- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Thermodynamic uncertainty relations in superconducting junctions

David Christian Ohnmacht1,*, Juan Carlos Cuevas2,3, Wolfgang Belzig1, Rosa López4, Jong Soo Lim5, and Kun Woo Kim6

  • *Contact author: david.ohnmacht@uni-konstanz.de
PDF

Phys. Rev. Research 7, L012075 – Published 20 March, 2025

DOI: https://doi.org/10.1103/PhysRevResearch.7.L012075

Abstract

It has recently been predicted that the thermodynamic uncertainty relation (TUR), which expresses a trade-off between the amount of dissipation and the absence of fluctuations, can be violated in the context of charge transport in normal quantum conductors. However, the required conditions are difficult to meet, and no experimental violation has been reported yet in mesoscopic quantum transport experiments. Here, we predict that TUR can be largely violated in superconducting (SC) contacts without introducing an energy dependency in the normal transmission coefficient. This violation originates from the coexistence of tunneling processes involving different numbers of transmitted charges, namely, quasiparticle tunneling and Andreev reflections. The SC junctions invoked here have been fabricated by many groups and constitute an ideal platform to demonstrate TUR breaking in charge transport experiments.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (47)

  1. M. Nahum, T. M. Eiles, and J. M. Martinis, Electronic microrefrigerator based on a normal-insulator-superconductor tunnel junction, Appl. Phys. Lett. 65, 3123 (1994).
  2. M. M. Leivo, J. P. Pekola, and D. V. Averin, Efficient peltier refrigeration by a pair of normal metal/insulator/superconductor junctions, Appl. Phys. Lett. 68, 1996 (1996).
  3. R. Sánchez, P. Burset, and A. L. Yeyati, Cooling by Cooper pair splitting, Phys. Rev. B 98, 241414(R) (2018).
  4. S.-Y. Hwang, B. Sothmann, and D. Sánchez, Superconductor–quantum dot hybrid coolers, Phys. Rev. B 107, 245412 (2023).
  5. G. Manzano and R. López, Quantum-enhanced performance in superconducting Andreev reflection engines, Phys. Rev. Res. 5, 043041 (2023).
  6. S. M. Tabatabaei, D. Sánchez, A. L. Yeyati, and R. Sánchez, Nonlocal quantum heat engines made of hybrid superconducting devices, Phys. Rev. B 106, 115419 (2022).
  7. G. Blasi, F. Taddei, L. Arrachea, M. Carrega, and A. Braggio, Nonlocal thermoelectric engines in hybrid topological Josephson junctions, Phys. Rev. B 103, 235434 (2021).
  8. G. Marchegiani, A. Braggio, and F. Giazotto, Nonlinear thermoelectricity with electron-hole symmetric systems, Phys. Rev. Lett. 124, 106801 (2020).
  9. G. Germanese, F. Paolucci, G. Marchegiani, A. Braggio, and F. Giazotto, Bipolar thermoelectric Josephson engine, Nat. Nanotechnol. 17, 1084 (2022).
  10. S. Battisti, G. De Simoni, L. Chirolli, A. Braggio, and F. Giazotto, Bipolar thermoelectric superconducting single-electron transistor, Phys. Rev. Res. 6, L012022 (2024).
  11. I. Khomchenko, H. Ouerdane, and G. Benenti, Voltage-amplified heat rectification in SIS junctions, Phys. Rev. B 106, 245413 (2022).
  12. A. C. Barato and U. Seifert, Thermodynamic uncertainty relation for biomolecular processes, Phys. Rev. Lett. 114, 158101 (2015).
  13. T. R. Gingrich, J. M. Horowitz, N. Perunov, and J. L. England, Dissipation bounds all steady-state fluctuations, Phys. Rev. Lett. 116, 120601 (2016).
  14. J. M. Horowitz and T. R. Gingrich, Thermodynamic uncertainty relations constrain non-equilibrium fluctuations, Nat. Phys. 16, 15 (2020).
  15. P. Pietzonka, A. C. Barato, and U. Seifert, Universal bounds on current fluctuations, Phys. Rev. E 93, 052145 (2016).
  16. P. Pietzonka, A. C. Barato, and U. Seifert, Universal bound on the efficiency of molecular motors, J. Stat. Mech. (2016) 124004.
  17. P. Pietzonka and U. Seifert, Universal trade-off between power, efficiency, and constancy in steady-state heat engines, Phys. Rev. Lett. 120, 190602 (2018).
  18. A. M. Timpanaro, G. Guarnieri, J. Goold, and G. T. Landi, Thermodynamic uncertainty relations from exchange fluctuation theorems, Phys. Rev. Lett. 123, 090604 (2019).
  19. B. K. Agarwalla and D. Segal, Assessing the validity of the thermodynamic uncertainty relation in quantum systems, Phys. Rev. B 98, 155438 (2018).
  20. D. Andrieux and P. Gaspard, A fluctuation theorem for currents and non-linear response coefficients, J. Stat. Mech. (2007) P02006.
  21. K. Brandner, T. Hanazato, and K. Saito, Thermodynamic bounds on precision in ballistic multiterminal transport, Phys. Rev. Lett. 120, 090601 (2018).
