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Gapless Andreev bound states in the quantum spin Hall insulator HgTe

Abstract

In recent years, Majorana physics has attracted considerable attention because of exotic new phenomena and its prospects for fault-tolerant topological quantum computation. To this end, one needs to engineer the interplay between superconductivity and electronic properties in a topological insulator, but experimental work remains scarce and ambiguous. Here, we report experimental evidence for topological superconductivity induced in a HgTe quantum well, a 2D topological insulator that exhibits the quantum spin Hall (QSH) effect. The a.c. Josephson effect demonstrates that the supercurrent has a 4π periodicity in the superconducting phase difference, as indicated by a doubling of the voltage step for multiple Shapiro steps. In addition, this response like that of a superconducting quantum interference device to a perpendicular magnetic field shows that the 4π-periodic supercurrent originates from states located on the edges of the junction. Both features appear strongest towards the QSH regime, and thus provide evidence for induced topological superconductivity in the QSH edge states.

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Figure 1: Physics in a topological Josephson junction.
Figure 2: Experimental realization of a topological Josephson junction.
Figure 3: Response to an RF excitation.
Figure 4: Shapiro response of a junction on a trivial quantum well.
Figure 5: Response of the critical current to a magnetic field.

References

  1. Kitaev, A. Unpaired Majorana fermions in quantum wires. Phys. Usp. 44, 16 (2001).

    Article  Google Scholar 

  2. Kwon, H. J., Yakovenko, V. M. & Sengupta, K. Fractional a.c. Josephson effect in unconventional superconductors. Low Temp. Phys. 30, 613–619 (2004).

    CAS  Article  Google Scholar 

  3. Alicea, J. New directions in the pursuit of Majorana fermions in solid state systems. Rep. Prog. Phys. 75, 076501 (2012).

    Article  Google Scholar 

  4. Beenakker, C. W. J. Search for Majorana fermions in superconductors. Annu. Rev. Cond. Mat. Phys. 4, 113–136 (2013).

    CAS  Article  Google Scholar 

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

    CAS  Article  Google Scholar 

  6. 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 

  7. Bernevig, B. A., Hughes, T. L. & Zhang, S.-C. Quantum spin Hall effect and topological phase transition in HgTe quantum wells. Science 314, 1757–1761 (2006).

    CAS  Article  Google Scholar 

  8. König, M. et al. Quantum spin Hall insulator state in HgTe quantum wells. Science 318, 766 (2007).

    Article  Google Scholar 

  9. Samkharadze, N. et al. High kinetic inductance superconducting nanowire resonators for circuit QED in a magnetic field. Phys. Rev. Applied 5, 044004 (2016).

    Article  Google Scholar 

  10. 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 

  11. Beenakker, C. W. J. et al. Fermion-parity anomaly of the critical supercurrent in the quantum spin-Hall effect. Phys. Rev. Lett. 110, 017003 (2013).

    CAS  Article  Google Scholar 

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

    CAS  Article  Google Scholar 

  13. Shapiro, S. Josephson currents in superconducting tunneling: the effect of microwaves and other observations. Phys. Rev. Lett. 11, 80–82 (1963).

    CAS  Article  Google Scholar 

  14. San-Jose, P., Prada, E. & Aguado, R. AC Josephson effect in finite-length nanowire junctions with Majorana modes. Phys. Rev. Lett. 108, 257001 (2012).

    Article  Google Scholar 

  15. 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 

  16. Badiane, D. M., Glazman, L. I., Houzet, M. & Meyer, J. S. AC Josephson effect in topological Josephson junctions. C. R. Phys. 14, 840–856 (2013).

    CAS  Article  Google Scholar 

  17. Barone, A. & Paterno, G. Physics and Applications of the Josephson Effect (Wiley and Sons, 1982).

    Book  Google Scholar 

  18. Roth, A. et al. Nonlocal transport in the quantum spin Hall state. Science 325, 294–297 (2009).

    CAS  Article  Google Scholar 

  19. Brüne, C. et al. Spin polarization of the quantum spin Hall edge states. Nat. Phys. 8, 485–490 (2012).

    Article  Google Scholar 

  20. Nowack, K. C. et al. Imaging currents in HgTe quantum wells in the quantum spin Hall regime. Nat. Mater. 12, 787–791 (2013).

    CAS  Article  Google Scholar 

  21. Zhou, B. et al. Finite size effects on helical edge states in a quantum spin-Hall system. Phys. Rev. Lett. 101, 246807 (2008).

    Article  Google Scholar 

  22. Brüne, C. et al. Evidence for the ballistic intrinsic spin Hall effect in HgTe nanostructures. Nat. Phys. 6, 448–454 (2010).

    Article  Google Scholar 

  23. Blonder, G. E., Tinkham, M. & Klapwijk, T. M. Transition from metallic to tunneling regimes in superconducting microconstrictions: excess current, charge imbalance, and supercurrent conversion. Phys. Rev. B 25, 4515–4532 (1982).

