Skip to main content

Thank you for visiting 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.

  • Letter
  • Published:

Thermal superconducting quantum interference proximity transistor


Superconductors are excellent thermal insulators at low temperatures owing to the presence of an energy gap in their density of states1. Through the so-called proximity effect2, superconductors can influence the density of states of nearby metallic or superconducting wires. In this way, the local density of states of a wire can be tuned by controlling the phase bias (φ) imposed across it3. Here we demonstrate a thermal superconducting quantum interference proximity transistor (T-SQUIPT) that enables the phase control of heat currents by exploiting the superconducting proximity effect. Our T-SQUIPT device comprises a quasi-one-dimensional aluminium nanowire forming the weak link embedded in a superconducting ring4,5. Controlling the phase bias by changing the magnetic flux through the ring shows temperature modulations of up to 16 mK, yielding a temperature-to-flux transfer function that reaches approximately 60 mK Φ0–1. We also demonstrate a hysteretic dependence of the local density of states of T-SQUIPTs on the applied magnetic field due to phase-slip transitions. This allows the T-SQUIPT device to operate as a phase-tunable thermal memory6,7, where the information is encoded in the temperature of the metallic mesoscopic island.

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

Access options

Buy this article

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

Fig. 1: Operation principle and implementation of T-SQUIPT.
Fig. 2: Low-temperature behaviour of T-SQUIPT.
Fig. 3: Bath-temperature evolution of the T-SQUIPT behaviour.
Fig. 4: T-SQUIPT operated as a thermal memory cell.

Similar content being viewed by others

Data availability

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

Code availability

The codes that support the findings of this study are available from the corresponding author E.S. upon reasonable request.


  1. 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, 217–274 (2006).

    Article  ADS  Google Scholar 

  2. de Gennes, P. G. & Pincus, P. A. Superconductivity of Metals and Alloys (CRC Press, 1966).

  3. Likharev, K. K. Superconducting weak links. Rev. Mod. Phys. 51, 100–159 (1979).

    Article  ADS  Google Scholar 

  4. Giazotto, F., Peltonen, J. & Meschke, M. et al. Superconducting quantum interference proximity transistor. Nat. Phys. 6, 254–259 (2010).

    Article  Google Scholar 

  5. Virtanen, P., Ronzani, A. & Giazotto, F. Spectral characteristics of a fully superconducting SQUIPT. Phys. Rev. Appl. 6, 054002 (2016).

    Article  ADS  Google Scholar 

  6. Fornieri, A., Timossi, G., Bosisio, R., Solinas, P. & Giazotto, F. Negative differential thermal conductance and heat amplification in superconducting hybrid devices. Phys. Rev. B 93, 134508 (2016).

    Article  ADS  Google Scholar 

  7. Guarcello, C., Solinas, P., Braggio, A., Di Ventra, M. & Giazotto, F. Josephson thermal memory. Phys. Rev. Appl. 9, 014021 (2018).

    Article  ADS  Google Scholar 

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

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

    Article  ADS  Google Scholar 

  10. Hwang, S.-Y. & Sothmann, B. Phase-coherent caloritronics with ordinary and topological Josephson junctions. Eur. Phys. J. Spec. Top. 229, 683–705 (2020).

    Article  Google Scholar 

  11. Ligato, N., Marchegiani, G., Virtanen, P., Strambini, E. & Giazotto, F. High operating temperature in V-based superconducting quantum interference proximity transistors. Sci. Rep. 7, 8810 (2017).

    Article  ADS  Google Scholar 

  12. Ronzani, A., D’Ambrosio, S., Virtanen, P., Giazotto, F. & Altimiras, C. Phase-driven collapse of the Cooper condensate in a nanosized superconductor. Phys. Rev. B 96, 214517 (2017).

    Article  ADS  Google Scholar 

  13. Ligato, N., Strambini, E., Paolucci, F. & Giazotto, F. Preliminary demonstration of a persistent Josephson phase-slip memory cell with topological protection. Nat. Commun. 12, 5200 (2021).

    Article  ADS  Google Scholar 

  14. Strambini, E., Bergeret, F. S. & Giazotto, F. Proximity nanovalve with large phase-tunable thermal conductance. Appl. Phys. Lett. 105, 082601 (2014).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  17. Parsons, A., Sosnin, I. A. & Petrashov, V. T. Reversal of thermopower oscillations in the mesoscopic Andreev interferometer. Phys. Rev. B 67, 140502(R) (2003).

    Article  ADS  Google Scholar 

  18. Paolucci, F., Marchegiani, G., Strambini, E. & Giazotto, F. Phase-tunable temperature amplifier. EPL 118, 68004 (2017).

    Article  ADS  Google Scholar 

  19. Paolucci, F., Marchegiani, G., Strambini, E. & Giazotto, F. Phase-tunable thermal logic: computation with heat. Phys. Rev. Appl. 10, 024003 (2018).

