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The invisible Majorana bound state at the helical edge

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Abstract

The presence of a Majorana bound state in condensed matter systems is often associated to a zero bias peak in conductance measurements. Here, we analyze a system were this paradigm is violated. A Majorana bound state is always present at the interface between a quantum spin Hall system that is magnetically gapped and a quantum spin Hall system gapped by proximity induced s-wave superconductivity. However, the linear conductance could be either zero or non-zero and quantized depending on the energy and length scales of the barriers. The transition between the two values is reminiscent of the topological phase transition in proximitized spin–orbit coupled quantum wires in the presence of an applied magnetic field. We interpret the behavior of the conductance in terms of scattering states at both zero and non-zero energy.

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References

  1. C.L. Kane, E.J. Mele, Phys. Rev. Lett. 95, 226801 (2005)

    Article  ADS  Google Scholar 

  2. C.L. Kane, E.J. Mele, Phys. Rev. Lett. 95, 146802 (2005)

    Article  ADS  Google Scholar 

  3. B.A. Bernevig, T.A. Hughes, S.-C. Zhang, Science 314, 1757 (2006)

    Article  ADS  Google Scholar 

  4. M. Knig, S. Wiedmann, C. Brüne, A. Roth, H. Buhmann, L.W. Molenkamp, X.-L. Qi, S.-C. Zhang, Science 318, 766 (2007)

    Article  ADS  Google Scholar 

  5. I. Knez, R.-R. Du, G. Sullivan, Phys. Rev. Lett. 107, 136603 (2011)

    Article  ADS  Google Scholar 

  6. X.-L. Qi, S.-C. Zhang, Rev. Mod. Phys. 83, 1057 (2011)

    Article  ADS  Google Scholar 

  7. D. Pesin, A.H. Macdonald, Nat. Mater. 11, 409 (2012)

    Article  ADS  Google Scholar 

  8. A. Roth, C. Brüne, H. Buhmann, L.W. Molenkamp, J. Maciejko, X.-L. Qi, S.-C. Zhang, Science 325, 5938 (2009)

    Article  Google Scholar 

  9. P. Michetti, B. Trauzettel, Appl. Phys. Lett. 102, 063505 (2013)

    Article  ADS  Google Scholar 

  10. L. Fu, C.L. Kane, Phys. Rev. Lett. 100, 096407 (2008)

    Article  ADS  Google Scholar 

  11. L. Fu, C.L. Kane, Phys. Rev. B 79, 161408 (2009)

    Article  ADS  Google Scholar 

  12. S. Hart, H. Ren, T. Wagner, P. Leubner, M. Mühlbauer, C. Brüne, H. Buhmann, L.W. Molenkamp, A. Yacoby, Nat. Phys. 10, 638 (2014)

    Article  Google Scholar 

  13. F. Domínguez, O. Kashuba, E. Bocquillon, J. Wiedenmann, R. S. Deacon, T.M. Klapwijk, G. Platero, L.W. Molenkamp, B. Trauzettel, E.M. Hankiewicz, Phys. Rev. B 95, 195430 (2017)