    CAS  Article  Google Scholar 

  24. Capper, P. Properties of Narrow Gap Cadmium-Based Compounds (Inspec, 1994).

    Google Scholar 

  25. Finck, A. D. K., Kurter, C., Hor, Y. S. & Van Harlingen, D. J. Phase coherence and Andreev reflection in topological insulator devices. Phys. Rev. X 4, 041022 (2014).

    Google Scholar 

  26. Galletti, L. et al. Influence of topological edge states on the properties of Bi2Se3/Al hybrid Josephson devices. Phys. Rev. B 89, 134512 (2014).

    Article  Google Scholar 

  27. Pikulin, D. I. & Nazarov, Y. V. Phenomenology and dynamics of a Majorana Josephson junction. Phys. Rev. B 86, 140504 (2012).

    Article  Google Scholar 

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

    CAS  Article  Google Scholar 

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

    Article  Google Scholar 

  30. Sau, J. D., Berg, E. & Halperin, B. I. On the possibility of the fractional a.c. Josephson effect in non-topological conventional superconductor–normal–superconductor junctions. Preprint at http://arxiv.org/abs/1206.4596 (2012).

  31. Zhang, F. & Kane, C. L. Time-reversal-invariant Z4 fractional Josephson effect. Phys. Rev. Lett. 113, 036401 (2014).

    Article  Google Scholar 

  32. Russer, P. Influence of microwave radiation on current–voltage characteristic of superconducting weak links. J. Appl. Phys. 43, 2008 (1972).

    Article  Google Scholar 

  33. Dai, X. et al. Helical edge and surface states in HgTe quantum wells and bulk insulators. Phys. Rev. B 77, 125319 (2008).

    Article  Google Scholar 

  34. Tkachov, G. & Hankiewicz, E. M. Helical Andreev bound states and superconducting Klein tunneling in topological insulator Josephson junctions. Phys. Rev. B 88, 075401 (2013).

    Article  Google Scholar 

  35. Tinkham, M. Introduction to Superconductivity (Dover, 2004).

    Google Scholar 

  36. 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 

  37. Lee, S.-P., Michaeli, K., Alicea, J. & Yacoby, A. Revealing topological superconductivity in extended quantum spin Hall Josephson junctions. Phys. Rev. Lett. 113, 197001 (2014).

    Article  Google Scholar 

  38. Baxevanis, B., Ostroukh, V. P. & Beenakker, C. W. J. Even–odd flux quanta effect in the Fraunhofer oscillations of an edge-channel Josephson junction. Phys. Rev. B 91, 041409 (2015).

    Article  Google Scholar 

  39. Tkachov, G., Burset, P., Trauzettel, B. & Hankiewicz, E. M. Quantum interference of edge supercurrents in a two-dimensional topological insulator. Phys. Rev. B 92, 045408 (2015).

    Article  Google Scholar 

  40. Pribiag, V. S. et al. Edge-mode superconductivity in a two-dimensional topological insulator. Nat. Nanotech. 10, 593–597 (2015).

    CAS  Article  Google Scholar 

  41. Dolcini, F., Houzet, M. & Meyer, J. S. Topological Josephson φ0 junctions. Phys. Rev. B 92, 035428 (2015).

    Article  Google Scholar 

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

    Article  Google Scholar 

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Acknowledgements

We thank V. Hock and L. Maier for technical assistance and acknowledge S. Tarucha, L. Glazman, Y. Peng, F. von Oppen, E.M. Hankiewicz, G. Tkachov and B. Trauzettel for enlightening discussions. This work is supported by the German Research Foundation (Leibniz Program, DFG-Sonderforschungsbereich 1170 ‘Tocotronics’ and DFG-Schwerpunktprogramme 1666), the Elitenetzwerk Bayern program Topologische Isolatoren. R.S.D. acknowledges support from Grants-in-Aid for Scientific Research A (No. 16H02204) and Young Scientists B (No. 26790008). T.M.K. is financially supported by the European Research Council Advanced Grant No.339306 (METIQUM). E.B., T.M.K. and L.W.M. thank the Alexander von Humboldt foundation for its support.

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E.B., R.S.D., J.W., T.M.K., K.I., C.B., H.B. and L.W.M. conceived the experiments. P.L. and C.B. grew the material, and contributed material analysis. J.W. prepared the samples, with inputs from E.B., and R.S.D. E.B. and J.W. performed the measurements and the analysis. All the authors contributed to analysing and interpreting the data, and to writing the manuscript.

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Correspondence to Erwann Bocquillon.

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The authors declare no competing financial interests.

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Bocquillon, E., Deacon, R., Wiedenmann, J. et al. Gapless Andreev bound states in the quantum spin Hall insulator HgTe. Nature Nanotech 12, 137–143 (2017). https://doi.org/10.1038/nnano.2016.159

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