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Unified scattering approach to Josephson current and thermal noise in BCS and topological superconducting junctions

  • Romain Jacquet
  • Jérôme RechEmail author
  • Thibaut Jonckheere
  • Alex Zazunov
  • Thierry Martin
Regular Article

Abstract

We present a unified description of a junction between s-wave (BCS) superconductors and a junction between p-wave superconductors in a topologically nontrivial phase, which relies on a scattering state expansion. We compute Josephson current and thermal noise in the two kinds of junction and exhibit some characteristic features for a junction of two topological superconductors hosting Majorana zero-energy modes.

Graphical abstract

Keywords

Solid State and Materials 

References

  1. 1.
    E. Majorana, Nuovo Cim. 14, 171 (1937) ADSCrossRefGoogle Scholar
  2. 2.
    S.R. Elliott, M. Franz, Rev. Mod. Phys. 87, 137 (2015) ADSCrossRefGoogle Scholar
  3. 3.
    N. Read, D. Green, Phys. Rev. B 61, 10267 (2000) ADSCrossRefGoogle Scholar
  4. 4.
    A.Y. Kitaev, Phys.-Uspekhi 44, 131 (2001) ADSCrossRefGoogle Scholar
  5. 5.
    L. Fu, C.L. Kane, Phys. Rev. Lett. 100, 096407 (2008) ADSCrossRefGoogle Scholar
  6. 6.
    J. Alicea, Rep. Prog. Phys. 75, 076501 (2012) ADSCrossRefGoogle Scholar
  7. 7.
    C. Beenakker, Annu. Rev. Condens. Matter Phys. 4, 113 (2013) ADSCrossRefGoogle Scholar
  8. 8.
    M. Leijnse, K. Flensberg, Semicond. Sci. Technol. 27, 124003 (2012) ADSCrossRefGoogle Scholar
  9. 9.
    D.A. Ivanov, Phys. Rev. Lett. 86, 268 (2001) ADSCrossRefGoogle Scholar
  10. 10.
    C. Nayak, S.H. Simon, A. Stern, M. Freedman, S. Das Sarma, Rev. Mod. Phys. 80, 1083 (2008) ADSCrossRefGoogle Scholar
  11. 11.
    A.Y. Kitaev, Ann. Phys. 303, 2 (2003) ADSCrossRefGoogle Scholar
  12. 12.
    J.D. Sau, R.M. Lutchyn, S. Tewari, S. Das Sarma, Phys. Rev. Lett. 104, 040502 (2010) ADSCrossRefGoogle Scholar
  13. 13.
    J. Alicea, Phys. Rev. B 81, 125318 (2010) ADSCrossRefGoogle Scholar
  14. 14.
    R.M. Lutchyn, J.D. Sau, S. Das Sarma, Phys. Rev. Lett. 105, 077001 (2010) ADSCrossRefGoogle Scholar
  15. 15.
    Y. Oreg, G. Refael, F. von Oppen, Phys. Rev. Lett. 105, 177002 (2010) ADSCrossRefGoogle Scholar
  16. 16.
    J. Alicea, Y. Oreg, G. Refael, F. von Oppen, M.P.A. Fisher, Nat. Phys. 7, 412 (2011) CrossRefGoogle Scholar
  17. 17.
    V. Mourik, K. Zuo, S.M. Frolov, S.R. Plissard, E.P.A.M. Bakkers, L.P. Kouwenhoven, Science 336, 1003 (2012) ADSCrossRefGoogle Scholar
  18. 18.
    A. Das, Y. Ronen, Y. Most, Y. Oreg, M. Heiblum, H. Shtrikman, Nat. Phys. 8, 887 (2012) CrossRefGoogle Scholar
  19. 19.
    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 (2013) ADSCrossRefGoogle Scholar
  20. 20.
    M.T. Deng, C.L. Yu, G.Y. Huang, M. Larsson, P. Caroff, H.Q. Xu, Nano Lett. 12, 6414 (2012) ADSCrossRefGoogle Scholar
  21. 21.
    A.D.K. Finck, D.J. Van Harlingen, P.K. Mohseni, K. Jung, X. Li, Phys. Rev. Lett. 110, 126406 (2013) ADSCrossRefGoogle Scholar
  22. 22.
    L. Fu, C.L. Kane, Phys. Rev. B 79, 161408 (2009) ADSCrossRefGoogle Scholar
  23. 23.
    L.P. Rokhinson, X. Liu, J.K. Furdyna, Nat. Phys. 8, 795 (2012) CrossRefGoogle Scholar
  24. 24.
    Y. Tanaka, S. Kashiwaya, Phys. Rev. B 53, 9371 (1996) ADSCrossRefGoogle Scholar
  25. 25.
    Y. Tanaka, S. Kashiwaya, Phys. Rev. B 56, 892 (1997) ADSCrossRefGoogle Scholar
  26. 26.
    S. Kashiwaya, Y. Tanaka, Rep. Prog. Phys. 63, 1641 (2000) ADSCrossRefGoogle Scholar