    Article  ADS  Google Scholar 

  14. J. Picó-Cortés, F. Domínguez, G. Platero, Phys. Rev. B 96, 125438 (2017)

    Article  ADS  Google Scholar 

  15. Y. Tanaka, Y. Tanuma, A.A. Golubov, Phys. Rev. B 76, 054522 (2007)

    Article  ADS  Google Scholar 

  16. Y. Tanaka, A.A. Golubov, S. Kashiwaya, M. Ueda, Phys. Rev. Lett. 99, 037005 (2007)

    Article  ADS  Google Scholar 

  17. M. Eschrig, T. Löfwander, T. Champel, J.C. Cuevas, J. Kopu, G. Schön, J. Low Temp. Phys. 147, 457 (2007)

    Article  ADS  Google Scholar 

  18. Y. Tanaka, M. Sato, N. Nagaosa, J. Phys. Soc. Jpn. 81, 011013 (2012)

    Article  ADS  Google Scholar 

  19. A.M. Black-Schaffer, A.V. Balatsky, Phys. Rev. B 86, 144506 (2012)

    Article  ADS  Google Scholar 

  20. Y. Asano, Y. Tanaka, Phys. Rev. B 87, 104513 (2013)

    Article  ADS  Google Scholar 

  21. F. Crépin, P. Burset, B. Trauzettel, Phys. Rev. B 92, 100507(R) (2015)

    Article  ADS  Google Scholar 

  22. O. Kashuba, B. Sothmann, P. Burset, B. Trauzettel, Phys. Rev. B 95, 174516 (2017)

    Article  ADS  Google Scholar 

  23. J. Cayao, A.M. Black-Schaffer, Phys. Rev. B 96, 155426 (2017)

    Article  ADS  Google Scholar 

  24. C. Fleckenstein, N. Traverso Ziani, B. Trauzettel, Phys. Rev. B 97, 134523 (2018)

    Article  ADS  Google Scholar 

  25. J. Cayao, A.M. Black-Schaffer, https://doi.org/arXiv:1805.07948

  26. Y. Tanaka, T. Yokoyama, N. Nagaosa, Phys. Rev. Lett. 103, 107002 (2009)

    Article  ADS  Google Scholar 

  27. J. Linder, J.W.A. Robinson, Nat. Phys. 11, 307 (2015)

    Article  Google Scholar 

  28. D. Breunig, P. Burset, B. Trauzettel, Phys. Rev. Lett. 120, 037701 (2018)

    Article  ADS  Google Scholar 

  29. C. Wu, B.A. Bernevig, S.-C. Zhang, Phys. Rev. Lett. 96, 106401 (2006)

    Article  ADS  Google Scholar 

  30. J. Maciejko, C. Liu, Y. Oreg, X.-L. Qi, C. Wu, S.-C. Zhang, Phys. Rev. Lett. 102, 256803 (2009)

    Article  ADS  Google Scholar 

  31. N. Traverso Ziani, F. Crépin, B. Trauzettel, Phys. Rev. Lett. 115, 206402 (2015)

    Article  ADS  Google Scholar 

  32. F. Zhang, C.L. Kane, Phys. Rev. Lett. 113, 036401 (2014)

    Article  ADS  Google Scholar 

  33. C.P. Orth, R.P. Tiwari, T. Meng, T.L. Schmidt, Phys. Rev. B 91, 081406(R) (2015)

    Article  ADS  Google Scholar 

  34. Y. Vinkler-Aviv, P.W. Brouwer, F. von Oppen, Phys. Rev. B, 96, 195421 (2017)

    Article  Google Scholar 

  35. C. Nayak, S.H. Simon, A. Stern, M. Freedman, S.D. Sarma, Rev. Mod. Phys. 80, 1083 (2008)

    Article  ADS  Google Scholar 

  36. V. Mourik, K. Zuo1, S.M. Frolov, S.R. Plissard, E.P.A.M. Bakkers, L.P. Kouwenhoven, Science 336, 1003 (2012)

    Article  ADS  Google Scholar 

  37. A. Das, Y. Ronen, Y. Most, Y. Oreg, M. Heiblum, H. Shtrikman, Nat. Phys. 89, 887 (2012)

    Article  Google Scholar 

  38. M.T. Deng, C.L. Yu, G.Y. Huang, M. Larsson, P. Caroff, H.Q. Xu, Nano Lett. 12, 6414 (2012)

    Article  ADS  Google Scholar 

  39. L.P. Rokhinson, X. Liu, J.K. Furdyna, Nat. Phys. 8, 795 (2012)

    Article  Google Scholar 

  40. A.D.K. Finck, D.J. Van Harlingen, P.K. Mohseni, K. Jung, X. Li, Phys. Rev. Lett. 110, 126406 (2013)

    Article  ADS  Google Scholar 

  41. H.O.H. Churchill, V. Fatemi, K. Grove-Rasmussen, M.T. Deng, P. Caroff, H.Q. Xu, C.M. Marcus, Phys. Rev. B 87, 241401(R) (2013)

    Article  ADS  Google Scholar 

  42. M. Kjaergaard, F. Nichele, H.J. Suominen, M.P. Nowak, M. Wimmer, A.R. Akhmerov, J.A. Folk, K. Flensberg, J. Shabani, C.J. Palmstrom, C.M. Marcus, Nat. Commun. 7, 12841 (2016)

    Article  ADS  Google Scholar 

  43. J. Wiedenmann, E. Bocquillon, R.S. Deacon, S. Hartinger, O. Herrmann, T.M. Klapwijk, L. Maier, C. Ames, C. Brüne, C. Gould, A. Oiwa, K. Ishibashi, S. Tarucha, H. Buhmann, L.W. Molenkamp, Nat. Commun. 7, 10303 (2016)

