Photon-assisted tunnelling of zero modes in a Majorana wire

Abstract

Hybrid nanowires with proximity-induced superconductivity in the topological regime host Majorana zero modes at their ends. Networks of such structures can produce topologically protected qubits where the fundamental energy scale is given by the inter-pair coupling EM between the zero modes belonging to different wire segments. Here we report on the spectroscopic measurement of EM in an InAs/Al double-island device by tracking the position of the microwave-induced quasiparticle excitations using a radiofrequency charge sensor. At zero magnetic field, photon-assisted tunnelling of Cooper pairs allows us to estimate the Josephson coupling between the islands. In the presence of a magnetic field aligned along the nanowire, we observe the 1e periodic excitation spectrum resulting from a zero-energy subgap state that emerges in a magnetic field. The discrete 1e periodic excitation spectrum is consistent with the coherent hybridization of single-electron states belonging to two opposite-parity branches. The dependence of excitation frequency on detuning indicates a sizable (GHz-scale) and controllable hybridization of zero modes across the junction separating islands, a requirement for applications related to Majorana-based qubits.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Fig. 1: Charge states of the semiconductor–superconductor double-island device for different magnetic field values.
Fig. 2: Characterization of tunnel conductance through the middle tunnel junction as a function of magnetic field parallel to the nanowire.
Fig. 3: Microwave spectroscopy at zero magnetic field.
Fig. 4: Microwave spectroscopy at B = 0.75 T.

Data availability

The data represented in the main text figures are available as source data with the online version of the paper. All other data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

References

  1. 1.

    Lafarge, P., Joyez, P., Esteve, D., Urbina, C. & Devoret, M. H. Two-electron quantization of the charge on a superconductor. Nature 365, 422–424 (1993).

    ADS  Article  Google Scholar 

  2. 2.

    Nakamura, Y., Pashkin, Y. A. & Tsai, J. S. Coherent control of macroscopic quantum states in a single-Cooper-pair box. Nature 398, 786–788 (1999).

    ADS  Article  Google Scholar 

  3. 3.

    Hützen, R., Zazunov, A., Braunecker, B., Yeyati, A. L. & Egger, R. Majorana single-charge transistor. Phys. Rev. Lett. 109, 166403 (2012).

    ADS  Article  Google Scholar 

  4. 4.

    van Veen, J. et al. Magnetic-field-dependent quasiparticle dynamics of nanowire single-Cooper-pair transistors. Phys. Rev. B 98, 174502 (2018).

    ADS  Article  Google Scholar 

  5. 5.

    Shen, J. et al. Parity transitions in the superconducting ground state of hybrid InSb-Al coulomb islands. Nat. Commun. 9, 4801 (2018).

    ADS  Article  Google Scholar 

  6. 6.

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

    ADS  Article  Google Scholar 

  7. 7.

    Aasen, D. et al. Milestones toward Majorana-based quantum computing. Phys. Rev. X 6, 031016 (2016).

    Google Scholar 

  8. 8.

    Karzig, T. et al. Scalable designs for quasiparticle-poisoning-protected topological quantum computation with Majorana zero modes. Phys. Rev. B 95, 235305 (2017).

    ADS  Article  Google Scholar 

  9. 9.

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

    ADS  Article  Google Scholar 

  10. 10.

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

    ADS  Article  Google Scholar 

  11. 11.

    Schoelkopf, R. J. The radio-frequency single-electron transistor (RF-SET): a fast and ultrasensitive electrometer. Science 280, 1238–1242 (1998).

    ADS  Article  Google Scholar 

  12. 12.

    Razmadze, D. et al. Radio-frequency methods for Majorana-based quantum devices: fast charge sensing and phase-diagram mapping. Phys. Rev. Appl. 11, 064011 (2019).

    ADS  Article  Google Scholar 

  13. 13.

    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 

  14. 14.

    Huang, Y. et al. Metamorphosis of Andreev bound states into Majorana bound states in pristine nanowires. Phys. Rev. B 98, 144511 (2018).

    ADS  Article  Google Scholar 

  15. 15.

    Joyez, P., Lafarge, P., Filipe, A., Esteve, D. & Devoret, M. H. Observation of parity-induced suppression of Josephson tunneling in the superconducting single electron transistor. Phys. Rev. Lett. 72, 2458–2461 (1994).

    ADS  Article  Google Scholar 

  16. 16.

    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 

  17. 17.

    Lafarge, P., Joyez, P., Esteve, D., Urbina, C. & Devoret, M. H. Measurement of the even–odd free-energy difference of an isolated superconductor. Phys. Rev. Lett. 70, 994–997 (1993).

    ADS  Article  Google Scholar 

  18. 18.

    Ingold, G. L. & Nazarov, Y. V. in Single Charge Tunneling: Coulomb Blockade Phenomena in Nanostructures (eds Grabert, H. & Devoret, M. H.) 21–107 (Plenum, 1992).

  19. 19.

    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 

  20. 20.

    Pekola, J. P. et al. Environment-assisted tunneling as an origin of the Dynes density of states. Phys. Rev. Lett. 105, 026803 (2010).

    ADS  Article  Google Scholar 

  21. 21.

    Zhang, H. et al. Quantized Majorana conductance. Nature 556, 74–79 (2018).

    ADS  Article  Google Scholar 

  22. 22.

    Deng, M. T. et al. Majorana bound state in a coupled quantum-dot hybrid-nanowire system. Science 354, 1557–1562 (2016).

    ADS  Article  Google Scholar 

  23. 23.

    Vaitiekènas, S., Deng, M.-T., NygÅrd, J., Krogstrup, P. & Marcus, C. M. Effective g factor of subgap states in hybrid nanowires. Phys. Rev. Lett. 121, 037703 (2018).

    ADS  Article  Google Scholar 

  24. 24.

    Mannila, E. T., Maisi, V. F., Nguyen, H. Q., Marcus, C. M. & Pekola, J. P. Detecting parity effect in a superconducting device in the presence of parity switches. Phys. Rev. B 100, 020502 (2019).

    ADS  Article  Google Scholar 

  25. 25.

    Lehnert, K. W. et al. Measurement of the excited-state lifetime of a microelectronic circuit. Phys. Rev. Lett. 90, 027002 (2003).

    ADS  Article  Google Scholar 

  26. 26.

    Duty, T., Gunnarsson, D., Bladh, K. & Delsing, P. Coherent dynamics of a Josephson charge qubit. Phys. Rev. B 69, 140503 (2004).

    ADS  Article  Google Scholar 

  27. 27.

    Lambert, N. J. et al. Microwave irradiation and quasiparticles in a superconducting double dot. Phys. Rev. B 95, 235413 (2017).

    ADS  Article  Google Scholar 

  28. 28.

    Petersson, K. D., Petta, J. R., Lu, H. & Gossard, A. C. Quantum coherence in a one-electron semiconductor charge qubit. Phys. Rev. Lett. 105, 246804 (2010).

    ADS  Article  Google Scholar 

  29. 29.

    Van Woerkom, D. J. et al. Microwave spectroscopy of spinful Andreev bound states in ballistic semiconductor Josephson junctions. Nat. Phys. 13, 876–881 (2017).

    Article  Google Scholar 

  30. 30.

    Zurich Instruments UHF User Manual (Zurich Instruments, 2018); https://www.zhinst.com/sites/default/files/download-center/ziUHF_UserManual_13.10_r20274.pdf

  31. 31.

    Stehlik, J. et al. Fast charge sensing of a cavity-coupled double quantum dot using a Josephson parametric amplifier. Phys. Rev. Appl. 4, 014018 (2015).

    ADS  Article  Google Scholar 

Download references

Acknowledgements

We thank S. Upadhyay for help with fabrication. The research is supported by Microsoft Project Q and the Danish National Research Foundation. J.S. acknowledges financial support from the Werner Siemens Foundation Switzerland. P.K. acknowledges support from the European Research Commission (grant no. 716655). C.M.M. acknowledges support from the Villum Foundation.

Author information

Affiliations

Authors

Contributions

P.K. developed and grew the InAs/Al nanowires. J.S. fabricated the devices. D.S., D.M.T.Z and J.S. performed the measurements with input from K.D.P. and C.M.M. Data were analysed by D.M.T.Z. and J.I.V., with input from D.I.P., D.S. and T.K. The theoretical model to analyse the data was developed by J.I.V., D.I.P. and T.K. The experiment was conceived by C.M.M. All authors contributed to the interpretation of the data. The manuscript was written by D.M.T.Z., D.S. and C.M.M., with contributions from J.S., J.I.V. and D.I.P. and suggestions from all authors.

Corresponding author

Correspondence to Charles M. Marcus.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Figs. 1–10 and Notes.

Source data

Source Data Fig. 1

Source data for Fig. 1.

Source Data Fig. 2

Source data for Fig. 2.

Source Data Fig. 3

Source data for Fig. 3.

Source Data Fig. 4

Source data for Fig. 4.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

van Zanten, D.M.T., Sabonis, D., Suter, J. et al. Photon-assisted tunnelling of zero modes in a Majorana wire. Nat. Phys. 16, 663–668 (2020). https://doi.org/10.1038/s41567-020-0858-0

Download citation

Further reading