- 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

Bipolar thermoelectric superconducting single-electron transistor

Sebastiano Battisti*, Giorgio De Simoni, Luca Chirolli, Alessandro Braggio†, and Francesco Giazotto‡

  • NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, I-56127 Pisa, Italy

  • *sebastiano.battisti@sns.it
  • †alessandro.braggio@nano.cnr.it
  • ‡francesco.giazotto@sns.it
PDF

Phys. Rev. Research 6, L012022 – Published 25 January, 2024

DOI: https://doi.org/10.1103/PhysRevResearch.6.L012022

Abstract

Thermoelectric effects in normal metals and superconductors are usually very small due to the presence of electron-hole symmetry. Here, we show that superconducting junctions brought out of equilibrium manifest a sizable bipolar thermoelectric effect that stems from a strong violation of the detailed balance determined by the crucial role of the interactions at the mean-field level. To fully control the effect, we consider a thermally biased SIS′IS junction where the capacitance of the central S′ region is small enough to establish a Coulomb blockade regime. By exploiting charging effects we are able to tune the Seebeck voltage, the thermocurrent, and thereby the power output of this structure, via an external gate voltage. We then analyze the main figures of merit of bipolar thermoelectricity and we prospect for possible applications.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (50)

  1. G. Benenti, G. Casati, K. Saito, and R. S. Whitney, Fundamental aspects of steady-state conversion of heat to work at the nanoscale, Phys. Rep. 694, 1 (2017).
  2. Y. Dubi and M. Di Ventra, Colloquium: Heat flow and thermoelectricity in atomic and molecular junctions, Rev. Mod. Phys. 83, 131 (2011).
  3. R. Kosloff, Quantum thermodynamics: A dynamical viewpoint, Entropy 15, 2100 (2013).
  4. U. Seifert, Stochastic thermodynamics, fluctuation theorems and molecular machines, Rep. Prog. Phys. 75, 126001 (2012).
  5. M. Campisi, P. Hanggi, and P. Talkner, Colloquium: Quantum fluctuation relations: Foundations and applications, Rev. Mod. Phys. 83, 771 (2011).
  6. F. Giazotto, T. T. Heikkilä, A. Luukanen, A. M. Savin, and J. P. Pekola, Opportunities for mesoscopics in thermometry and refrigeration: Physics and applications, Rev. Mod. Phys. 78, 217 (2006).
  7. A. Fornieri and F. Giazotto, Towards phase-coherent caloritronics in superconducting circuits, Nat. Nanotechnol. 12, 944 (2017).
  8. J. T. Muhonen, M. Meschke, and J. P. Pekola, Micrometre-scale refrigerators, Rep. Prog. Phys. 75, 046501 (2012).
  9. N. Brunner, N. Linden, S. Popescu, and P. Skrzypczyk, Virtual qubits, virtual temperatures, and the foundations of thermodynamics, Phys. Rev. E 85, 051117 (2012).
  10. A. C. Barato and U. Seifert, Thermodynamic uncertainty relation for biomolecular processes, Phys. Rev. Lett. 114, 158101 (2015).
  11. M. Polettini, G. Verley, and M. Esposito, Efficiency statistics at all times: Carnot limit at finite power, Phys. Rev. Lett. 114, 050601 (2015).
  12. G. Verley, M. Esposito, T. Willaert, and C. Van den Broeck, The unlikely Carnot efficiency, Nat. Commun. 5, 4721 (2014).
  13. P. Pietzonka and U. Seifert, Universal trade-off between power, efficiency, and constancy in steady-state heat engines, Phys. Rev. Lett. 120, 190602 (2018).
  14. S. K. Manikandan, L. Dabelow, R. Eichhorn, and S. Krishnamurthy, Efficiency fluctuations in microscopic machines, Phys. Rev. Lett. 122, 140601 (2019).
  15. J. P. Pekola, F. Giazotto, and O.-P. Saira, Radio-frequency single-electron refrigerator, Phys. Rev. Lett. 98, 037201 (2007).
  16. O.-P. Saira, M. Meschke, F. Giazotto, A. M. Savin, M. Möttönen, and J. P. Pekola, Heat transistor: Demonstration of gate-controlled electronic refrigeration, Phys. Rev. Lett. 99, 027203 (2007).
  17. A. Fornieri, M. J. Martínez-Pérez, and F. Giazotto, A normal metal tunnel-junction heat diode, Appl. Phys. Lett. 104, 183108 (2014).
  18. S. Tirelli, A. M. Savin, C. P. Garcia, J. P. Pekola, F. Beltram, and F. Giazotto, Manipulation and generation of supercurrent in out-of-equilibrium Josephson tunnel nanojunctions, Phys. Rev. Lett. 101, 077004 (2008).
  19. B. Sothmann, F. Giazotto, and E. M. Hankiewicz, High-efficiency thermal switch based on topological Josephson junctions, New J. Phys. 19, 023056 (2017).
  20. N. R. Claughton and C. J. Lambert, Thermoelectric properties of mesoscopic superconductors, Phys. Rev. B 53, 6605 (1996).
  21. A. Ozaeta, P. Virtanen, F. S. Bergeret, and T. T. Heikkilä, Predicted very large thermoelectric effect in ferromagnet-superconductor junctions in the presence of a spin-splitting magnetic field, Phys. Rev. Lett. 112, 057001 (2014).
  22. F. Vischi, M. Carrega, P. Virtanen, E. Strambini, A. Braggio, and F. Giazotto, Thermodynamic cycles in Josephson junctions, Sci. Rep. 9, 3238 (2019).