    Article  ADS  Google Scholar 

  44. M.T. Deng, S. Vaitiekunas, E.B. Hansen, J. Danon, M. Leijnse, K. Flensberg, J. Nygiard, P. Krogstrup, C.M. Marcus, Science 354, 1557 (2016)

    Article  ADS  Google Scholar 

  45. S.M. Albrecht, A.P. Higginbotham, M. Madsen, F. Kuemmeth, T.S. Jespersen, J. Nygard, P. Krogstrup, C.M. Marcus, Nature 531, 206 (2016)

    Article  ADS  Google Scholar 

  46. J. Chen, P. Yu, J. Stenger, M. Hocevar, D. Car, S.R. Plissard, E.P.A.M. Bakkers, T.D. Stanescu, S.M. Frolov, Sci. Adv. 3, e1701476 (2017)

    Article  ADS  Google Scholar 

  47. H. Zhang, Ö. Gül, S. Conesa-Boj, M.P. Nowak, M. Wimmer, K. Zuo, V. Mourik, F.K. de Vries, J. van Veen, M.W.A. de Moor, J.D.S. Bommer, D.J. van Woerkom, D. Car, S. R Plissard, E.P.A.M. Bakkers, M. Quintero-Prez, M.C. Cassidy, S. Koelling, S. Goswami, K. Watanabe, T. Taniguchi, L.P. Kouwenhoven, Nat. Commun. 8, 16025 (2017)

    Article  ADS  Google Scholar 

  48. H.J. Suominen, M. Kjaergaard, A.R. Hamilton, J. Shabani, C.J. Palmstrom, C.M. Marcus, F. Nichele, Phys. Rev. Lett. 119, 176805 (2017)

    Article  ADS  Google Scholar 

  49. F. Nichele, A.C.C. Drachmann, A.M. Whiticar, E. C.T. OFarrell, H.J. Suominen, A. Fornieri, T. Wang, G.C. Gardner, C. Thomas, A.T. Hatke, P. Krogstrup, M.J. Manfra, K. Flensberg, C.M. Marcus, Phys. Rev. Lett. 119, 136803 (2017)

    Article  ADS  Google Scholar 

  50. E. Bocquillon, R.S. Deacon, J. Wiedenmann, P. Leubner, T.M. Klapwijk, C. Brüne, K. Ishibashi, H. Buhmann, L.W. Molenkamp, Nat. Nanotech. 12, 137 (2017)

    Article  ADS  Google Scholar 

  51. R.S. Deacon, J. Wiedenmann, E. Bocquillon, F. Domnguez, T.M. Klapwijk, P. Leubner, C. Brüne, E.M. Hankiewicz, S. Tarucha, K. Ishibashi, H. Buhmann, L.W. Molenkamp, Phys. Rev. X 7, 021011 (2017)

    Google Scholar 

  52. H. Zhang, C.-X. Liu, S. Gazibegovic, D. Xu, J.A. Logan, G. Wang, N. van Loo, J.D.S. Bommer, M.W.A. de Moor, D. Car, R.L.M.O. het Veld, P.J. van Veldhoven, S. Koelling, M.A. Verheijen, M. Pendharkar, D.J. Pennachio, B. Shojaei, J. Sue Lee, C.J. Palmstrm, E.P.A.M. Bakkers, S. Das Sarma, L.P. Kouwenhoven, Nature 556, 74 (2018)

    Article  ADS  Google Scholar 

  53. D. Laroche, D. Bouman, D.J. van Woerkom, A. Proutski, C. Murthy, D.I. Pikulin, C. Nayak, R.J.J. van Gulik, J. Nygard, P. Krogstrup, L.P. Kouwenhoven, A. Geresdi, https://doi.org/arXiv:1712.08459

  54. P. Streda, P. Seba, Phys. Rev. Lett. 90, 256601 (2003)

    Article  ADS  Google Scholar 

  55. C.H.L. Quay, T.L. Hughes, J.A. Sulpizio, L.N. Pfeiffer, K.W. Baldwin, K.W. West, D. Goldhaber Gordon, R. De Picciotto, Nat. Phys. 6, 336 (2010)

