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Current–phase relations of few-mode InAs nanowire Josephson junctions

Nature Physics volume 13, pages 1177–1181 (2017)Cite this article

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Abstract

Gate-tunable semiconductor nanowires with superconducting leads have great potential for quantum computation1,2,3 and as model systems for mesoscopic Josephson junctions4,5. The supercurrent, I, versus the phase, φ, across the junction is called the current–phase relation (CPR). It can reveal not only the amplitude of the critical current, but also the number of modes and their transmission. We measured the CPR of many individual InAs nanowire Josephson junctions, one junction at a time. Both the amplitude and shape of the CPR varied between junctions, with small critical currents and skewed CPRs indicating few-mode junctions with high transmissions. In a gate-tunable junction, we found that the CPR varied with gate voltage: near the onset of supercurrent, we observed behaviour consistent with resonant tunnelling through a single, highly transmitting mode. The gate dependence is consistent with modelled subband structure that includes an effective tunnelling barrier due to an abrupt change in the Fermi level at the boundary of the gate-tuned region. These measurements of skewed, tunable, few-mode CPRs are promising both for applications that require anharmonic junctions6,7 and for Majorana readout proposals8.

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Figure 1: Current–phase relation of a few-mode InAs nanowire junction as measured by scanning SQUID microscopy shows significant forward skew.
Figure 2: Fluctuations in the forward skew and amplitude of the current–phase relation of a bottom-gated junction with gate voltage.
Figure 3: Peak-like behaviour in the shape and skewness of the current–phase relation at low gate voltages.
Figure 4: Backward-skewed current–phase relations for a narrow range of gate voltages.
Figure 5: The forward-skewness of the current–phase relation for many junctions with various lengths.

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References

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  4. Beenakker, C. W. J. Transport Phenomena in Mesoscopic Systems 235–253 (Springer, 1992).

    Book  Google Scholar 

  5. Furusaki, A., Takayanagi, H. & Tsukada, M. Josephson effect of the superconducting quantum point contact. Phys. Rev. B 45, 10563–10575 (1992).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  8. Hyart, T. et al. Flux-controlled quantum computation with Majorana fermions. Phys. Rev. B 88, 035121 (2013).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  10. Günel, H. Y. et al. Supercurrent in Nb/InAs-nanowire/Nb Josephson junctions. J. Appl. Phys. 112, 034316 (2012).

    Article  ADS  Google Scholar 

  11. Abay, S. et al. Quantized conductance and its correlation to the supercurrent in a nanowire connected to superconductors. Nano Lett. 13, 3614–3617 (2013).

    Article  ADS  Google Scholar 

  12. Nilsson, H. A., Samuelsson, P., Caroff, P. & Xu, H. Q. Supercurrent and multiple Andreev reflections in an InSb nanowire Josephson junction. Nano Lett. 12, 228–233 (2011).

    Article  ADS  Google Scholar 

  13. Li, S. et al. Coherent charge transport in ballistic InSb nanowire Josephson junctions. Sci. Rep. 6, 24822 (2016).

    Article  ADS  Google Scholar 

  14. Jackel, L. D., Webb, W. W., Lukens, J. E. & Pei, S. S. Measurement of the probability distribution of thermally excited fluxoid quantum transitions in a superconducting ring closed by a Josephson junction. Phys. Rev. B 9, 115–118 (1974).

    Article  ADS  Google Scholar 

  15. Sochnikov, I. et al. Direct measurement of current-phase relations in superconductor/topological insulator/superconductor junctions. Nano Lett. 13, 3086–3092 (2013).

    Article  ADS  Google Scholar 

  16. Sochnikov, I. et al. Nonsinusoidal current-phase relationship in Josephson junctions from the 3d topological insulator HgTe. Phys. Rev. Lett. 114, 066801 (2015).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  18. Golubov, A. A., Kupriyanov, M. Yu. & Il’Ichev, E. The current-phase relation in Josephson junctions. Rev. Mod. Phys. 76, 411–469 (2004).

    Article  ADS  Google Scholar 

  19. Scheer, E., Joyez, P., Esteve, D., Urbina, C. & Devoret, M. H. Conduction channel transmissions of atomic-size aluminum contacts. Phys. Rev. Lett. 78, 3535–3538 (1997).

    Article  ADS  Google Scholar 

  20. Della Rocca, M. L. et al. Measurement of the current-phase relation of superconducting atomic contacts. Phys. Rev. Lett. 99, 127005 (2007).

    Article  ADS  Google Scholar 

  21. English, C. D. et al. Observation of nonsinusoidal current-phase relation in graphene Josephson junctions. Phys. Rev. B 94, 115435 (2016).

    Article  ADS  Google Scholar 

  22. Groth, C. W., Wimmer, M., Akhmerov, A. R. & Waintal, X. Kwant: a software package for quantum transport. New J. Phys. 16, 063065 (2014).

    Article  ADS  Google Scholar 

  23. Dell’Anna, L., Zazunov, A., Egger, R. & Martin, T. Josephson current through a quantum dot with spin-orbit coupling. Phys. Rev. B 75, 085305 (2007).

    Article  ADS  Google Scholar 

  24. Vecino, E., Martín-Rodero, A. & Levy Yeyati, A. Josephson current through a correlated quantum level: Andreev states and π junction behavior. Phys. Rev. B 68, 035105 (2003).

    Article  ADS  Google Scholar 

  25. Lee, E. J. H. et al. Spin-resolved Andreev levels and parity crossings in hybrid superconductor-semiconductor nanostructures. Nat. Nanotech. 9, 79–84 (2014).

    Article  ADS  Google Scholar 

  26. Hart, S. et al. Induced superconductivity in the quantum spin Hall edge. Nat. Phys. 10, 638–643 (2014).

    Google Scholar 

  27. Allen, M. T. et al. Spatially resolved edge currents and guided-wave electronic states in graphene. Nat. Phys. 12, 128–133 (2016).

    Article  Google Scholar 

  28. Alicea, J., Oreg, Y., Refael, G., von Oppen, F. & Fisher, M. P. A. Non-Abelian statistics and topological quantum information processing in 1D wire networks. Nat. Phys. 7, 412–417 (2011).

    Article  Google Scholar 

  29. Fu, L. & Kane, C. L. Josephson current and noise at a superconductor/quantum-spin-Hall-insulator/superconductor junction. Phys. Rev. B 79, 161408 (2009).

    Article  ADS  Google Scholar 

  30. Gardner, B. W. et al. Scanning superconducting quantum interference device susceptometry. Rev. Sci. Instrum. 72, 2361–2364 (2001).

    Article  ADS  Google Scholar 

  31. Huber, M. E. et al. Gradiometric micro-SQUID susceptometer for scanning measurements of mesoscopic samples. Rev. Sci. Instrum. 79, 053704 (2008).

    Article  ADS  Google Scholar 

  32. Brandt, E. H. Thin superconductors and SQUIDs in perpendicular magnetic field. Phys. Rev. B 72, 024529 (2005).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We thank S. Hart, J. Kirtley and C. Beenakker for useful discussions and C. Watson, Z. Cui and I. Sochnikov for useful discussions and experimental assistance. The scanning SQUID measurements were supported by the Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, under Contract No. DE-AC02-76SF00515. Nanowire growth and device fabrication was supported by Microsoft Project Q, the Danish National Research Foundation, the Lundbeck Foundation, the Carlsberg Foundation, and the European Commission. C.M.M. acknowledges support from the Villum Foundation.

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Authors and Affiliations

  1. Stanford Institute for Materials and Energy Sciences, SLAC National Accelerator Laboratory, Menlo Park, California, 94025, USA

    Eric M. Spanton & Kathryn A. Moler

  2. Department of Physics, Stanford University, Stanford, California, 94305, USA

    Eric M. Spanton & Kathryn A. Moler

  3. Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute, University of Copenhagen, Copenhagen DK-2100, Denmark

    Mingtang Deng, Saulius Vaitiekėnas, Peter Krogstrup, Jesper Nygård & Charles M. Marcus

  4. State Key Laboratory of High Performance Computing, NUDT, Changsha 410073, China

    Mingtang Deng

  5. Department of Physics, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany

    Saulius Vaitiekėnas

  6. Department of Applied Physics, Stanford University, Stanford, California, 94305, USA

    Kathryn A. Moler

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  1. Eric M. Spanton
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Contributions

P.K. and J.N. developed the nanowire materials, M.D. and S.V. fabricated the devices and E.M.S. performed the scanning SQUID measurements, analysed the data, and performed simulations. E.M.S. and K.A.M. wrote the manuscript with input from all coauthors.

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Correspondence to Kathryn A. Moler.

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The authors declare no competing financial interests.

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Spanton, E., Deng, M., Vaitiekėnas, S. et al. Current–phase relations of few-mode InAs nanowire Josephson junctions. Nature Phys 13, 1177–1181 (2017). https://doi.org/10.1038/nphys4224

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