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High-resolution studies of the Majorana atomic chain platform

Nature Physics volume 13, pages 286–291 (2017)Cite this article

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Abstract

Ordered assemblies of magnetic atoms on the surface of conventional superconductors can be used to engineer topological superconducting phases and realize Majorana fermion quasiparticles (MQPs) in a condensed matter setting. Recent experiments have shown that chains of Fe atoms on Pb generically have the required electronic characteristics to form a one-dimensional topological superconductor and have revealed spatially resolved signatures of localized MQPs at the ends of such chains. Here we report higher-resolution measurements of the same atomic chain system performed using a dilution refrigerator scanning tunnelling microscope (STM). With significantly better energy resolution than previous studies, we show that the zero-bias peak (ZBP) in Fe chains has no detectable splitting from hybridization with other states. The measurements also reveal that the ZBP exhibits a distinctive ‘double eye’ spatial pattern on nanometre length scales. Theoretically we show that this is a general consequence of STM measurements of MQPs with substantial spectral weight in the superconducting substrate, a conclusion further supported by measurements of Pb overlayers deposited on top of the Fe chains. Finally, we report experiments performed with superconducting tips in search of the particle–hole symmetric MQP signature expected in such measurements.

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Figure 1: Zero-bias end mode in Fe chains on Pb.
Figure 2: ‘Double eye’ pattern and spatial dependence of the ZBP.
Figure 3: Theoretical model of the zero-bias end mode.
Figure 4: Theoretical model of the ‘double eye’ spatial pattern of the ZBP.
Figure 5: ZBP in Pb overlayer above Fe chain.
Figure 6: Superconducting tip spectra and electron–hole symmetry of the zero-energy end mode.

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References

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  3. Beenakker, C. W. J. Search for Majorana fermions in superconductors. Ann. Rev. Condens. Matter Phys. 4, 113–136 (2013).

    Article  ADS  Google Scholar 

  4. Majorana, E. Teoria simmetrica dell’elettrone e del positrone. Il Nuovo Cimento 14, 171–184 (1937).

    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. Nayak, C., Simon, S. H., Stern, A., Freedman, M. & Das Sarma, S. Non-Abelian anyons and topological quantum computation. Rev. Mod. Phys. 80, 1083–1159 (2008).

    Article  ADS  MathSciNet  Google Scholar 

  7. Salomaa, M. M. & Volovik, G. E. Cosmiclike domain walls in superfluid 3He-B: instantons and diabolical points in (k, r) space. Phys. Rev. B 37, 9298–9311 (1988).

    Article  ADS  MathSciNet  Google Scholar 

  8. Ivanov, D. A. Non-abelian statistics of half-quantum vortices in p-wave superconductors. Phys. Rev. Lett. 86, 268–271 (2001).

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  10. 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 

  11. 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  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  13. 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 

  14. Choy, T. P., Edge, J. M., Akhmerov, A. R. & Beenakker, C. W. J. Majorana fermions emerging from magnetic nanoparticles on a superconductor without spin–orbit coupling. Phys. Rev. B 84, 195442 (2011).

    Article  ADS  Google Scholar 

  15. Kjaergaard, M., Wölms, K. & Flensberg, K. Majorana fermions in superconducting nanowires without spin–orbit coupling. Phys. Rev. B 85, 020503 (2012).

    Article  ADS  Google Scholar 

  16. Nadj-Perge, S., Drozdov, I. K., Bernevig, B. A. & Yazdani, A. Proposal for realizing Majorana fermions in chains of magnetic atoms on a superconductor. Phys. Rev. B 88, 020407 (2013).

    Article  ADS  Google Scholar 

  17. Pientka, F., Glazman, L. I. & von Oppen, F. Topological superconducting phase in helical Shiba chains. Phys. Rev. B 88, 155420 (2013).

    Article  ADS  Google Scholar 

  18. Klinovaja, J., Stano, P., Yazdani, A. & Loss, D. Topological superconductivity and Majorana fermions in RKKY systems. Phys. Rev. Lett. 111, 186805 (2013).

    Article  ADS  Google Scholar 

  19. Braunecker, B. & Simon, P. Interplay between classical magnetic moments and superconductivity in quantum one-dimensional conductors: toward a self-sustained topological Majorana phase. Phys. Rev. Lett. 111, 147202 (2013).

