- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Applied

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
  • Open Access

Finite-length effects and Coulomb interaction in Josephson junctions based on Ge quantum wells and probed with microwave spectroscopy

S.C. ten Kate1, D.C. Ohnmacht2, M. Coraiola1, T. Antonelli1, S. Paredes1, F.J. Schupp1, M. Hinderling1, S.W. Bedell3, W. Belzig2 et al.

J.C. Cuevas4, A.E. Svetogorov2, F. Nichele1,*, and D. Sabonis1,†

  • *Contact author: fni@zurich.ibm.com
  • †Contact author: Deividas.Sabonis@ibm.com
PDF

Phys. Rev. Applied 24, 064005 – Published 1 December, 2025

DOI: https://doi.org/10.1103/hb1h-8jn9

Abstract

Proximitized Ge quantum wells have emerged as a platform for studying Andreev bound states (ABSs) due to their expected strong spin-orbit interaction and high mobility. Here, we used microwave spectroscopy techniques to investigate ABSs in Josephson junctions (JJs) realized in proximitized Ge quantum wells. Spectroscopic signatures observed in a 350-nm junction indicated the presence of multiple ABSs and were reproduced with a model including finite-length effects. The ABS spectra measured for a 1.2-μm junction were explained by a model including three ABSs in two conduction channels and finite Coulomb interaction. Our work highlights the importance of interactions in JJs and serves as a basis for understanding and manipulating ABSs in Ge-based hybrid devices.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (46)

