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The fractional a.c. Josephson effect in a semiconductor–superconductor nanowire as a signature of Majorana particles

Nature Physics volume 8, pages 795–799 (2012)Cite this article

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Abstract

Topological superconductors that support Majorana fermions have been predicted when one-dimensional semiconducting wires are coupled to a superconductor1,2,3. Such excitations are expected to exhibit non-Abelian statistics and can be used to realize quantum gates that are topologically protected from local sources of decoherence4,5. Here we report the observation of the fractional a.c. Josephson effect in a hybrid semiconductor–superconductor InSb/Nb nanowire junction, a hallmark of topological matter. When the junction is irradiated with a radiofrequency f0 in the absence of an external magnetic field, quantized voltage steps (Shapiro steps) with a height Δ V = h f0/2e are observed, as is expected for conventional superconductor junctions, where the supercurrent is carried by charge- 2e Cooper pairs. At high magnetic fields the height of the first Shapiro step is doubled to h f0/e, suggesting that the supercurrent is carried by charge- e quasiparticles. This is a unique signature of the Majorana fermions, predicted almost 80 years ago6.

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Figure 1: Devices layout.
Figure 2: Characterization of Josephson junctions.
Figure 3: a.c. Josephson effect and Shapiro steps.
Figure 4: Evolution of Shapiro steps with rf power.

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References

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  3. 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. Nature Phys. 7, 412–417 (2011).

    Article  ADS  Google Scholar 

  4. Kitaev, A. Y. Unpaired Majorana fermions in quantum wires. Phys.-Usp. 44, 131–136 (2001).

    Article  ADS  Google Scholar 

  5. Kitaev, A. Y. Fault-tolerant quantum computation by anyons. Ann. Phys. 303, 2–30 (2003).

    Article  ADS  MathSciNet  Google Scholar 

  6. Majorana, E. Symmetrical theory of electrons and positrons. Nuovo Cimento. 14, 171–184 (1937).

    Article  Google Scholar 

  7. Dirac, P. A. M. The quantum theory of the electron. Proc. R. Soc. Lond. A 117, 610–624 (1928).

    Article  ADS  Google Scholar 

  8. Wilczek, F. Majorana returns. Nature Phys. 5, 614–618 (2009).

    Article  ADS  Google Scholar 

  9. Cho, A. The sterile neutrino: Fertile concept or dead end? Science 334, 304–306 (2011).

    Article  ADS  Google Scholar 

  10. Moore, G. & Read, N. Nonabelions in the fractional quantum Hall effect. Nucl. Phys. B 360, 362–396 (1991).

    Article  ADS  MathSciNet  Google Scholar 

  11. Sengupta, K., Žutić, I., Kwon, H-J., Yakovenko, V. M. & Das Sarma, S. Midgap edge states and pairing symmetry of quasi-one-dimensional organic superconductors. Phys. Rev. B 63, 144531 (2001).

    Article  ADS  Google Scholar 

  12. Das Sarma, S., Nayak, C. & Tewari, S. Proposal to stabilize and detect half-quantum vortices in strontium ruthenate thin films: Non-abelian braiding statistics of vortices in a p x+i p y superconductor. Phys. Rev. B 73, 220502 (2006).

    Article  Google Scholar 

  13. Read, N. & Green, D. Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect. Phys. Rev. B 61, 10267–10297 (2000).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  15. Sau, J., Lutchyn, R., Tewari, S. & Das Sarma, S. Generic new platform for topological quantum computation using semiconductor heterostructures. Phys. Rev. Lett. 104, 040502 (2010).

    Article  ADS  Google Scholar 

  16. Quay, C. et al. Observation of a one-dimensional spin–orbit gap in a quantum wire. Nature Phys. 6, 336–339 (2010).

    Article  ADS  Google Scholar 

  17. Alicea, J. Majorana fermions in a tunable semiconductor device. Phys. Rev. B 81, 125318 (2010).

    Article  ADS  Google Scholar 

  18. Lutchyn, R. M., Stanescu, T. & Sarma, S. D. Search for Majorana fermions in multiband semiconducting nanowires. Phys. Rev. Lett. 106, 127001 (2011).

    Article  ADS  Google Scholar 

  19. Potter, A. C. & Lee, P. A. Multichannel generalization of Kitaev’s Majorana end states and a practical route to realize them in thin films. Phys. Rev. Lett. 105, 227003 (2010).

    Article  ADS  Google Scholar 

  20. Stanescu, T., Lutchyn, R. M. & Sarma, S. D. Majorana fermions in semiconductor nanowires. Phys. Rev. B 84, 144522 (2011).

    Article  ADS  Google Scholar 

  21. Law, K. T., Lee, P. A. & Ng, T. K. Majorana fermion induced resonant Andreev reflection. Phys. Rev. Lett. 103, 237001 (2009).

    Article  ADS  Google Scholar 

  22. Sau, J. D., Tewari, S., Lutchyn, R., Stanescu, T. & Sarma, S. D. Non-abelian quantum order in spin–orbit-coupled semiconductors: The search for topological Majorana particles in solid state systems. Phys. Rev. B 82, 214509 (2010).

    Article  ADS  Google Scholar 

  23. Koren, G., Kirzhner, T., Lahoud, E., Chashka, K. B. & Kanigel, A. Proximity-induced superconductivity in topological Bi2Te2Se and Bi2Se3 films: Robust zero-energy bound state possibly due to Majorana fermions. Phys. Rev. B 84, 224521 (2011).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  25. Deng, M. T. et al. Observation of Majorana fermions in a Nb-InSb nanowire-Nb hybrid quantum device. Preprint at http://arxiv.org/abs/1204.4130 (2012).

  26. Goldhaber-Gordon, D. et al. Kondo effect in a single-electron transistor. Nature 391, 156–159 (1998).

    Article  ADS  Google Scholar 

  27. Rokhinson, L. P., Guo, L. J., Chou, S. Y. & Tsui, D. C. Kondo-like zero-bias anomaly in electronic transport through an ultrasmall Si quantum dot. Phys. Rev. B 60, R16319–R16321 (1999).

    Article  ADS  Google Scholar 

  28. Cronenwett, S. M. et al. Low-temperature fate of the 0.7 structure in a point contact: A Kondo-like correlated state in an open system. Phys. Rev. Lett. 88, 226805 (2002).

    Article  ADS  Google Scholar 

  29. Rokhinson, L., Pfeiffer, L. & West, K. Spontaneous spin polarization in quantum point contacts. Phys. Rev. Lett. 96, 156602 (2006).

    Article  ADS  Google Scholar 

  30. Kwon, H-J., Sengupta, K. & Yakovenko, V. Fractional a.c. Josephson effect in p- and d-wave superconductors. Eur. Phys. J. B 37, 349–361 (2003).

    Article  ADS  Google Scholar 

  31. 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 

  32. Akhmerov, A. R., Dahlhaus, J. P., Hassler, F., Wimmer, M. & Beenakker, C. W. J. Quantized conductance at the Majorana phase transition in a disordered superconducting wire. Phys. Rev. Lett. 106, 057001 (2011).

    Article  ADS  Google Scholar 

  33. Sau, J. D., Tewari, S. & Das Sarma, S. Experimental and materials considerations for the topological superconducting state in electron and hole doped semiconductors: searching for non-Abelian Majorana modes in 1D nanowires and 2D heterostructures. Phys. Rev. B 85, 064512 (2012).

    Article  ADS  Google Scholar 

  34. Tinkham, M. Introduction to Superconductivity (McGraw-Hill, 1996).

    Google Scholar 

  35. Andreev, A. Thermal conductivity of the intermediate state of superconductors. Zh. Eksp. Teor. Fiz. 46, 1823–1828 (1964).

    Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  38. Likharev, K. K. Dynamics of Josephson Junctions and Circuits (Gordon and Breach Science Publishing, 1984).

    Google Scholar 

  39. Jiang, L. et al. Unconventional Josephson signatures of Majorana bound states. Phys. Rev. Lett. 107, 236401 (2011).

    Article  ADS  Google Scholar 

  40. Pikulin, D. I. & Nazarov, Y. V. Phenomenology and dynamics of Majorana Josephson junction. Preprint at http://arxiv.org/abs/1112.6368 (2011).

  41. San-Jose, P., Prada, E. & Aguado, R. AC Josephson effect in finite-length nanowire junctions with Majorana modes. Phys. Rev. Lett. 108, 257001 (2011).

    Article  ADS  Google Scholar 

  42. Domínguez, F., Hassler, F. & Platero, G. On the dynamical detection of Majorana fermions in current-biased nanowires. Preprint at http://arxiv.org/abs/1202.0642 (2012).

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Acknowledgements

The work was partially supported by ARO grant W911NF-09-1-0498 (L.P.R.) and by NSF grant DMR10-05851 (J.K.F., X.L.). L.P.R. benefited from discussions with Roman Lutchyn.

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Authors and Affiliations

  1. Department of Physics, Birck Nanotechnology Center and School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, USA

    Leonid P. Rokhinson

  2. Department of Physics, University of Notre Dame, Notre Dame, Indiana 46556, USA

    Xinyu Liu & Jacek K. Furdyna

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  1. Leonid P. Rokhinson
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  2. Xinyu Liu
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  3. Jacek K. Furdyna
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Contributions

L.P.R. conceived and performed the experiments; J.K.F. and X.L. designed and grew the heterostructures; all authors contributed to the writing of the manuscript.

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Correspondence to Leonid P. Rokhinson.

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Rokhinson, L., Liu, X. & Furdyna, J. The fractional a.c. Josephson effect in a semiconductor–superconductor nanowire as a signature of Majorana particles. Nature Phys 8, 795–799 (2012). https://doi.org/10.1038/nphys2429

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