  27. 27.
    C.-K. Chiu, J.D. Sau, S. Das Sarma, Phys. Rev. B 97, 035310 (2018) ADSCrossRefGoogle Scholar
  28. 28.
    E.B. Hansen, J. Danon, K. Flensberg, Phys. Rev. B 97, 041411 (2018) ADSCrossRefGoogle Scholar
  29. 29.
    S.M. Albrecht, A.P. Higginbotham, M. Madsen, F. Kuemmeth, T.S. Jespersen, J. Nygård, P. Krogstrup, C.M. Marcus, Nature 531, 206 (2016) ADSCrossRefGoogle Scholar
  30. 30.
    F. Nichele, A.C.C. Drachmann, A.M. Whiticar, E.C.T. O’Farrell, 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) ADSCrossRefGoogle Scholar
  31. 31.
    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. Op het Veld, P.J. van Veld-hoven, S. Koelling, M.A. Verheijen, M. Pendharkar, D.J. Pennachio, B. Shojaei, J.S. Lee, C.J. Palmstrøm, E.P.A.M. Bakkers, S.D. Sarma, L.P. Kouwenhoven, Nature 556, 74 (2018) ADSCrossRefGoogle Scholar
  32. 32.
    A. Furusaki, M. Tsukada, Physica B 165–166, 967 (1990) CrossRefGoogle Scholar
  33. 33.
    C.W.J. Beenakker, H. van Houten, Phys. Rev. Lett. 66, 3056 (1991) ADSCrossRefGoogle Scholar
  34. 34.
    C.W.J. Beenakker, Phys. Rev. Lett. 67, 3836 (1991) ADSCrossRefGoogle Scholar
  35. 35.
    A. Martín-Rodero, A.L. Yeyati, F.J. García-Vidal, Phys. Rev. B 53, R8891 (1996) ADSCrossRefGoogle Scholar
  36. 36.
    V.S. Shumeiko, G. Wendin, E.N. Bratus’, Phys. Rev. B 48, 13129 (1993) ADSCrossRefGoogle Scholar
  37. 37.
    A. Zazunov, V.S. Shumeiko, E.N. Bratus’, J. Lantz, G. Wendin, Phys. Rev. Lett. 90, 087003 (2003) ADSCrossRefGoogle Scholar
  38. 38.
    A. Zazunov, V.S. Shumeiko, G. Wendin, E.N. Bratus’, Phys. Rev. B 71, 214505 (2005) ADSCrossRefGoogle Scholar
  39. 39.
    D.G. Olivares, A.L. Yeyati, L. Bretheau, Ç.Ö. Girit, H. Pothier, C. Urbina, Phys. Rev. B 89, 104504 (2014) ADSCrossRefGoogle Scholar
  40. 40.
    A. Zazunov, A. Brunetti, A.L. Yeyati, R. Egger, Phys. Rev. B 90, 104508 (2014) ADSCrossRefGoogle Scholar
  41. 41.
    R.-P. Riwar, M. Houzet, J.S. Meyer, Y.V. Nazarov, J. Phys.:Condens. Matter 27, 095701 (2015) ADSGoogle Scholar
  42. 42.
    P. Ghaemi, V.P. Nair, Phys. Rev. Lett. 116, 037001 (2016) ADSCrossRefGoogle Scholar
  43. 43.
    A. Zazunov, R. Egger, A. Levy Yeyati, Phys. Rev. B 94, 014502 (2016) ADSCrossRefGoogle Scholar
  44. 44.
    S. Ryu, A.P. Schnyder, A. Furusaki, A.W.W. Ludwig, New J. Phys. 12, 065010 (2010) ADSCrossRefGoogle Scholar
  45. 45.
    R. Lutchyn, E. Bakkers, L. Kouwenhoven, P. Krogstrup, C. Marcus, Y. Oreg, Nat. Rev. Mater. 3, 52 (2018) ADSCrossRefGoogle Scholar
  46. 46.
    T.D. Stanescu, S. Das Sarma, Phys. Rev. B 97, 045410 (2018) ADSCrossRefGoogle Scholar
  47. 47.
    F. Kos, S.E. Nigg, L.I. Glazman, Phys. Rev. B 87, 174521 (2013) ADSCrossRefGoogle Scholar
  48. 48.
    M. Trif, O. Dmytruk, H. Bouchiat, R. Aguado, P. Simon, Phys. Rev. B 97, 041415 (2018) ADSCrossRefGoogle Scholar
  49. 49.
    M. Zgirski, L. Bretheau, Q. Le Masne, H. Pothier, D. Esteve, C. Urbina, Phys. Rev. Lett. 106, 257003 (2011) ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences / Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Romain Jacquet
    • 1
  • Jérôme Rech
    • 1
    Email author
  • Thibaut Jonckheere
    • 1
  • Alex Zazunov
    • 2
  • Thierry Martin
    • 1
  1. 1.Aix Marseille Univ, Université de Toulon, CNRS, CPTMarseilleFrance
  2. 2.Institut für Theoretische Physik IV, Heinrich Heine UniversitätDüsseldorfGermany

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