    Article  Google Scholar 

  56. T. Meng, D. Loss, Phys. Rev. B 88, 035437 (2013)

    Article  ADS  Google Scholar 

  57. F.M. Gambetta, N. Traverso Ziani, F. Cavaliere, M. Sassetti, Europhys. Lett. 107, 47010 (2014)

    Article  ADS  Google Scholar 

  58. C.J. Pedder, T. Meng, R.P. Tiwari, T.L. Schmidt, Phys. Rev. B 94, 245414 (2016)

    Article  ADS  Google Scholar 

  59. S. Heedt, N. Traverso Ziani, F. Crépin, W. Prost, S. Trellenkamp, J. Schubert, D. Grtzmacher, B. Trauzettel, T. Schpers, Nat. Phys. 13, 563 (2017)

    Article  Google Scholar 

  60. S. Porta, F.M. Gambetta, N. Traverso Ziani, D.M. Kennes, M. Sassetti, F. Cavaliere, Phys. Rev. B 97, 035433 (2018)

    Article  ADS  Google Scholar 

  61. R.M. Lutchyn, J.D. Sau, S. Das Sarma, Phys. Rev. Lett. 105, 077001 (2010)

    Article  ADS  Google Scholar 

  62. Y. Oreg, G. Refael, F. von Oppen, Phys. Rev. Lett. 105, 177002 (2010)

    Article  ADS  Google Scholar 

  63. E. Prada, P. San-Jose, R. Aguado, Phys. Rev. B 86, 180503 (2012)

    Article  ADS  Google Scholar 

  64. I.C. Fulga, F. Hassler, A.R. Akhmerov, C.W.J. Beenakker, Phys. Rev. B 83, 155429 (2011)

    Article  ADS  Google Scholar 

  65. I.C. Fulga, F. Hassler, A.R. Akhmerov, Phys. Rev. B 85, 165409 (2012)

    Article  ADS  Google Scholar 

  66. C.W.J. Beenakker, Rev. Mod. Phys. 87, 1037 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  67. C.J. Bolech, E. Demler, Phys. Rev. Lett. 98, 237002 (2007)

    Article  ADS  Google Scholar 

  68. K.T. Law, P.A. Lee, T.K. Ng, Phys. Rev. Lett. 103, 237001 (2009)

    Article  ADS  Google Scholar 

  69. K. Flensberg, Phys. Rev. B 82, 180516 (2010)

    Article  ADS  Google Scholar 

  70. F. Crépin, B. Trauzettel, F. Dolcini, Phys. Rev. B 89, 205115 (2014)

    Article  ADS  Google Scholar 

  71. Y. Nazarov, Y. Blanter, Quantum Transport: Introduction to Nanoscience (Cambridge University Press, Cambridge, England, 2009)

  72. G.E. Blonder, M. Tinkham, T.M Klapwijk, Phys. Rev. B 25, 4515 (1982)

    Article  ADS  Google Scholar 

  73. C. Timm, Phys. Rev. B 86, 155456 (2012)

    Article  ADS  Google Scholar 

  74. G. Dolcetto, N. Traverso Ziani, M. Biggio, F. Cavaliere, M. Sassetti, Phys. Status Solidi RRL 7, 1059 (2013)

    Article  Google Scholar 

  75. K. Fleckenstein, N. Traverso Ziani, B. Trauzettel, Phys. Rev. B 94, 241406 (2016)

    Article  ADS  Google Scholar 

  76. N. Traverso Ziani, C. Fleckenstein, G. Dolcetto, B. Trauzettel, Phys. Rev. B 95, 205418 (2017)

    Article  ADS  Google Scholar 

  77. J. Klinovaja, D. Loss, Phys. Rev. B 86, 085408 (2012)

    Article  ADS  Google Scholar 

  78. D. Rainis, L. Trifunovic, J. Klinovaja, D. Loss, Phys. Rev. B 87, 024515 (2013)

    Article  ADS  Google Scholar 

  79. C. Fleckenstein, F. Domínguez, N.T. Ziani, B. Trauzettel, Phys. Rev. B 97, 155425 (2018)

    Article  ADS  Google Scholar 

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  1. Institute for Theoretical Physics and Astrophysics, University of Würzburg, Am Hubland, 97074, Wurzburg, Germany

    Christoph Fleckenstein, Felix Keidel, Björn Trauzettel & Niccoló Traverso Ziani

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  1. Christoph Fleckenstein
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  2. Felix Keidel
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Correspondence to Niccoló Traverso Ziani.

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Fleckenstein, C., Keidel, F., Trauzettel, B. et al. The invisible Majorana bound state at the helical edge. Eur. Phys. J. Spec. Top. 227, 1377–1386 (2018). https://doi.org/10.1140/epjst/e2018-800093-5

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