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Zero-bias peaks and splitting in an Al–InAs nanowire topological superconductor as a signature of Majorana fermions

Nature Physics volume 8, pages 887–895 (2012)Cite this article

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Abstract

Majorana fermions are the only fermionic particles that are expected to be their own antiparticles. Although elementary particles of the Majorana type have not been identified yet, quasi-particles with Majorana-like properties, born from interacting electrons in the solid, have been predicted to exist. Here, we present thorough experimental studies, backed by numerical simulations, of a system composed of an aluminium superconductor in proximity to an indium arsenide nanowire, with the latter possessing strong spin–orbit coupling and Zeeman splitting. An induced one-dimensional topological superconductor, supporting Majorana fermions at both ends, is expected to form. We concentrate on the characteristics of a distinct zero-bias conductance peak and its splitting in energy—both appearing only with a small magnetic field applied along the wire. The zero-bias conductance peak was found to be robustly tied to the Fermi energy over a wide range of system parameters. Although not providing definite proof of a Majorana state, the presented data and the simulations support its existence.

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Figure 1: Energy dispersion of InAs nanowire excitations (Bogoliubov–de Gennes spectrum), in proximity to an Al superconductor.
Figure 2: A suspended Al–InAs nanowire on gold pedestals above p-type silicon.
Figure 3: Evolution of the ZBP with chemical potential and magnetic field, for the VRG range 1.17–1.24 V at VGG = −18.3 V for a type II device (D4).
Figure 4: Low-bias conductance as a function of applied magnetic field parallel to the wire axis (type II device, D4).
Figure 5: Low-bias conductance as a function of applied magnetic field parallel to the wire axis (type II device, D4), at a higher chemical potential.
Figure 6: Temperature and magnetic field orientation dependence of the ZBP of device D3 at B = 70 mT.

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References

  1. Dirac, P. A. M. Quantum mechanics of many-electron systems. Proc. R. Soc. Lond. Ser. A 123, 714–733 (1929).

    Article  ADS  Google Scholar 

  2. Majorana, E. Teoria simmetrica dell elettronee del positrone. Il Nuovo Cimento (1924-1942) 14, 171–184 (1937).

    Article  Google Scholar 

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

    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. Kopnin, N. & Salomaa, M. Mutual friction in superfluid 3He: Effects of bound states in the vortex core. Phys. Rev. B 44, 9667–9677 (1991).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  7. Beenakker, C. Search for Majorana fermions in superconductors. Preprint at http://arxiv.org/abs/1112.1950 (2011).

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

    Article  ADS  MathSciNet  Google Scholar 

  9. Halperin, B. I. et al. Adiabatic manipulations of Majorana fermions in a three-dimensional network of quantum wires. Phys. Rev. B 85, 144501 (2012).

    Article  ADS  Google Scholar 

  10. Sau, J. D., Clarke, D. J. & Tewari, S. Controlling non-Abelian statistics of Majorana fermions in semiconductor nanowires. Phys. Rev. B 84, 094505 (2011).

    Article  ADS  Google Scholar 

  11. 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 (2000).

    Article  ADS  Google Scholar 

  12. Kitaev, A. Anyons in an exactly solved model and beyond. Ann. Phys. 321, 2–111 (2006).

    Article  ADS  MathSciNet  Google Scholar 

  13. Alicea, J., Oreg, Y., Refael, G., Oppen, F. V. & 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 

  14. Fu, L. & Kane, C. L. Superconducting proximity effect and Majorana fermions at the surface of a topological insulator. Phys. Rev. Lett. 100, 96407 (2008).

    Article  ADS  Google Scholar 

  15. Sau, J. D., Lutchyn, R. M., Tewari, S. & Sarma, S. D. Generic new platform for topological quantum computation using semiconductor heterostructures. Phys. Rev. Lett. 104, 40502 (2010).