  1. A. F. Andreev, The thermal conductivity of the intermediate state in superconductors, J. Exp. Theor. Phys. 46, 1823 (1964).
  2. 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).
  3. C. W. J. Beenakker, Universal limit of critical-current fluctuations in mesoscopic Josephson junctions, Phys. Rev. Lett. 67, 3836 (1991).
  4. A. Furusaki and M. Tsukada, Current-carrying states in Josephson junctions, Phys. Rev. B 43, 10164 (1991).
  5. J.-D. Pillet, P. Joyez, R. Žitko, and M. F. Goffman, Tunneling spectroscopy of a single quantum dot coupled to a superconductor: From Kondo ridge to Andreev bound states, Phys. Rev. B 88, 045101 (2013).
  6. F. Nichele, E. Portolés, A. Fornieri, A. M. Whiticar, A. C. C. Drachmann, S. Gronin, T. Wang, G. C. Gardner, C. Thomas, A. T. Hatke, M. J. Manfra, and C. M. Marcus, Relating Andreev bound states and supercurrents in hybrid Josephson junctions, Phys. Rev. Lett. 124, 226801 (2020).
  7. M. Coraiola, D. Z. Haxell, D. Sabonis, H. Weisbrich, A. E. Svetogorov, M. Hinderling, S. C. ten Kate, E. Cheah, F. Krizek, R. Schott, W. Wegscheider, J. C. Cuevas, W. Belzig, and F. Nichele, Phase-engineering the Andreev band structure of a three-terminal Josephson junction, Nat. Commun. 14, 6784 (2023).
  8. C. Janvier, L. Tosi, L. Bretheau, Ç. Ö. Girit, M. Stern, P. Bertet, P. Joyez, D. Vion, D. Esteve, M. F. Goffman, H. Pothier, and C. Urbina, Coherent manipulation of Andreev states in superconducting atomic contacts, Science 349, 1199 (2015).
  9. M. Hays, G. de Lange, K. Serniak, D. J. van Woerkom, D. Bouman, P. Krogstrup, J. Nygård, A. Geresdi, and M. H. Devoret, Direct microwave measurement of Andreev-bound-state dynamics in a semiconductor-nanowire Josephson junction, Phys. Rev. Lett. 121, 047001 (2018).
  10. L. Tosi, C. Metzger, M. F. Goffman, C. Urbina, H. Pothier, S. Park, A. L. Yeyati, J. Nygård, and P. Krogstrup, Spin-orbit splitting of Andreev states revealed by microwave spectroscopy, Phys. Rev. X 9, 011010 (2019).
  11. M. Hays, V. Fatemi, K. Serniak, D. Bouman, S. Diamond, G. de Lange, P. Krogstrup, J. Nygård, A. Geresdi, and M. H. Devoret, Continuous monitoring of a trapped superconducting spin, Nat. Phys. 16, 1103 (2020).
  12. M. Hays, V. Fatemi, D. Bouman, J. Cerrillo, S. Diamond, K. Serniak, T. Connolly, P. Krogstrup, J. Nygaard, A. Levy Yeyati et al., Coherent manipulation of an Andreev spin qubit, Science 373, 430 (2021).
  13. V. Chidambaram, A. Kringhøj, L. Casparis, F. Kuemmeth, T. Wang, C. Thomas, S. Gronin, Geoffrey C. Gardner, Z. Cui, C. Liu, K. Moors, Michael J. Manfra, Karl D. Petersson, and Malcolm R. Connolly, Microwave sensing of Andreev bound states in a gate-defined superconducting quantum point contact, Phys. Rev. Res. 4, 023170 (2022).
  14. F. J. Matute-Cañadas, C. Metzger, S. Park, L. Tosi, P. Krogstrup, J. Nygård, M. F. Goffman, C. Urbina, H. Pothier, and A. L. Yeyati, Signatures of interactions in the Andreev spectrum of nanowire Josephson junctions, Phys. Rev. Lett. 128, 197702 (2022).
  15. P. Zellekens, R. S. Deacon, P. Perla, D. Grützmacher, M. I. Lepsa, T. Schäpers, and K. Ishibashi, Microwave spectroscopy of Andreev states in InAs nanowire-based hybrid junctions using a flip-chip layout, Commun. Phys. 5, 267 (2022).
  16. V. Fatemi, P. D. Kurilovich, M. Hays, D. Bouman, T. Connolly, S. Diamond, N. E. Frattini, V. D. Kurilovich, P. Krogstrup, J. Nygård, A. Geresdi, L. I. Glazman, and M. H. Devoret, Microwave susceptibility observation of interacting many-body Andreev states, Phys. Rev. Lett. 129, 227701 (2022).
  17. M. Hinderling, D. Sabonis, S. Paredes, D. Z. Haxell, M. Coraiola, S. C. ten Kate, E. Cheah, F. Krizek, R. Schott, W. Wegscheider, and F. Nichele, Flip-chip-based microwave spectroscopy of Andreev bound states in a planar Josephson junction, Phys. Rev. Appl. 19, 054026 (2023).
  18. J. J. Wesdorp, F. J. Matute-Cañadas, A. Vaartjes, L. Grünhaupt, T. Laeven, S. Roelofs, L. J. Splitthoff, M. Pita-Vidal, A. Bargerbos, D. J. van Woerkom, P. Krogstrup, L. P. Kouwenhoven, C. K. Andersen, A. L. Yeyati, B. van Heck, and G. de Lange, Microwave spectroscopy of interacting Andreev spins, Phys. Rev. B 109, 045302 (2024).
  19. M. Hinderling, S. C. ten Kate, M. Coraiola, D. Z. Haxell, M. Stiefel, M. Mergenthaler, S. Paredes, S. W. Bedell, D. Sabonis, and F. Nichele, Direct microwave spectroscopy of Andreev bound states in planar Ge Josephson junctions, PRX Quantum 5, 030357 (2024).
  20. B. H. Elfeky, K. Dindial, David S. Brandão, B. Pekerten, J. Lee, William M. Strickland, Patrick J. Strohbeen, A. Danilenko, L. Baker, M. Mikalsen, W. Schiela, Z. Liang, J. Issokson, I. Levy, I. Žutić, and J. Shabani, Microwave Andreev bound state spectroscopy in a semiconductor-based planar Josephson junction, Phys. Rev. Res. 7, 013248 (2025).
  21. Pavel D. Kurilovich, Vladislav D. Kurilovich, V. Fatemi, Michel H. Devoret, and Leonid I. Glazman, Microwave response of an Andreev bound state, Phys. Rev. B 104, 174517 (2021).