  22. E. Potanina, C. Flindt, M. Moskalets, and K. Brandner, Thermodynamic bounds on coherent transport in periodically driven conductors, Phys. Rev. X 11, 021013 (2021).
  23. R. López, J. S. Lim, and K. W. Kim, Optimal superconducting hybrid machine, Phys. Rev. Res. 5, 013038 (2023).
  24. K. Prech, P. Johansson, E. Nyholm, G. T. Landi, C. Verdozzi, P. Samuelsson, and P. P. Potts, Entanglement and thermokinetic uncertainty relations in coherent mesoscopic transport, Phys. Rev. Res. 5, 023155 (2023).
  25. S. Katz, J. L. Lebowitz, and H. Spohn, Phase transitions in stationary nonequilibrium states of model lattice systems, Phys. Rev. B 28, 1655 (1983).
  26. K. Ptaszyński, Coherence-enhanced constancy of a quantum thermoelectric generator, Phys. Rev. B 98, 085425 (2018).
  27. J. Liu and D. Segal, Thermodynamic uncertainty relation in quantum thermoelectric junctions, Phys. Rev. E 99, 062141 (2019).
  28. T. Ehrlich and G. Schaller, Broadband frequency filters with quantum dot chains, Phys. Rev. B 104, 045424 (2021).
  29. F. Taddei and R. Fazio, Thermodynamic uncertainty relations for systems with broken time reversal symmetry: The case of superconducting hybrid systems, Phys. Rev. B 108, 115422 (2023).
  30. H. M. Friedman, B. K. Agarwalla, O. Shein-Lumbroso, O. Tal, and D. Segal, Thermodynamic uncertainty relation in atomic-scale quantum conductors, Phys. Rev. B 101, 195423 (2020).
  31. H. Förster and M. Büttiker, Fluctuation relations without microreversibility in nonlinear transport, Phys. Rev. Lett. 101, 136805 (2008).
  32. J. Tobiska and Y. V. Nazarov, Inelastic interaction corrections and universal relations for full counting statistics in a quantum contact, Phys. Rev. B 72, 235328 (2005).
  33. R. López, J. S. Lim, and D. Sánchez, Fluctuation relations for spintronics, Phys. Rev. Lett. 108, 246603 (2012).
  34. L. S. Levitov, H. Lee, and G. B. Lesovik, Electron counting statistics and coherent states of electric current, J. Math. Phys. 37, 4845 (1996).
  35. I. Klich, An elementary derivation of Levitov's formula, in Quantum Noise in Mesoscopic Physics, edited by Y. V. Nazarov (Springer Netherlands, Dordrecht, 2003), pp. 397–402.
  36. W. Belzig, Full counting statistics of superconductor-normal-metal heterostructures, in Quantum Noise in Mesoscopic Physics, edited by Y. V. Nazarov (Springer Netherlands, Dordrecht, 2003), pp. 463–496.
  37. G. E. Blonder, M. Tinkham, and T. M. Klapwijk, Transition from metallic to tunneling regimes in superconducting microconstrictions: Excess current, charge imbalance, and supercurrent conversion, Phys. Rev. B 25, 4515 (1982).
  38. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.7.L012075 for more detailed information on the charge-resolved probabilities.
  39. J. C. Cuevas and W. Belzig, Full counting statistics of multiple Andreev reflections, Phys. Rev. Lett. 91, 187001 (2003).
  40. J. C. Cuevas and W. Belzig, dc transport in superconducting point contacts: A full-counting-statistics view, Phys. Rev. B 70, 214512 (2004).
  41. E. Scheer, P. Joyez, D. Esteve, C. Urbina, and M. H. Devoret, Conduction channel transmissions of atomic-size aluminum contacts, Phys. Rev. Lett. 78, 3535 (1997).
  42. E. Scheer, N. Agraït, J. C. Cuevas, A. L. Yeyati, B. Ludoph, A. Martín-Rodero, G. R. Bollinger, J. M. van Ruitenbeek, and C. Urbina, The signature of chemical valence in the electrical conduction through a single-atom contact, Nature (London) 394, 154 (1998).
  43. J. C. Cuevas, A. Levy Yeyati, A. Martín-Rodero, G. R. Bollinger, C. Untiedt, and N. Agraït, Evolution of conducting channels in metallic atomic contacts under elastic deformation, Phys. Rev. Lett. 81, 2990 (1998).
  44. R. Cron, M. F. Goffman, D. Esteve, and C. Urbina, Multiple-charge-quanta shot noise in superconducting atomic contacts, Phys. Rev. Lett. 86, 4104 (2001).
  45. J. Senkpiel, S. Dambach, M. Etzkorn, R. Drost, C. Padurariu, B. Kubala, W. Belzig, A. L. Yeyati, J. C. Cuevas, J. Ankerhold et al., Single channel Josephson effect in a high transmission atomic contact, Commun. Phys. 3, 131 (2020).
  46. J. Senkpiel, J. C. Klöckner, M. Etzkorn, S. Dambach, B. Kubala, W. Belzig, A. L. Yeyati, J. C. Cuevas, F. Pauly, J. Ankerhold et al., Dynamical Coulomb blockade as a local probe for quantum transport, Phys. Rev. Lett. 124, 156803 (2020).
  47. D. C. Ohnmacht, W. Belzig, and J. C. Cuevas, Full counting statistics of Yu-Shiba-Rusinov bound states, Phys. Rev. Res. 5, 033176 (2023).

Outline

Information

Phys. Rev. Research 7, L012075– Published 20 March, 2025
  • Received 25 June 2024
  • Accepted 17 December 2024
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation