- Featured in Physics
- Editors' Suggestion
- Open Access
Sextets in four-terminal Josephson junctions
Phys. Rev. B 112, 195430 – Published 19 November, 2025
DOI: https://doi.org/10.1103/phvj-vfnx
Abstract
Multiterminal superconducting junctions have revitalized the investigation of the Josephson effect. One of the most interesting aspects of these hybrid systems is the occurrence of multi-Cooper pair tunneling processes that have no analog in two-terminal devices. Such correlated tunneling events are also intimately connected to the Andreev bound states (ABSs) supported by these structures. Josephson junctions with four superconducting terminals have attracted special attention because they are predicted to support ABSs with nontrivial topological properties. Here, we present a theoretical study of sextets, which are correlated tunneling processes involving three Cooper pairs and four different superconducting terminals. We investigate how sextets can be identified from the analysis of the current-phase relation, show how sextets are connected to the hybridization of ABSs, and discuss their existence in recent experiments on four-terminal devices realized in hybrid Al/InAs heterostructures.
Physics Subject Headings (PhySH)
synopsis
Six Electrons Tunnel as One
Simultaneous tunneling of three electron pairs may occur in some superconducting devices.
See more in Physics
Article Text
References (58)
- B. Josephson, Possible new effects in superconductive tunnelling, Phys. Lett. 1, 251 (1962).
- A. Barone and G. Paterno, Physics and Applications of the Josephson Effect (John Wiley & Sons, Hoboken, NJ, 1982).
- C. W. J. Beenakker and H. van Houten, Josephson current through a superconducting quantum point contact shorter than the coherence length, Phys. Rev. Lett. 66, 3056 (1991).
- A. Furusaki and M. Tsukada, Current-carrying states in Josephson junctions, Phys. Rev. B 43, 10164 (1991).
- J.-D. Pillet, C. H. L. Quay, P. Morfin, C. Bena, A. L. Yeyati, and P. Joyez, Andreev bound states in supercurrent-carrying carbon nanotubes revealed, Nat. Phys. 6, 965 (2010).
- W. Chang, V. E. Manucharyan, T. S. Jespersen, J. Nygård, and C. M. Marcus, Tunneling spectroscopy of quasiparticle bound states in a spinful Josephson junction, Phys. Rev. Lett. 110, 217005 (2013).
- L. Bretheau, Ç. Ö. Girit, H. Pothier, D. Esteve, and C. Urbina, Exciting Andreev pairs in a superconducting atomic contact, Nature (London) 499, 312 (2013).
- L. Bretheau, Ç. Ö. Girit, C. Urbina, D. Esteve, and H. Pothier, Supercurrent spectroscopy of Andreev states, Phys. Rev. X 3, 041034 (2013).
- 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).
- L. Bretheau, J. I.-J. Wang, R. Pisoni, K. Watanabe, T. Taniguchi, and P. Jarillo-Herrero, Tunnelling spectroscopy of Andreev states in graphene, Nat. Phys. 13, 756 (2017).
- D. J. van Woerkom, A. Proutski, B. van Heck, D. Bouman, J. I. Väyrynen, L. I. Glazman, P. Krogstrup, J. Nygård, L. P. Kouwenhoven, and A. Geresdi, Microwave spectroscopy of spinful Andreev bound states in ballistic semiconductor Josephson junctions, Nat. Phys. 13, 876 (2017).
- 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).
- 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).
- 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).
- 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).
- M. Hays, V. Fatemi, D. Bouman, J. Cerrillo, S. Diamond, K. Serniak, T. Connolly, P. Krogstrup, J. Nygård, A. Levy Yeyati, A. Geresdi, and M. H. Devoret, Coherent manipulation of an Andreev spin qubit, Science 373, 430 (2021).
- M. Pita-Vidal, A. Bargerbos, R. Žitko, L. J. Splitthoff, L. Grünhaupt, J. J. Wesdorp, Y. Liu, L. P. Kouwenhoven, R. Aguado, B. van Heck et al., Direct manipulation of a superconducting spin qubit strongly coupled to a transmon qubit, Nat. Phys. 19, 1110 (2023).
- 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).
- J. J. Wesdorp, F. J. Matute-Caňadas, 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).
- A. W. Draelos, M.-T. Wei, A. Seredinski, H. Li, Y. Mehta, K. Watanabe, T. Taniguchi, I. V. Borzenets, F. Amet, and G. Finkelstein, Supercurrent flow in multiterminal graphene Josephson junctions, Nano Lett. 19, 1039 (2019).
- G. V. Graziano, J. S. Lee, M. Pendharkar, C. J. Palmstrøm, and V. S. Pribiag, Transport studies in a gate-tunable three-terminal Josephson junction, Phys. Rev. B 101, 054510 (2020).
- N. Pankratova, H. Lee, R. Kuzmin, K. Wickramasinghe, W. Mayer, J. Yuan, M. G. Vavilov, J. Shabani, and V. E. Manucharyan, Multiterminal Josephson effect, Phys. Rev. X 10, 031051 (2020).
- E. G. Arnault, T. F. Q. Larson, A. Seredinski, L. Zhao, S. Idris, A. McConnell, K. Watanabe, T. Taniguchi, I. Borzenets, F. Amet, and G. Finkelstein, Multiterminal inverse AC Josephson effect, Nano Lett. 21, 9668 (2021).
- G. V. Graziano, M. Gupta, M. Pendharkar, J. T. Dong, C. P. Dempsey, C. Palmstrøm, and V. S. Pribiag, Selective control of conductance modes in multi-terminal Josephson junctions, Nat. Commun. 13, 5933 (2022).
- M. Gupta, G. V. Graziano, M. Pendharkar, J. T. Dong, C. P. Dempsey, C. Palmstrøm, and V. S. Pribiag, Gate-tunable superconducting diode effect in a three-terminal Josephson device, Nat. Commun. 14, 3078 (2023).
- E. G. Arnault, J. Chiles, T. F. Q. Larson, C.-C. Chen, L. Zhao, K. Watanabe, T. Taniguchi, F. Amet, and G. Finkelstein, Multiplet supercurrents in a Josephson circuit, Phys. Rev. Lett. 134, 067001 (2025).
- T. Yokoyama and Y. V. Nazarov, Singularities in the andreev spectrum of a multiterminal Josephson junction, Phys. Rev. B 92, 155437 (2015).
- R.-P. Riwar, M. Houzet, J. S. Meyer, and Y. V. Nazarov, Multi-terminal Josephson junctions as topological matter, Nat. Commun. 7, 11167 (2016).
- E. Eriksson, R.-P. Riwar, M. Houzet, J. S. Meyer, and Y. V. Nazarov, Topological transconductance quantization in a four-terminal Josephson junction, Phys. Rev. B 95, 075417 (2017).
- J. S. Meyer and M. Houzet, Nontrivial Chern numbers in three-terminal Josephson junctions, Phys. Rev. Lett. 119, 136807 (2017).
- H.-Y. Xie, M. G. Vavilov, and A. Levchenko, Topological Andreev bands in three-terminal Josephson junctions, Phys. Rev. B 96, 161406(R) (2017).
- H.-Y. Xie and A. Levchenko, Topological supercurrents interaction and fluctuations in the multiterminal Josephson effect, Phys. Rev. B 99, 094519 (2019).
- E. V. Repin, Y. Chen, and Y. V. Nazarov, Topological properties of multiterminal superconducting nanostructures: Effect of a continuous spectrum, Phys. Rev. B 99, 165414 (2019).
- L. Peralta Gavensky, G. Usaj, and C. A. Balseiro, Topological phase diagram of a three-terminal Josephson junction: From the conventional to the Majorana regime, Phys. Rev. B 100, 014514 (2019).
- M. Houzet and J. S. Meyer, Majorana-Weyl crossings in topological multiterminal junctions, Phys. Rev. B 100, 014521 (2019).
- R. L. Klees, G. Rastelli, J. C. Cuevas, and W. Belzig, Microwave spectroscopy reveals the quantum geometric tensor of topological Josephson matter, Phys. Rev. Lett. 124, 197002 (2020).
- H. Weisbrich, R. L. Klees, G. Rastelli, and W. Belzig, Second Chern number and non-Abelian Berry phase in topological superconducting systems, PRX Quantum 2, 010310 (2021).
- H.-Y. Xie, J. Hasan, and A. Levchenko, Non-Abelian monopoles in the multiterminal Josephson effect, Phys. Rev. B 105, L241404 (2022).
- H. Barakov and Y. V. Nazarov, Abundance of Weyl points in semiclassical multiterminal superconducting nanostructures, Phys. Rev. B 107, 014507 (2023).
- L. Teshler, H. Weisbrich, J. Sturm, R. L. Klees, G. Rastelli, and W. Belzig, Ground state topology of a four-terminal superconducting double quantum dot, SciPost Phys. 15, 214 (2023).
- M. Coraiola, D. Z. Haxell, D. Sabonis, H. Weisbrich, A. E. Svetogorov, M. Hinderling, S. C. ten Kate, E. Cheah, F. Krizek, R. Schott et al., Phase-engineering the Andreev band structure of a three-terminal Josephson junction, Nat. Commun. 14, 6784 (2023).
- T. Antonelli, M. Coraiola, D. C. Ohnmacht, A. E. Svetogorov, D. Sabonis, S. C. ten Kate, E. Cheah, F. Krizek, R. Schott, J. C. Cuevas et al., Exploring the energy spectrum of a four-terminal Josephson junction: Towards topological Andreev band structures, Phys. Rev. X 15, 031066 (2025).
- M. Coraiola, A. E. Svetogorov, D. Z. Haxell, D. Sabonis, M. Hinderling, S. C. Ten Kate, E. Cheah, F. Krizek, R. Schott, W. Wegscheider et al., Flux-tunable Josephson diode effect in a hybrid four-terminal Josephson junction, ACS Nano 18, 9221 (2024).
- D. C. Ohnmacht, V. Wilhelm, H. Weisbrich, and W. Belzig, Non-Hermitian topology in multiterminal superconducting junctions, Phys. Rev. Lett. 134, 156601 (2025).
- A. Freyn, B. Douçot, D. Feinberg, and R. Mélin, Production of nonlocal quartets and phase-sensitive entanglement in a superconducting beam splitter, Phys. Rev. Lett. 106, 257005 (2011).
- T. Jonckheere, J. Rech, T. Martin, B. Douçot, D. Feinberg, and R. Mélin, Multipair dc Josephson resonances in a biased all-superconducting bijunction, Phys. Rev. B 87, 214501 (2013).
- J. Rech, T. Jonckheere, T. Martin, B. Douçot, D. Feinberg, and R. Mélin, Proposal for the observation of nonlocal multipair production, Phys. Rev. B 90, 075419 (2014).
- D. Feinberg, T. Jonckheere, J. Rech, T. Martin, B. Douçot, and R. Mélin, Quartets and the current-phase structure of a double quantum dot superconducting bijunction at equilibrium, Eur. Phys. J. B 88, 99 (2015).
- A. Melo, V. Fatemi, and A. R. Akhmerov, Multiplet supercurrent in Josephson tunneling circuits, SciPost Phys. 12, 017 (2022).
- R. Mélin, R. Danneau, and C. B. Winkelmann, Proposal for detecting the -shifted Cooper quartet supercurrent, Phys. Rev. Res. 5, 033124 (2023).
- A. H. Pfeffer, J. E. Duvauchelle, H. Courtois, R. Mélin, D. Feinberg, and F. Lefloch, Subgap structure in the conductance of a three-terminal Josephson junction, Phys. Rev. B 90, 075401 (2014).
- Y. Cohen, Y. Ronen, J.-H. Kang, M. Heiblum, D. Feinberg, R. Mélin, and H. Shtrikman, Nonlocal supercurrent of quartets in a three-terminal Josephson junction, Proc. Natl. Acad. Sci. USA 115, 6991 (2018).
- K.-F. Huang, Y. Ronen, R. Mélin, D. Feinberg, K. Watanabe, T. Taniguchi, and P. Kim, Evidence for charge of Cooper quartets in a biased multi-terminal graphene-based Josephson junction, Nat. Commun. 13, 3032 (2022).
- E. G. Arnault, S. Idris, A. McConnell, L. Zhao, T. F. Larson, K. Watanabe, T. Taniguchi, G. Finkelstein, and F. Amet, Dynamical stabilization of multiplet supercurrents in multiterminal Josephson junctions, Nano Lett. 22, 7073 (2022).
- M. Gupta, V. Khade, C. Riggert, L. Shani, G. Menning, P. J. Lueb, J. Jung, R. Mélin, E. P. Bakkers, and V. S. Pribiag, Evidence for -shifted Cooper quartets and few-mode transport in PbTe nanowire three-terminal Josephson junctions, Nano Lett. 24, 13903 (2024).
- D. C. Ohnmacht, M. Coraiola, J. J. García-Esteban, D. Sabonis, F. Nichele, W. Belzig, and J. C. Cuevas, Quartet tomography in multiterminal Josephson junctions, Phys. Rev. B 109, L241407 (2024).
- D. C. Ohnmacht, V. Wilhelm, and W. Belzig, Reflectionless modes as a source of Weyl nodes in multiterminal junctions, arXiv:2503.10874.
- M. Coraiola, D. Z. Haxell, D. Sabonis, M. Hinderling, S. C. ten Kate, E. Cheah, F. Krizek, R. Schott, W. Wegscheider, and F. Nichele, Spin-degeneracy breaking and parity transitions in three-terminal Josephson junctions, Phys. Rev. X 14, 031024 (2024).