    Article  ADS  Google Scholar 

  16. Sau, J., Tewari, S., Lutchyn, R. & Stanescu, T. Non-Abelian quantum order in spin-orbit-coupled semiconductors: Search for topological Majorana particles in solid-state systems. Phys. Rev. B 82, 1–59 (2010).

    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., Sau, J. D. & Sarma, S. D. Majorana fermions and a topological phase transition in semiconductor-superconductor heterostructures. Phys. Rev. Lett. 105, 77001 (2010).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  21. 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).

  22. 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 

  23. Pientka, F., Kells, G., Romito, A., Brouwer, P. W. & von Oppen, F. Enhanced zero-bias Majorana peak in disordered multi-subband quantum wires. Preprint at http://arxiv.org/abs/1206.0723 (2012).

  24. Rainis, D., Trifunovic, L., Klinovajo, J. & Loss, D. Realistic transport modeling for a superconducting nanowire with Majorana fermions. Preprint at http://arxiv.org/abs/1207.5907v1 (2012).

  25. Bychkov, Y. A. & Rashba, E. Oscillatory effects and the magnetic susceptibility of carriers in inversion layers. J. Phys. C 17, 6039–6045 (1984).

    Article  ADS  Google Scholar 

  26. Wimmer, M., Akhmerov, A., Dahlhaus, J. & Beenakker, C. Quantum point contact as a probe of a topological superconductor. New J. Phys. 13, 053016 (2011).

    Article  ADS  Google Scholar 

  27. Bolech, C. & Demler, E. Observing majorana bound states in p-wave superconductors using noise measurements in tunneling experiments. Phys. Rev. Lett. 98, 237002 (2007).

    Article  ADS  Google Scholar 

  28. Shtrikman, H., Popovitz-Biro, R., Kretinin, A. V. & Kacman, P. GaAs and InAs nanowires for ballistic transport. IEEE J. Selected Top. Quant. Electron. 17, 922–934 (2011).

    Article  ADS  Google Scholar 

  29. Das, A. et al. Entangling electrons by splitting Cooper pairs: Two-particle conductance resonance and time coincidence measurements. Preprint at http://arxiv.org/abs/1205.2455 (2012).

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

    Article  ADS  Google Scholar 

  31. Lin, C. H., Sau, J. D. & Sarma, S. D. Zero bias conductance peak in Majorana wires made of semiconductor-superconductor hybrid structures. Preprint at http://arxiv.org/abs/1204.3085 (2012).

  32. Qu, C., Zhang, Y., Mao, L. & Zhang, C. Signature of majorana fermions in charge transport in semiconductor nanowires. Preprint at http://arxiv.org/abs/1109.4108 (2011).

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

    Article  ADS  Google Scholar 

  34. Prada, E., San-Jose, P. & Aguado, R. Transport spectroscopy of NS nanowire junctions with Majorana fermions. Preprint at http://arxiv.org/abs/1203.4488 (2012).

  35. Andreev, A. Thermal conductivity of superconductors intermediate state. Soviet Phys. ZhETP 46, 1823–1828 (1964).

    Google Scholar 

  36. Marmorkos, I., Beenakker, C. & Jalabert, R. Three signatures of phase-coherent Andreev reflection. Phys. Rev. B 48, 2811–2814 (1993).

    Article  ADS  Google Scholar 

  37. Kastalsky, A. et al. Observation of pair currents in superconductor-semiconductor contacts. Phys. Rev. Lett. 67, 3026–3029 (1991).

    Article  ADS  Google Scholar 

  38. Pillet, J. et al. Andreev bound states in supercurrent-carrying carbon nanotubes revealed. Nature Phys. 6, 965–969 (2010).

    Article  ADS  Google Scholar 

  39. Klapwijk, T., Blonder, G. & Tinkham, M. Explanation of subharmonic energy gap structure in superconducting contacts. Physica B + C 109, 1657–1664 (1982).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  41. Kretinin, A. V. et al. Spin-1/2 Kondo effect in an InAs nanowire quantum dot: Unitary limit, conductance scaling, and Zeeman splitting. Phys. Rev. B 84, 245316 (2011).