  22. Pavel D. Kurilovich, Vladislav D. Kurilovich, Aleksandr E. Svetogorov, W. Belzig, Michel H. Devoret, and Leonid I. Glazman, On-demand population of Andreev levels by their ionization in the presence of Coulomb blockade, Phys. Rev. B 110, 184508 (2024).
  23. A. Tosato, V. Levajac, J.-Y. Wang, C. J. Boor, F. Borsoi, M. Botifoll, C. N. Borja, S. Martí-Sánchez, J. Arbiol, A. Sammak, M. Veldhorst, and G. Scappucci, Hard superconducting gap in germanium, Commun. Mater. 4, 23 (2023).
  24. M. Lodari, A. Tosato, D. Sabbagh, M. A. Schubert, G. Capellini, A. Sammak, M. Veldhorst, and G. Scappucci, Light effective hole mass in undoped Ge/SiGe quantum wells, Phys. Rev. B 100, 041304(R) (2019).
  25. G. Scappucci, C. Kloeffel, F. A. Zwanenburg, D. Loss, M. Myronov, J.-J. Zhang, S. De Franceschi, G. Katsaros, and M. Veldhorst, The germanium quantum information route, Nat. Rev. Mater. 6, 926 (2021).
  26. L. Lakic, W. I. L. Lawrie, D. van Driel, L. E. A. Stehouwer, Y. Su, M. Veldhorst, G. Scappucci, F. Kuemmeth, and A. Chatterjee, A quantum dot in germanium proximitized by a superconductor, Nat. Mater. 24, 552 (2025).
  27. M. Hinderling, S. C. Ten Kate, D. Z. Haxell, M. Coraiola, S. Paredes, E. Cheah, F. Krizek, R. Schott, W. Wegscheider, D. Sabonis, and F. Nichele, Flip-chip-based fast inductive parity readout of a planar superconducting island, PRX Quantum 5, 030337 (2024).
  28. S. Probst, F. B. Song, P. A. Bushev, A. V. Ustinov, and M. Weides, Efficient and robust analysis of complex scattering data under noise in microwave resonators, Rev. Sci. Instrum. 86, 024706 (2015).
  29. S. W. Bedell, S. Hart, S. Bangsaruntip, C. Durfee, J. A. Ott, M. Hopstaken, M. S. Carroll, and P. Gumann, (Invited) Low-temperature growth of strained germanium quantum wells for high mobility applications, ECS Trans. 98, 215 (2020).
  30. J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Theory of superconductivity, Phys. Rev. 108, 1175 (1957).
  31. M. Watanabe, K. Inomata, T. Yamamoto, and Jaw S. Tsai, Power-dependent internal loss in Josephson bifurcation amplifiers, Phys. Rev. B 80, 174502 (2009).
  32. G. Romero, I. Lizuain, V. S. Shumeiko, E. Solano, and F. S. Bergeret, Circuit quantum electrodynamics with a superconducting quantum point contact, Phys. Rev. B 85, 180506(R) (2012).
  33. S. Park, C. Metzger, L. Tosi, M. F. Goffman, C. Urbina, H. Pothier, and A. L. Yeyati, From adiabatic to dispersive readout of quantum circuits, Phys. Rev. Lett. 125, 077701 (2020).
  34. C. Metzger, S. Park, L. Tosi, C. Janvier, A. A. Reynoso, M. F. Goffman, C. Urbina, A. Levy Yeyati, and H. Pothier, Circuit-QED with phase-biased Josephson weak links, Phys. Rev. Res. 3, 013036 (2021).
  35. R. Haller, G. Fülöp, D. Indolese, J. Ridderbos, R. Kraft, L. Y. Cheung, J. H. Ungerer, K. Watanabe, T. Taniguchi, D. Beckmann, R. Danneau, P. Virtanen, and C. Schönenberger, Phase-dependent microwave response of a graphene Josephson junction, Phys. Rev. Res. 4, 013198 (2022).
  36. Philip F. Bagwell, Suppression of the Josephson current through a narrow, mesoscopic, semiconductor channel by a single impurity, Phys. Rev. B 46, 12573 (1992).
  37. M. R. Sahu, F. J. Matute-Cañadas, M. Benito, P. Krogstrup, J. Nygård, M. F. Goffman, C. Urbina, A. L. Yeyati, and H. Pothier, Ground-state phase diagram and parity-flipping microwave transitions in a gate-tunable Josephson junction, Phys. Rev. B 109, 134506 (2024).
  38. L. Massai, B. Hetényi, M. Mergenthaler, F. J. Schupp, L. Sommer, S. Paredes, S. W. Bedell, P. Harvey-Collard, G. Salis, A. Fuhrer, and N. W. Hendrickx, Impact of interface traps on charge noise and low-density transport properties in Ge/SiGe heterostructures, Commun. Mater. 5, 151 (2024).
  39. S. Park and A. L. Yeyati, Andreev spin qubits in multichannel Rashba nanowires, Phys. Rev. B 96, 125416 (2017).
  40. S. Bosco, M. Benito, C. Adelsberger, and D. Loss, Squeezed hole spin qubits in Ge quantum dots with ultrafast gates at low power, Phys. Rev. B 104, 115425 (2021).
  41. C. Adelsberger, S. Bosco, J. Klinovaja, and D. Loss, Enhanced orbital magnetic field effects in Ge hole nanowires, Phys. Rev. B 106, 235408 (2022).
  42. S. Hoffman and C. Tahan, Resolving Andreev spin qubits in germanium-based Josephson junctions, ArXiv:2506.13988.
  43. M. Luethi, K. Laubscher, S. Bosco, D. Loss, and J. Klinovaja, Planar Josephson junctions in germanium: Effect of cubic spin-orbit interaction, Phys. Rev. B 107, 035435 (2023).
  44. D. Costa, P. D. Vecchio, K. Hudson, L. E. A. Stehouwer, A. Tosato, D. D. Esposti, M. Lodari, S. Bosco, and G. Scappucci, Buried unstrained germanium channels: A lattice-matched platform for quantum technology, ArXiv:2506.04724.
  45. O. O. Shvetsov, A. Khola, V. Buccheri, I. P. C. Cools, N. Trnjanin, A. Geresdi, T. Kanne, and J. Nygård, Approaching the ultrastrong-coupling regime between an Andreev level and a microwave resonator, Phys. Rev. Appl. 24, 044015 (2025).
  46. https://doi.org/10.5281/zenodo.17580733.

Outline

Information

Phys. Rev. Applied 24, 064005– Published 1 December, 2025
  • Received 8 August 2025
  • Revised 31 October 2025
  • Accepted 4 November 2025
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