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.

Microwave spectroscopy of spinful Andreev bound states in ballistic semiconductor Josephson junctions


The superconducting proximity effect in semiconductor nanowires has recently enabled the study of new superconducting architectures, such as gate-tunable superconducting qubits and multiterminal Josephson junctions. As opposed to their metallic counterparts, the electron density in semiconductor nanosystems is tunable by external electrostatic gates, providing a highly scalable and in situ variation of the device properties. In addition, semiconductors with large g-factor and spin–orbit coupling have been shown to give rise to exotic phenomena in superconductivity, such as φ0 Josephson junctions and the emergence of Majorana bound states. Here, we report microwave spectroscopy measurements that directly reveal the presence of Andreev bound states (ABS) in ballistic semiconductor channels. We show that the measured ABS spectra are the result of transport channels with gate-tunable, high transmission probabilities up to 0.9, which is required for gate-tunable Andreev qubits and beneficial for braiding schemes of Majorana states. For the first time, we detect excitations of a spin-split pair of ABS and observe symmetry-broken ABS, a direct consequence of the spin–orbit coupling in the semiconductor.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Device schematics and working principle.
Figure 2: Gate dependence of Andreev bound states.
Figure 3: Theoretical description of the transitions.
Figure 4: Spectroscopy of spin-split Andreev bound states in a Rashba nanowire.
Figure 5: Time-reversal symmetry-broken ABS in magnetic field.


  1. 1

    Landauer, R. Can a length of perfect conductor have a resistance? Phys. Lett. A 85, 91–93 (1981).

    ADS  Article  Google Scholar 

  2. 2

    Kulik, I. O. Macroscopic quantization and the proximity effect in SNS junctions. Sov. J. Exp. Theor. Phys. 30, 944–950 (1970).

    ADS  Google Scholar 

  3. 3

    Beenakker, C. W. J. Universal limit of critical-current fluctuations in mesoscopic Josephson junctions. Phys. Rev. Lett. 67, 3836–3839 (1991).

    ADS  Article  Google Scholar 

  4. 4

    Bretheau, L., Girit, Ç. Ö., Pothier, H., Esteve, D. & Urbina, C. Exciting Andreev pairs in a superconducting atomic contact. Nature 499, 312–315 (2013).

    ADS  Article  Google Scholar 

  5. 5

    Pillet, J.-D. et al. Andreev bound states in supercurrent-carrying carbon nanotubes revealed. Nat. Phys. 6, 965–969 (2010).

    Article  Google Scholar 

  6. 6

    Chang, W., Manucharyan, V., Jespersen, T. S., Nygård, J. & Marcus, C. M. Tunneling spectroscopy of quasiparticle bound states in a spinful Josephson junction. Phys. Rev. Lett. 110, 217005 (2013).

    ADS  Article  Google Scholar 

  7. 7

    Kos, F., Nigg, S. E. & Glazman, L. I. Frequency-dependent admittance of a short superconducting weak link. Phys. Rev. B 87, 174521 (2013).

    ADS  Article  Google Scholar 

  8. 8

    Janvier, C. et al. Coherent manipulation of Andreev states in superconducting atomic contacts. Science 349, 1199–1202 (2015).

    ADS  Article  Google Scholar 

  9. 9

    Väyrynen, J. I., Rastelli, G., Belzig, W. & Glazman, L. I. Microwave signatures of Majorana states in a topological Josephson junction. Phys. Rev. B 92, 134508 (2015).

    ADS  Article  Google Scholar 

  10. 10

    Lutchyn, R. M., Sau, J. D. & Das Sarma, S. Majorana fermions and a topological phase transition in semiconductor–superconductor heterostructures. Phys. Rev. Lett. 105, 077001 (2010).

    ADS  Article  Google Scholar 

  11. 11

    Oreg, Y., Refael, G. & von Oppen, F. Helical liquids and Majorana bound states in quantum wires. Phys. Rev. Lett. 105, 177002 (2010).

