, Y. & Di Ventra, M. Colloquium: heat flow and thermoelectricity in atomic and molecular junctions. Rev. Mod. Phys. 83, 131 (2011).

    Article  CAS  Google Scholar 

  28. Ono, K., Shevchenko, S. N., Mori, T., Moriyama, S. & Nori, F. Analog of a quantum heat engine using a single-spin qubit. Phys. Rev. Lett. 125, 166802 (2020).

    Article  CAS  Google Scholar 

  29. Marchegiani, G., Braggio, A. & Giazotto, F. Nonlinear thermoelectricity with electron-hole symmetric systems. Phys. Rev. Lett. 124, 106801 (2020).

    Article  CAS  Google Scholar 

  30. Roddaro, S. et al. Giant thermovoltage in single InAs nanowire field-effect transistors. Nano Lett. 13, 3638–3642 (2013).

    Article  CAS  Google Scholar 

  31. Soleimani, Z., Zoras, S., Ceranic, B., Shazad, S. & Cui, Y. A review on recent developments of thermoelectric materials for room-temperature applications. Sustain. Energy Technol. Assess. 37, 100604 (2020).

    Google Scholar 

  32. Mani, P., Nakpathomkun, N. & Linke, H. Intrinsic Seebeck coefficient of quantum dots. J. Electron. Mater. 38, 1163–1165 (2009).

    Article  CAS  Google Scholar 

  33. Prete, D. et al. Thermoelectric conversion at 30 K in InAs/InP nanowire quantum dots. Nano Lett. 19, 3033–3039 (2019).

    Article  CAS  Google Scholar 

  34. Marchegiani, G., Braggio, A. & Giazotto, F. Phase-tunable thermoelectricity in a Josephson junction. Phys. Rev. Res. 2, 043091 (2020).

    Article  CAS  Google Scholar 

  35. Marchegiani, G., Braggio, A. & Giazotto, F. Superconducting nonlinear thermoelectric heat engine. Phys. Rev. B 101, 214509 (2020).

    Article  CAS  Google Scholar 

  36. Giazotto, F., Paolucci, F., Braggio, A., Marchegiani, G. & Germanese G. Superconducting bipolar thermoelectric memory and method for writing a superconducting bipolar thermoelectric memory. Italian patent: 102021000032042 (2021).

  37. Kemppinen, A. et al. Suppression of the critical current of a balanced superconducting quantum interference device. Appl. Phys. Lett. 92, 052110 (2008).

    Article  Google Scholar 

  38. Fornieri, A., Blanc, C., Bosisio, R., D’Ambrosio, S. & Giazotto, F. Nanoscale phase engineering of thermal transport with a Josephson heat modulator. Nat. Nanotechnol. 11, 258–262 (2016).

    Article  CAS  Google Scholar 

  39. Giazotto, F., Heikkilä, T. T., Luukanen, A., Savin, A. M. & Pekola, J. P. Opportunities for mesoscopics in thermometry and refrigeration: physics and applications. Rev. Mod. Phys. 78, 217 (2006).

    Article  CAS  Google Scholar 

  40. Fornieri, A. & Giazotto, F. Towards phase-coherent caloritronics in superconducting circuits. Nat. Nanotechnol. 12, 944–952 (2017).

    Article  CAS  Google Scholar 

  41. Aronov, A. G. & Spivak, B. Z. Photoeffect in a Josephson junction. JETP Lett. 22, 101–102 (1975).

    Google Scholar 

  42. Gershenzon, M. E. & Falei, M. I. Absolute negative resistance of a tunnel contact between superconductors with a nonequilibrium quasiparticle distribution function. JETP Lett. 44, 682–686 (1986).

    Google Scholar 

  43. Bogoliubov, N. N. Lectures on Quantum Statistics (Gordon and Breach, 1970).

  44. Strocchi, F. Symmetry Breaking (Springer, 2008).

  45. Timofeev, A. V. et al. Recombination-limited energy relaxation in a Bardeen-Cooper-Schrieffer superconductor. Phys. Rev. Lett. 102, 017003 (2009).

    Article  CAS  Google Scholar 

  46. Ladd, T. D. et al. Quantum computers. Nature 464, 45–53 (2010).

    Article  CAS  Google Scholar 

  47. Siddiqi, I. Engineering high-coherence superconducting qubits. Nat. Rev. Mater. 6, 875–891 (2021).

    Article  Google Scholar 

  48. Polini, M. et al. Materials and devices for fundamental quantum science and quantum technologies. Preprint at arXiv https://doi.org/10.48550/arXiv.2201.09260 (2022).

  49. Braginski, A. I. Superconductor electronics: status and outlook. J. Supercond. Nov. Magn. 32, 23–44 (2019).

    Article  CAS  Google Scholar 

  50. Heikkilä, T. T. et al. Thermoelectric radiation detector based on superconductor-ferromagnet systems. Phys. Rev. Appl. 10, 034053 (2018).

    Article  Google Scholar 

  51. Martinez-Perez, M. J. & Giazotto, F. A quantum diffractor for thermal flux. Nat. Commun. 5, 3579 (2014).

    Article  Google Scholar 

  52. Tinkham, M. Introduction to Superconductivity (McGraw-Hill,1996).

  53. Dynes, R. C., Garno, J. P., Hertel, G. B. & Orlando, T. P. Tunneling study of superconductivity near the metal-insulator transition. Phys. Rev. Lett. 53, 2437–2440 (1984).

    Article  CAS  Google Scholar 

  54. Shapiro, S., Smith, P. H., Nicol, J., Miles, J. L. & Strong, P. F. Superconductivity and electron tunneling. IBM J. Res. Dev. 6, 34–43 (1962).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

We thank T. Novotny, K. Michaeli, L. Amico and F. Strocchi for useful discussions. We acknowledge the European Research Council under grant agreement no. 899315-TERASEC and the EU’s Horizon 2020 research and innovation programme under grant agreements no. 800923 (SUPERTED) and no. 964398 (SUPERGATE) for partial financial support. A.B. acknowledges the Scuola Normal Superiore - Weizmann Institute of Science (SNS-WIS) joint lab QUANTRA, funded by the Italian Ministry of Foreign Affairs and International Cooperation and the Royal Society through the International Exchanges between the UK and Italy (grants no. IEC R2 192166 and no. IEC R2 212041).

Author information

Authors and Affiliations

  1. NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, Pisa, Italy

    Gaia Germanese, Federico Paolucci, Alessandro Braggio & Francesco Giazotto

  2. Dipartimento di Fisica, Università di Pisa, Pisa, Italy

    Gaia Germanese

  3. Quantum Research Centre, Technology Innovation Institute, Abu Dhabi, UAE

    Giampiero Marchegiani

Authors
  1. Gaia Germanese
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Federico Paolucci
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Giampiero Marchegiani
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Alessandro Braggio
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Francesco Giazotto
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

F.P. fabricated the devices. G.G. and F.P. performed the experiments and analysed the data with input from F.G.; G.M. and A.B. developed the theoretical model describing the experiment. All the authors wrote the manuscript. F.P. and F.G. conceived the experiment. F.G. supervised and coordinated the project. All authors discussed the results and their implications equally at all stages.

Corresponding authors

Correspondence to Federico Paolucci or Francesco Giazotto.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Nanotechnology thanks Heiner Linke and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Figs. 1–6 and Sections I–IV.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Germanese, G., Paolucci, F., Marchegiani, G. et al. Bipolar thermoelectric Josephson engine. Nat. Nanotechnol. 17, 1084–1090 (2022). https://doi.org/10.1038/s41565-022-01208-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41565-022-01208-y

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing