4π-periodic Andreev bound states in a Dirac semimetal

Abstract

Although signatures of superconductivity in Dirac semimetals have been reported, for instance by applying pressure or using point contacts, our understanding of the topological aspects of Dirac semimetal superconductivity is still developing. Here, we utilize nanoscale phase-sensitive junction technology to induce superconductivity in the Dirac semimetal Bi1−xSbx. Our radiofrequency irradiation experiments then reveal a significant contribution of 4π-periodic Andreev bound states to the supercurrent in Nb–Bi0.97Sb0.03–Nb Josephson junctions. The conditions for a substantial 4π contribution to the supercurrent are favourable because of the Dirac cone’s very broad transmission resonances and a measurement frequency faster than the quasiparticle poisoning rate. In addition, we show that a magnetic field applied in the plane of the junction allows tuning of the Josephson junctions from 0 to π regimes. Our results open the technologically appealing avenue of employing the topological bulk properties of Dirac semimetals for topological superconductivity research and topological quantum computer development.

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Fig. 1: Josephson effect in a DSM junction.
Fig. 2: Magneto-transport in Bi0.97Sb0.03.
Fig. 3: Fractional Josephson effect.
Fig. 4: Finite momentum pairing.

Data availability

The data that support the findings of this study are available from the corresponding author on request.

References

  1. 1.

    Liu, Z. K. et al. Discovery of a three-dimensional topological Dirac semimetal, Na3Bi. Science 343, 864–867 (2014).

    CAS  Article  Google Scholar 

  2. 2.

    Neupane, M. et al. Observation of a three-dimensional topological Dirac semimetal phase in high-mobility Cd3As2. Nat. Commun. 5, 3786 (2014).

    CAS  Article  Google Scholar 

  3. 3.

    Borisenko, S. et al. Experimental realization of a three-dimensional Dirac semimetal. Phys. Rev. Lett. 113, 027603 (2014).

    Article  Google Scholar 

  4. 4.

    Kim, H. J. et al. Dirac versus Weyl fermions in topological insulators: Adler–Bell–Jackiw anomaly in transport phenomena. Phys. Rev. Lett. 111, 246603 (2013).

    Article  Google Scholar 

  5. 5.

    Shin, D. et al. Violation of Ohm’s law in a Weyl metal. Nat. Mater. 16, 1096–1099 (2017).

    CAS  Article  Google Scholar 

  6. 6.

    Qi, X. L. & Zhang, S. C. Topological insulators and superconductors. Rev. Mod. Phys. 83, 1057–1110 (2011).

    CAS  Article  Google Scholar 

  7. 7.

    Fu, L. & Kane, C. L. Superconducting proximity effect and Majorana fermions at the surface of a topological insulator. Phys. Rev. Lett. 100, 096407 (2008).

    Article  Google Scholar 

  8. 8.

    Das Sarma, S., Freedman, M. & Nayak, C. Majorana zero modes and topological quantum computation. npj Quant. Inf. 1, 15001 (2015).

    Article  Google Scholar 

  9. 9.

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

    CAS  Article  Google Scholar 

  10. 10.

    Rokhinson, L. P., Liu, X. & Furdyna, J. K. The fractional a.c. Josephson effect in a semiconductor-superconductor nanowire as a signature of Majorana particles. Nat. Phys. 8, 795–799 (2012).

    CAS  Article  Google Scholar 

  11. 11.

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

    CAS  Article  Google Scholar 

  12. 12.

    Nadj-Perge, S. et al. Observation of Majorana fermions in ferromagnetic atomic chains on a superconductor. Science 31, 602–607 (2014).

    Article  Google Scholar 

  13. 13.

    Wiedenmann, J. et al. 4π-Periodic Josephson supercurrent in HgTe-based topological Josephson junctions. Nat. Commun. 7, 10303 (2016).

    CAS  Article  Google Scholar 

  14. 14.

    Sun, H. H. et al. Majorana zero mode detected with spin selective Andreev reflection in the vortex of a topological superconductor. Phys. Rev. Lett. 116, 257003 (2016).

    Article  Google Scholar 

  15. 15.

    He, L. et al. Pressure-induced superconductivity in the three-dimensional topological Dirac semimetal Cd3As2. npj Quant. Mater. 1, 16014 (2016).

    Article  Google Scholar 

  16. 16.

    Aggarwal, L. et al. Unconventional superconductivity at mesoscopic point contacts on the 3D Dirac semimetal Cd3As2. Nat. Mater. 15, 32–37 (2016).

    CAS  Article  Google Scholar 

  17. 17.

    Wang, H. et al. Observation of superconductivity induced by a point contact on 3D Dirac semimetal Cd3As2 crystals. Nat. Mater. 15, 38–42 (2016).

    CAS  Article  Google Scholar 

  18. 18.

    Parameswaran, S. A., Grover, T., Abanin, D. A., Pesin, D. A. & Vishwanath, A. Probing the chiral anomaly with nonlocal transport in three dimensional topological semimetals. Phys. Rev. X 4, 031035 (2014).

    Google Scholar 

  19. 19.

    Snelder, M., Veldhorst, M., Golubov, A. A. & Brinkman, A. Andreev bound states and current–phase relations in three-dimensional topological insulators. Phys. Rev. B 87, 104507 (2013).

    Article  Google Scholar 

  20. 20.

    Badiane, D. M., Houzet, M. & Meyer, J. S. Nonequilibrium Josephson effect through helical edge states. Phys. Rev. Lett. 107, 177002 (2011).

    Article  Google Scholar 

  21. 21.

    Wolff, P. A. Matrix elements and selection rules for the two-band model of bismuth. J. Phys. Chem. Solids 25, 1057–1068 (1964).

    CAS  Article  Google Scholar 

  22. 22.

    Tichovoisky, E. J. & Mavroides, J. G. Magnetoreflection studies on the band structure of bismuth-antimony alloys. Solid State Commun. 7, 927–931 (1969).

    Article  Google Scholar 

  23. 23.

    Yang, B. J. & Nagaosa, N. Classification of stable three-dimensional Dirac semimetals with nontrivial topology. Nat. Commun. 5, 4898 (2014).

    CAS  Article  Google Scholar 

  24. 24.

    Hsieh, D. et al. A topological Dirac insulator in a quantum spin Hall phase. Nature 452, 970–974 (2008).

    CAS  Article  Google Scholar 

  25. 25.

    Hsieh, D. et al. Observation of unconventional quantum spin textures in topological insulators. Science 323, 919–922 (2009).

    CAS  Article  Google Scholar 

  26. 26.

    Xiong, J. et al. Evidence for the chiral anomaly in the Dirac semimetal Na3Bi. Science 350, 413–416 (2015).

    CAS  Article  Google Scholar 

  27. 27.

    Dominguez, F., Hassler, F. & Platero, G. Dynamical detection of Majorana fermions in current-biased nanowires. Phys. Rev. B 86, 140503 (2012).

    Article  Google Scholar 

  28. 28.

    Bocquillon, E. et al. Gapless Andreev bound states in the quantum spin Hall insulator HgTe. Nat. Nanotech. 12, 13743 (2017).

    Article  Google Scholar 

  29. 29.

    Pico-Cortes, J., Dominguez, F. & Platero, G. Signatures of a 4π-periodic supercurrent in the voltage response of capacitively shunted topological Josephson junctions. Phys. Rev. B 96, 125438 (2017).

    Article  Google Scholar 

  30. 30.

    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  Google Scholar 

  31. 31.

    Beenakker, C. W. J., Pikulin, D. I., Hyart, T., Schomerus, H. & Dahlhaus, J. P. Fermion-parity anomaly of the critical supercurrent in the quantum spin-Hall effect. Phys. Rev. Lett. 110, 017003 (2013).

    CAS  Article  Google Scholar 

  32. 32.

    Zhang, F. & Kane, C. L. Anomalous topological pumps and fractional Josephson effects. Phys. Rev. B 90, 020501 (2014).

    Article  Google Scholar 

  33. 33.

    Zhang, F. & Kane, C. L. Time-reversal-invariant Z 4 fractional Josephson effect. Phys. Rev. Lett. 113, 036401 (2014).