    Article  ADS  Google Scholar 

  20. Vazifeh, M. M. & Franz, M. Self-organized topological state with Majorana fermions. Phys. Rev. Lett. 111, 206802 (2013).

    Article  ADS  Google Scholar 

  21. Nakosai, S., Tanaka, Y. & Nagaosa, N. Two-dimensional p-wave superconducting states with magnetic moments on a conventional s-wave superconductor. Phys. Rev. B 88, 180503 (2013).

    Article  ADS  Google Scholar 

  22. Rontynen, J. & Ojanen, T. Topological superconductivity and high Chern numbers in 2D ferromagnetic Shiba lattices. Phys. Rev. Lett. 114, 236803 (2015).

    Article  ADS  Google Scholar 

  23. Nadj-Perge, S. et al. Observation of Majorana fermions in ferromagnetic atomic chains on a superconductor. Science 346, 602–607 (2014).

    Article  ADS  Google Scholar 

  24. Li, J. et al. Topological superconductivity induced by ferromagnetic metal chains. Phys. Rev. B 90, 235433 (2014).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  26. 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  ADS  Google Scholar 

  27. Das, A. et al. Zero-bias peaks and splitting in an Al–InAs nanowire topological superconductor as a signature of Majorana fermions. Nat. Phys. 8, 887–895 (2012).

    Article  Google Scholar 

  28. Deng, M. T. et al. Anomalous zero-bias conductance peak in a Nb–InSb nanowire–Nb hybrid device. Nano Lett. 12, 6414–6419 (2012).

    Article  ADS  Google Scholar 

  29. Finck, A. D. K., Van Harlingen, D. J., Mohseni, P. K., Jung, K. & Li, X. Anomalous modulation of a zero-bias peak in a hybrid nanowire-superconductor device. Phys. Rev. Lett. 110, 126406 (2013).

    Article  ADS  Google Scholar 

  30. 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).

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  32. Liu, J., Potter, A. C., Law, K. T. & Lee, P. A. Zero-Bias peaks in the tunneling conductance of spin-orbit-coupled superconducting wires with and without Majorana end-states. Phys. Rev. Lett. 109, 267002 (2012).

    Article  ADS  Google Scholar 

  33. Lee, E. J. H. et al. Zero-bias anomaly in a nanowire quantum dot coupled to superconductors. Phys. Rev. Lett. 109, 186802 (2012).

    Article  ADS  Google Scholar 

  34. Churchill, H. O. H. et al. Superconductor-nanowire devices from tunneling to the multichannel regime: zero-bias oscillations and magnetoconductance crossover. Phys. Rev. B 87, 241401 (2013).

    Article  ADS  Google Scholar 

  35. Pikulin, D. I., Dahlhaus, J. P., Wimmer, M., Schomerus, H. & Beenakker, C. W. J. A zero-voltage conductance peak from weak antilocalization in a Majorana nanowire. New J. Phys. 14, 125011 (2012).

    Article  ADS  Google Scholar 

  36. Kells, G., Meidan, D. & Brouwer, P. W. Near-zero-energy end states in topologically trivial spin–orbit coupled superconducting nanowires with a smooth confinement. Phys. Rev. B 86, 100503 (2012).

    Article  ADS  Google Scholar 

  37. Zhang, H. et al. Ballistic Majorana nanowire devices. Preprint at http://arXiv.org/abs/1603.04069 (2016).

  38. Pawlak, R. et al. Probing atomic structure and Majorana wavefunctions in mono-atomic Fe-chains on superconducting Pb-surface. Preprint at http://arXiv.org/abs/1505.06078 (2015).

  39. Ruby, M. et al. End states and subgap structure in proximity-coupled chains of magnetic adatoms. Phys. Rev. Lett. 115, 197204 (2015).

    Article  ADS  Google Scholar 

  40. Dumitrescu, E., Roberts, B., Tewari, S., Sau, J. D. & DasSarma, S. Majorana fermions in chiral topological ferromagnetic nanowires. Phys. Rev. B 91, 094505 (2015).

    Article  ADS  Google Scholar 

  41. Peng, Y., Pientka, F., Glazman, L. I. & von Oppen, F. Strong localization of Majorana end states in chains of magnetic adatoms. Phys. Rev. Lett. 114, 106801 (2015).