    Article  ADS  Google Scholar 

  42. Pikulin, D., Dahlhaus, J., Wimmer, M. & Beenakker, C. Zero-voltage conductance peak from weak antilocalization in a Majorana nanowire. Preprint at http://arxiv.org/abs/1206.6687 (2012).

  43. Csonka, S. et al. Giant fluctuations and gate control of the g-factor in InAs nanowire quantum dots. Nano Lett. 8, 3932–3935 (2008).

    Article  ADS  Google Scholar 

  44. Kretinin, A. V., Popovitz-Biro, R., Mahalu, D. & Shtrikman, H. Multimode Fabry–Perot conductance oscillations in suspended stacking-faults-free InAs nanowires. Nano Lett. 10, 3439–3445 (2010).

    Article  ADS  Google Scholar 

  45. Fasth, C., Fuhrer, A., Samuelson, L., Golovach, V. N. & Loss, D. Direct measurement of the spin-orbit interaction in a two-electron InAs nanowire quantum dot. Phys. Rev. Lett. 98, 266801 (2007).

    Article  ADS  Google Scholar 

  46. Kanai, Y. et al. Electrically tuned spin-orbit interaction in an InAs self-assembled quantum dot. Nature Nanotech. 6, 511–516 (2011).

    Article  ADS  Google Scholar 

  47. Fu, L. Electron teleportation via Majorana bound states in a mesoscopic superconductor. Phys. Rev. Lett. 104, 56402 (2010).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  49. Nilsson, J., Akhmerov, A. & Beenakker, C. Splitting of a Cooper pair by a pair of Majorana bound states. Phys. Rev. Lett. 101, 120403 (2008).

    Article  ADS  Google Scholar 

  50. Chevallier, D., Sticlet, D., Simon, P. & Bena, C. Mutation of Andreev into Majorana bound states in long superconductor- normal and superconductor-normal-superconductor junctions. Phys. Rev. B 85, 235307 (2012).

    Article  ADS  Google Scholar 

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Acknowledgements

We thank A. Haim, A. Stern, F. von Oppen and G. Refael for useful discussions. We are grateful to R. Popovitz-Biro and D. Mahalu for their professional contribution and to A. Kretinin for laying the groundwork for nanowire device physics, and S. Ilani and A. Joshua for enabling us to perform the tilted field measurement. M.H. acknowledges the partial support of the Israeli Science Foundation (ISF), the Minerva foundation, the US-Israel Bi-National Science Foundation (BSF) and the European Research Council under the European Community’s Seventh Framework Program (FP7/2007-2013)/ERC Grant agreement # 227716. Y.O. acknowledges the partial support of the DFG, Minerva and that of the BSF. H.S. acknowledges the partial support of the ISF and the Israeli Ministry of Science and Technology (IMOST).

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  1. Anindya Das and Yuval Ronen: These authors contributed equally to this work

Authors and Affiliations

  1. Department of Condensed Matter Physics, Braun Center for Submicron Research, Weizmann Institute of Science, Rehovot 76100, Israel

    Anindya Das, Yuval Ronen, Yonatan Most, Yuval Oreg, Moty Heiblum & Hadas Shtrikman

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  1. Anindya Das
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Contributions

A.D. and Y.R. contributed to sample design, device fabrication, set-up, data acquisition, analysis and writing of the paper. M.H. contributed to design, data interpretation and writing of the paper. Y.M. contributed to theory, simulations and writing of the paper. Y.O. contributed to theory, simulations, experimental insight and writing of the paper. H.S contributed to the Au-assisted vapour-liquid–solid molecular beam epitaxy growth and structural study of InAs nanowires, discussions and editing of the manuscript.

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Correspondence to Moty Heiblum.

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Das, A., Ronen, Y., Most, Y. et al. Zero-bias peaks and splitting in an Al–InAs nanowire topological superconductor as a signature of Majorana fermions. Nature Phys 8, 887–895 (2012). https://doi.org/10.1038/nphys2479

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