    Article  Google Scholar 

  34. 34.

    Peng, Y., Pientka, F., Berg, E., Oreg, Y. & Von Oppen, F. Signatures of topological Josephson junctions. Phys. Rev. B 94, 085409 (2016).

    Article  Google Scholar 

  35. 35.

    Houzet, M., Meyer, J. S., Badiane, D. M. & Glazman, L. I. Dynamics of Majorana states in a topological Josephson junction. Phys. Rev. Lett. 111, 046401 (2013).

    Article  Google Scholar 

  36. 36.

    Zhu, Z., Fauqué, B., Fuseya, Y. & Behnia, K. Angle-resolved Landau spectrum of electrons and holes in bismuth. Phys. Rev. B 84, 115137 (2011).

    Article  Google Scholar 

  37. 37.

    Ryazanov, V. V. et al. Coupling of two superconductors through a ferromagnet: evidence for a π junction. Phys. Rev. Lett. 86, 2427–2430 (2001).

    CAS  Article  Google Scholar 

  38. 38.

    Kontos, T. et al. Josephson junction through a thin ferromagnetic layer: negative coupling. Phys. Rev. Lett. 89, 137007 (2002).

    CAS  Article  Google Scholar 

  39. 39.

    Blum, Y., Tsukernik, A., Karpovski, M. & Palevski, A. Oscillations of the superconducting critical current in Nb–Cu–Ni–Cu–Nb junctions. Phys. Rev. Lett. 89, 187004 (2002).

    CAS  Article  Google Scholar 

  40. 40.

    Hart, S. et al. Controlled finite momentum pairing and spatially varying order parameter in proximitized HgTe quantum wells. Nat. Phys. 13, 87–93 (2017).

    CAS  Article  Google Scholar 

  41. 41.

    Demler, E. A., Arnold, G. B. & Beasley, M. R. Superconducting proximity effects in magnetic metals. Phys. Rev. B 55, 15174–15182 (1997).

    CAS  Article  Google Scholar 

  42. 42.

    Li, C. et al. Zeeman effect induced 0−π transitions in ballistic Dirac semimetal Josephson junctions (2018). Preprint at https://arXiv.org/abs/1807.07725

  43. 43.

    Yu, W. et al. π and 4π Josephson effects mediated by a Dirac semimetal. Phys. Rev. Lett. 120, 177704 (2018).

    CAS  Article  Google Scholar 

  44. 44.

    Tang, S. & Dresselhaus, M. S. Constructing a large variety of Dirac-cone materials in the Bi1−xSbx thin film system. Nanoscale 4, 7786–7790 (2012).

    CAS  Article  Google Scholar 

  45. 45.

    Zhu, Z., Collaudin, A., Fauqué, B., Kang, W. & Behnia, K. Field-induced polarization of Dirac valleys in bismuth. Nat. Phys. 8, 89–94 (2012).

    CAS  Article  Google Scholar 

Download references

Acknowledgements

The authors thank the Diamond Light Source for access to beamline I05 (proposal no. 12969), which contributed to the results presented here, and A. Schiphorst, T. Kim and M. Hoesch for assistance with ARPES experiments. The authors thank R. Lier for numerical calculations. This work was financially supported by the Foundation for Fundamental Research on Matter (FOM), associated with the Netherlands Organization for Scientific Research (NWO), and the European Research Council (ERC) through a Consolidator Grant.

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Contributions

Y.H. made single crystals. C.L. and B.d.R. fabricated devices. C.L, J.C.d.B., B.d.R. and A.d.V. performed transport measurements. C.L., J.C.d.B., B.d.R., A.A.G. and A.B. analysed and modelled transport data. S.V.R., E.v.H. and M.S.G. performed and analysed ARPES measurements. All authors contributed to writing the manuscript.

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Correspondence to Alexander Brinkman.

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Supplementary Information

Supplementary Figures 1–16, Supplementary Tables 1–2, Supplementary References 1–26

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Li, C., de Boer, J.C., de Ronde, B. et al. 4π-periodic Andreev bound states in a Dirac semimetal. Nature Mater 17, 875–880 (2018). https://doi.org/10.1038/s41563-018-0158-6

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