    Article  ADS  Google Scholar 

  42. Yu, L. Bound state in superconductors with paramagnetic impurities. Acta Phys. Sin. 21, 75–91 (1965).

    Google Scholar 

  43. Shiba, H. Classical spins in superconductors. Progr. Theor. Phys. 40, 435–451 (1968).

    Article  ADS  Google Scholar 

  44. Rusinov, A. I. On theory of gapless superconductivity in alloys containing paramagnetic impurities. Sov. Phys. Jetp-Ussr 29, 1101–1106 (1969).

    ADS  Google Scholar 

  45. Peng, Y., Pientka, F., Vinkler-Aviv, Y., Glazman, L. I. & von Oppen, F. Robust Majorana conductance peaks for a superconducting lead. Phys. Rev. Lett. 115, 266804 (2015).

    Article  ADS  Google Scholar 

  46. Misra, S. et al. Design and performance of an ultra-high vacuum scanning tunneling microscope operating at dilution refrigerator temperatures and high magnetic fields. Rev. Sci. Instrum. 84, 103903 (2013).

    Article  ADS  Google Scholar 

  47. Ruby, M., Heinrich, B. W., Pascual, J. I. & Franke, K. J. Experimental demonstration of a two-band superconducting state for lead using scanning tunneling spectroscopy. Phys. Rev. Lett. 114, 157001 (2015).

    Article  ADS  Google Scholar 

  48. 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 

  49. Sau, J. D. & Brydon, P. M. R. Bound states of a ferromagnetic wire in a superconductor. Phys. Rev. Lett. 115, 127003 (2015).

    Article  ADS  Google Scholar 

  50. Meng, T., Klinovaja, J., Hoffman, S., Simon, P. & Loss, D. Superconducting gap renormalization around two magnetic impurities: from Shiba to Andreev bound states. Phys. Rev. B 92, 064503 (2015).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  52. Li, J., Neupert, T., Bernevig, B. A. & Yazdani, A. Manipulating Majorana zero modes on atomic rings with an external magnetic field. Nat. Commun. 7, 10395 (2016).

    Article  ADS  Google Scholar 

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Acknowledgements

The work at Princeton has been supported by ONR-N00014-14-1-0330, ONR-N00014-11-1-0635, ONR-N00014-13-10661, NSF-MRSEC programs through the Princeton Center for Complex Materials DMR-142054, NSF-DMR-1104612, NSF-DMR-1420541, NSF EAGER Award NOA-AWD1004957, DOE DE-SC0016239, Simons Investigator Award, Packard Foundation and Schmidt Fund for Innovative Research, and by the Gordon and Betty Moore Foundation as part of EPiQS initiative (GBMF4530). This project was also made possible using the facilities at Princeton Nanoscale Microscopy Laboratory supported by grants through ARO-MURI Program W911NF-12-1-0461, DOE-BES, LPS and ARO-W911NF-1-0606, and Eric and Wendy Schmidt Transformative Technology Fund at Princeton. B.E.F. acknowledges financial support from the Dicke Fellowship. M.T.R. acknowledges support from the NSF Graduate Research Fellowship Program.

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Author notes

  1. Ilya K. Drozdov

    Present address: Present address: Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, New York 11973, USA.,

  2. Benjamin E. Feldman, Mallika T. Randeria, Jian Li and Ilya K. Drozdov: These authors contributed equally to this work.

Authors and Affiliations

  1. Joseph Henry Laboratories and Department of Physics, Princeton University, Princeton, New Jersey 08544, USA

    Benjamin E. Feldman, Mallika T. Randeria, Jian Li, Sangjun Jeon, Yonglong Xie, Zhijun Wang, Ilya K. Drozdov, B. Andrei Bernevig & Ali Yazdani

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Contributions

B.E.F., M.T.R. and I.K.D. performed the dilution refrigerator STM measurements. S.J., Y.X. and I.K.D. conducted the measurements on Fe chains capped with Pb overlayers. J.L., Z.W. and B.A.B. performed the theoretical modelling and simulations. All authors contributed to analysing the data and writing the manuscript.

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Correspondence to Ali Yazdani.

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Feldman, B., Randeria, M., Li, J. et al. High-resolution studies of the Majorana atomic chain platform. Nature Phys 13, 286–291 (2017). https://doi.org/10.1038/nphys3947

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