    ADS  Article  Google Scholar 

  12. 12

    Mourik, V. et al. Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices. Science 336, 1003–1007 (2012).

    ADS  Article  Google Scholar 

  13. 13

    Krogstrup, P. et al. Epitaxy of semiconductor-superconductor nanowires. Nat. Mater. 14, 400–406 (2015).

    ADS  Article  Google Scholar 

  14. 14

    Holst, T., Esteve, D., Urbina, C. & Devoret, M. H. Effect of a transmission line resonator on a small capacitance tunnel junction. Phys. Rev. Lett. 73, 3455–3458 (1994).

    ADS  Article  Google Scholar 

  15. 15

    Ambegaokar, V. & Baratoff, A. Tunneling between superconductors. Phys. Rev. Lett. 10, 486–489 (1963).

    ADS  Article  Google Scholar 

  16. 16

    Chang, W. et al. Hard gap in epitaxial semiconductor-superconductor nanowires. Nat. Nanotech. 10, 232–236 (2015).

    ADS  Article  Google Scholar 

  17. 17

    Doh, Y.-J. et al. Tunable supercurrent through semiconductor nanowires. Science 309, 272–275 (2005).

    ADS  Article  Google Scholar 

  18. 18

    Larsen, T. W. et al. Semiconductor-nanowire-based superconducting qubit. Phys. Rev. Lett. 115, 127001 (2015).

    ADS  Article  Google Scholar 

  19. 19

    de Lange, G. et al. Realization of microwave quantum circuits using hybrid superconducting-semiconducting nanowire Josephson elements. Phys. Rev. Lett. 115, 127002 (2015).

    ADS  Article  Google Scholar 

  20. 20

    Bretheau, L. et al. Theory of microwave spectroscopy of Andreev bound states with a Josephson junction. Phys. Rev. B 90, 134506 (2014).

    ADS  Article  Google Scholar 

  21. 21

    Zazunov, A., Shumeiko, V. S., Bratus, E. N., Lantz, J. & Wendin, G. Andreev level qubit. Phys. Rev. Lett. 90, 087003 (2003).

    ADS  Article  Google Scholar 

  22. 22

    Zazunov, A., Shumeiko, V. S., Wendin, G. & Bratus, E. N. Dynamics and phonon-induced decoherence of Andreev level qubit. Phys. Rev. B 71, 214505 (2005).

    ADS  Article  Google Scholar 

  23. 23

    Cheng, M. & Lutchyn, R. M. Josephson current through a superconductor/semiconductor-nanowire/superconductor junction: effects of strong spin–orbit coupling and Zeeman splitting. Phys. Rev. B 86, 134522 (2012).

    ADS  Article  Google Scholar 

  24. 24

    Das, A. et al. Zero-bias peaks and splitting in an Al-InAs nanowire topological superconductor as a signature of Majorana fermions. Nat. Phys. 8, 887–895 (2012).

    Article  Google Scholar 

  25. 25

    Higginbotham, A. P. et al. Parity lifetime of bound states in a proximitized semiconductor nanowire. Nat. Phys. 11, 1017–1021 (2015).

    Article  Google Scholar 

  26. 26

    Albrecht, S. M. et al. Exponential protection of zero modes in Majorana islands. Nature 531, 206–209 (2016).

    ADS  Article  Google Scholar 

  27. 27

    Michelsen, J., Shumeiko, V. S. & Wendin, G. Manipulation with Andreev states in spin active mesoscopic Josephson junctions. Phys. Rev. B 77, 184506 (2008).

    ADS  Article  Google Scholar 

  28. 28

    Nijholt, B. & Akhmerov, A. R. Orbital effect of magnetic field on the Majorana phase diagram. Phys. Rev. B 93, 235434 (2016).

    ADS  Article  Google Scholar 

  29. 29

    Meservey, R. & Tedrow, P. Properties of very thin aluminum films. J. Appl. Phys. 42, 51–53 (1971).