  23. G. Marchegiani, P. Virtanen, F. Giazotto, and M. Campisi, Self-oscillating Josephson quantum heat engine, Phys. Rev. Appl. 6, 054014 (2016).
  24. K. Brandner, K. Saito, and U. Seifert, Strong bounds on Onsager coefficients and efficiency for three-terminal thermoelectric transport in a magnetic field, Phys. Rev. Lett. 110, 070603 (2013).
  25. B. Sothmann, R. Sánchez, and A. N. Jordan, Thermoelectric energy harvesting with quantum dots, Nanotechnology 26, 032001 (2015).
  26. M. Esposito, K. Lindenberg, and C. V. den Broeck, Thermoelectric efficiency at maximum power in a quantum dot, Europhys. Lett. 85, 60010 (2009).
  27. R. S. Whitney, Most efficient quantum thermoelectric at finite power output, Phys. Rev. Lett. 112, 130601 (2014).
  28. F. Ronetti, L. Vannucci, G. Dolcetto, M. Carrega, and M. Sassetti, Spin-thermoelectric transport induced by interactions and spin-flip processes in two-dimensional topological insulators, Phys. Rev. B 93, 165414 (2016).
  29. M. Kamp and B. Sothmann, Phase-dependent heat and charge transport through superconductor–quantum dot hybrids, Phys. Rev. B 99, 045428 (2019).
  30. R. Hussein, M. Governale, S. Kohler, W. Belzig, F. Giazotto, and A. Braggio, Nonlocal thermoelectricity in a Cooper-pair splitter, Phys. Rev. B 99, 075429 (2019).
  31. N. F. Mott, H. Jones, H. Jones, and H. Jones, The Theory of the Properties of Metals and Alloys (Dover, Mineola, New York, 1958).
  32. G. Marchegiani, A. Braggio, and F. Giazotto, Nonlinear thermoelectricity with electron-hole symmetric systems, Phys. Rev. Lett. 124, 106801 (2020).
  33. G. Marchegiani, A. Braggio, and F. Giazotto, Superconducting nonlinear thermoelectric heat engine, Phys. Rev. B 101, 214509 (2020).
  34. G. Germanese, F. Paolucci, G. Marchegiani, A. Braggio, and F. Giazotto, Bipolar thermoelectric Josephson engine, Nat. Nanotechnol. 17, 1084 (2022).
  35. G. Germanese, F. Paolucci, G. Marchegiani, A. Braggio, and F. Giazotto, Phase control of bipolar thermoelectricity in Josephson tunnel junctions, Phys. Rev. Appl. 19, 014074 (2023).
  36. L. Bernazzani, G. Marchegiani, F. Giazotto, S. Roddaro, and A. Braggio, Bipolar thermoelectricity in bilayer-graphene–superconductor tunnel junctions, Phys. Rev. Appl. 19, 044017 (2023).
  37. F. Paolucci, G. Germanese, A. Braggio, and F. Giazotto, A highly sensitive broadband superconducting thermoelectric single-photon detector, Appl. Phys. Lett. 122, 173503 (2023).
  38. G. Marchegiani, A. Braggio, and F. Giazotto, Phase-tunable thermoelectricity in a Josephson junction, Phys. Rev. Res. 2, 043091 (2020).
  39. D. Averin and K. Likharev, Single electronics: A correlated transfer of single electrons and Cooper pairs in systems of small tunnel junctions, in Modern Problems in Condensed Matter Sciences (Elsevier, Amsterdam, 1991), Vol. 30, pp. 173–271.
  40. J. P. Pekola, J. J. Vartiainen, M. Möttönen, O.-P. Saira, M. Meschke, and D. V. Averin, Hybrid single-electron transistor as a source of quantized electric current, Nat. Phys. 4, 120 (2008).
  41. R. C. Dynes, J. P. Garno, G. B. Hertel, and T. P. Orlando, Tunneling study of superconductivity near the metal-insulator transition, Phys. Rev. Lett. 53, 2437 (1984).
  42. V. F. Maisi, S. V. Lotkhov, A. Kemppinen, A. Heimes, J. T. Muhonen, and J. P. Pekola, Excitation of single quasiparticles in a small superconducting Al island connected to normal-metal leads by tunnel junctions, Phys. Rev. Lett. 111, 147001 (2013).
  43. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.6.L012022 for a derivation of necessary and sufficient conditions for the bipolar thermoelectric effect to arise, and for a detailed discussion on the analogies and differences between this effect and the conventional one.
  44. Y. V. Nazarov and Y. M. Blanter, Quantum Transport: Introduction to Nanoscience (Cambridge University Press, Cambridge, 2009).
  45. D. A. Bagrets and Y. V. Nazarov, Full counting statistics of charge transfer in Coulomb blockade systems, Phys. Rev. B 67, 085316 (2003).
  46. A. Braggio, J. König, and R. Fazio, Full counting statistics in strongly interacting systems: Non-Markovian effects, Phys. Rev. Lett. 96, 026805 (2006).
  47. C. W. J. Beenakker, Theory of Coulomb-blockade oscillations in the conductance of a quantum dot, Phys. Rev. B 44, 1646 (1991).
  48. A. A. M. Staring, L. W. Molenkamp, B. W. Alphenaar, H. van Houten, O. J. A. Buyk, M. A. A. Mabesoone, C. W. J. Beenakker, and C. T. Foxon, Coulomb-blockade oscillations in the thermopower of a quantum dot, Europhys. Lett. 22, 57 (1993).
  49. G. D. Mahan and J. O. Sofo, The best thermoelectric, Proc. Natl. Acad. Sci. USA 93, 7436 (1996).
  50. H. Goldsmid, Thermoelectric Refrigeration (Springer, Berlin, 2013).

Outline

Information

Phys. Rev. Research 6, L012022– Published 25 January, 2024
  • Received 24 May 2023
  • Accepted 22 November 2023
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