    Article  ADS  Google Scholar 

  20. Little, W. A. Decay of persistent currents in small superconductors. Phys. Rev. 156, 396–403 (1967).

    Article  ADS  Google Scholar 

  21. Petkovic, I., Lollo, A., Glazman, L. I. & Har, J. G. E. Deterministic phase slips in mesoscopic superconducting rings. Nat. Commun. 7, 13551 (2016).

    Article  ADS  Google Scholar 

  22. Mooij, J. E. & Harmans, C. J. P. M. Phase-slip flux qubits. New J. Phys. 7, 219 (2005).

    Article  ADS  MathSciNet  Google Scholar 

  23. Arutyunov, K. Y., Golubev, D. S. & Zaikin, A. D. Superconductivity in one dimension. Phys. Rep. 464, 1–70 (2008).

    Article  ADS  Google Scholar 

  24. Giazotto, F. & Martínez-Pérez, M. The Josephson heat interferometer. Nature 492, 401–405 (2012).

    Article  ADS  Google Scholar 

  25. Wellstood, F. C., Urbina, C. & Clarke, J. Hot-electron effects in metals. Phys. Rev. B 49, 5942–5955 (1994).

    Article  ADS  Google Scholar 

  26. Baek, B., Rippard, W. H., Ben, S. P., Russek, S. E. & Dresselhaus, P. D. Hybrid superconducting-magnetic memory device using competing order parameters. Nat. Commun. 5, 3888 (2014).

    Article  ADS  Google Scholar 

  27. Golod, T., Iovan, A. & Krasnov, V. M. Single Abrikosov vortices as quantized information bits. Nat. Commun. 6, 8628 (2015).

    Article  ADS  Google Scholar 

  28. Gingrich, E. C. et al. Controllable 0–π Josephson junctions containing a ferromagnetic spin valve. Nat. Phys. 12, 564–567 (2016).

    Article  Google Scholar 

  29. Beenakker, C. W. J. Random-matrix theory of Majorana fermions and topological superconductors. Rev. Mod. Phys. 87, 1037 (2015).

    Article  ADS  MathSciNet  Google Scholar 

  30. Bours, L. et al. Phase-tunable thermal rectification in the topological SQUIPT. Phys. Rev. Appl. 11, 044073 (2019).

    Article  ADS  Google Scholar 

  31. Scharf, B., Braggio, A., Strambini, E., Giazotto, F. & Hankiewicz, E. M. Topological Josephson heat engine. Commun. Phys. 3, 198 (2020).

    Article  Google Scholar 

  32. Banerjee, M. et al. Observation of half-integer thermal Hall conductance. Nature 559, 205–210 (2018).

    Article  ADS  Google Scholar 

  33. Ronzani, A., Altimiras, C. & Giazotto, F. Highly sensitive superconducting quantum-interference proximity transistor. Phys. Rev. Appl. 2, 024005 (2014).

    Article  ADS  Google Scholar 

  34. Jabdaraghi, R. N., Peltonen, J. T., Saira, O. P. & Pekola, J. P. Low-temperature characterization of Nb-Cu-Nb weak links with Ar ion-cleaned interfaces. Appl. Phys. Lett. 108, 042604 (2016).

    Article  ADS  Google Scholar 

  35. Pop, E. Energy dissipation and transport in nanoscale devices. Nano Res. 3, 147–169 (2010).

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  37. Sothmann, B., Sánschez, R. & Jordan, A. N. Thermoelectric energy harvesting with quantum dots. Nanotechnology 26, 032001 (2014).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  40. Iorio, A., Strambini, E., Haack, G., Campisi, M. & Giazotto, F. Photonic heat rectification in a system of coupled qubits. Phys. Rev. Appl. 15, 054050 (2021).

    Article  ADS  Google Scholar 

  41. 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 (1984).

Download references


We acknowledge the European Research Council under grant agreement no. 899315-TERASEC, and the EU’s Horizon 2020 research and innovation programme under grant agreement no. 800923 (SUPERTED) and no. 964398 (SUPERGATE) for partial financial support.

Author information

Authors and Affiliations



E.S. and F.G. conceived the experiment. N.L. fabricated the samples with inputs from F.P. N.L., F.P. and E.S. performed the measurements. N.L. analysed the experimental data with inputs from F.P., E.S. and F.G. E.S. and F.G. developed the theoretical model. N.L and F.P. wrote the manuscript with inputs from all the authors. All the authors equally discussed the results and their implications at all the stages.

Corresponding authors

Correspondence to Elia Strambini or Francesco Giazotto.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Physics thanks Olivier Maillet 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 refs. 1–7.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ligato, N., Paolucci, F., Strambini, E. et al. Thermal superconducting quantum interference proximity transistor. Nat. Phys. 18, 627–632 (2022).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


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