    ADS  Article  Google Scholar 

  30. 30

    Yokoyama, T., Eto, M. & Nazarov, Y. V. Josephson current through semiconductor nanowire with spin–orbit interaction in magnetic field. J. Phys. Soc. Jpn 82, 054703 (2013).

    ADS  Article  Google Scholar 

  31. 31

    Krive, I. V., Gorelik, L. Y., Shekhter, R. I. & Jonson, M. Chiral symmetry breaking and the Josephson current in a ballistic superconductor–quantum wire–superconductor junction. Low Temp. Phys. 30, 398–404 (2004).

    ADS  Article  Google Scholar 

  32. 32

    Buzdin, A. Direct coupling between magnetism and superconducting current in the Josephson φ0 junction. Phys. Rev. Lett. 101, 107005 (2008).

    ADS  Article  Google Scholar 

  33. 33

    Szombati, D. B. et al. Josephson φ0-junction in nanowire quantum dots. Nat. Phys. 12, 568–572 (2016).

    Article  Google Scholar 

  34. 34

    Liu, J.-F. & Chan, K. S. Relation between symmetry breaking and the anomalous Josephson effect. Phys. Rev. B 82, 125305 (2010).

    ADS  Article  Google Scholar 

  35. 35

    Rasmussen, A. et al. Effects of spin–orbit coupling and spatial symmetries on the Josephson current in SNS junctions. Phys. Rev. B 93, 155406 (2016).

    ADS  Article  Google Scholar 

  36. 36

    Konschelle, F., Tokatly, I. V. & Bergeret, F. S. Theory of the spin-galvanic effect and the anomalous phase shift φ0 in superconductors and Josephson junctions with intrinsic spin–orbit coupling. Phys. Rev. B 92, 125443 (2015).

    ADS  Article  Google Scholar 

  37. 37

    Villegas, J. E. et al. A superconducting reversible rectifier that controls the motion of magnetic flux quanta. Science 302, 1188–1191 (2003).

    ADS  Article  Google Scholar 

  38. 38

    Reynoso, A. A., Usaj, G., Balseiro, C. A., Feinberg, D. & Avignon, M. Anomalous Josephson current in junctions with spin polarizing quantum point contacts. Phys. Rev. Lett. 101, 107001 (2008).

    ADS  Article  Google Scholar 

  39. 39

    van Woerkom, D. J. et al. Microwave Spectroscopy of Spinful Andreev Bound States in Ballistic Semiconductor Josephson Junctions (QuTech, 2017);

    Google Scholar 

Download references


The authors thank L. Bretheau, Ç. Ö. Girit, L. DiCarlo, M. P. Nowak and A. R. Akhmerov for fruitful discussions, and R. van Gulik, T. Kriváchy, A. Bruno, N. de Jong, J. D. Watson, M. C. Cassidy, R. N. Schouten and T. S. Jespersen for assistance with fabrication and experiments. This work has been supported by the Danish National Research Foundation, the Villum Foundation, the Dutch Organization for Fundamental Research on Matter (FOM), the Netherlands Organization for Scientific Research (NWO) by a Veni grant, Microsoft Corporation Station Q and a Synergy Grant of the European Research Council. B.v.H. was supported by ONR Grant Q00704. L.I.G. and J.I.V. acknowledge the support by NSF Grant DMR-1603243.

Author information




D.J.v.W., A.P. and D.B. performed the experiments. B.v.H., J.I.V. and L.I.G. developed the theory to analyse the data. P.K. and J.N. contributed to the nanowire growth. D.J.v.W., A.P. and D.B. fabricated the samples. L.P.K. and A.G. designed and supervised the experiments. D.J.v.W., B.v.H., L.P.K. and A.G. analysed the data. The manuscript has been prepared with contributions from all the authors.

Corresponding author

Correspondence to Attila Geresdi.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

Supplementary information (PDF 2207 kb)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

van Woerkom, D., Proutski, A., van Heck, B. et al. Microwave spectroscopy of spinful Andreev bound states in ballistic semiconductor Josephson junctions. Nature Phys 13, 876–881 (2017).

Download citation

Further reading


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