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Coulomb Blockade and Multiple Andreev Reflection in a Superconducting Single-Electron Transistor

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Abstract

In superconducting quantum point contacts, multiple Andreev reflection (MAR), which describes the coherent transport of m quasiparticles each carrying an electron charge with \(m\ge 3\), sets in at voltage thresholds \(eV = 2\Delta /m\). In single-electron transistors, Coulomb blockade, however, suppresses the current at low voltage. The required voltage for charge transport increases with the square of the effective charge \(eV\propto \left( me\right) ^2\). Thus, studying the charge transport in all-superconducting single-electron transistors (SSETs) sets these two phenomena into competition. In this article, we present the fabrication as well as a measurement scheme and transport data for a SSET with one junction in which the transmission and thereby the MAR contributions can be continuously tuned. All regimes from weak to strong coupling are addressed. We extend the Orthodox theory by incorporating MAR processes to describe the observed data qualitatively. We detect a new transport process the nature of which is unclear at present. Furthermore, we observe a renormalization of the charging energy when approaching the strong coupling regime.

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Notes

  1. The used parameters are \(E_\mathrm {C}\,={122}\, \upmu \hbox {eV}\), \(\delta C/C_\Sigma =-0.557\), \(C_\mathrm{G}={75}\, \hbox {aF}\), \(\Delta ={190}\, \upmu \hbox {eV}\), \(Q_0/e=0.625\).

  2. Including (M)AR in the master equation simulation of this regime even with very low conductance will cause numerical artefacts affecting the height and width of the J-QP cycle over the TB.

  3. The used parameters are \(E_\mathrm {C}\,={123}\, \upmu \hbox {eV}\), \(\delta C/C_\Sigma =-0.557\), \(C_\mathrm{G}={74}\, \hbox {aF}\), \(\Delta ={190}\, \upmu \hbox {eV}\), \(Q_0=0.425\).

  4. The used parameters are \(E_\mathrm {C}\,={58}\, \upmu \hbox {eV}\), \(\delta CC_\Sigma =0.252\), \(C_\mathrm{G}={75}\, \hbox {aF}\), \(\Delta ={190}\, \upmu \hbox {eV}\), \(Q_0/e=0.002\).

  5. The AR line is not on top of the ridge intentionally. We expect the maximum in the Andreev conduction to be not at the threshold but at slightly higher bias values for high transmissions as seen in point contacts [32]. The harder criterion is in our opinion the beginning of the J-QP cycle at the intersection to the quasiparticle line.

References

  1. K. Likharev, IEEE Trans. Magn. 23, 1142 (1987). https://doi.org/10.1109/TMAG.1987.1065001

    Article  ADS  Google Scholar 

  2. D.V. Averin, K.K. Likharev, J. Low Temp. Phys. 62, 345 (1986). https://doi.org/10.1007/BF00683469

    Article  ADS  Google Scholar 

  3. T.A. Fulton, G.J. Dolan, Phys. Rev. Lett. 59, 109 (1987). https://doi.org/10.1103/PhysRevLett.59.109

    Article  ADS  Google Scholar 

  4. P. Joyez, The Single Cooper Pair Transistor: A Macroscopic Quantum System. Ph.D. Thesis, Université Pierre et Marie Curie-Paris VI (1995)

  5. D. Chouvaev, L.S. Kuzmin, D.S. Golubev, A.D. Zaikin, Phys. Rev. B 59, 10599 (1999). https://doi.org/10.1103/PhysRevB.59.10599

    Article  ADS  Google Scholar 

  6. C. Wallisser, B. Limbach, P. vom Stein, R. Schäfer, in International Workshop on Superconducting Nano-Electronics Devices, ed. by J. Pekola, B. Ruggiero, P. Silvestrini (Springer, Boston, 2002), pp. 123–132. https://doi.org/10.1007/978-1-4615-0737-6_14

    Chapter  Google Scholar 

  7. S. Jezouin, Z. Iftikhar, A. Anthore, F.D. Parmentier, U. Gennser, A. Cavanna, A. Ouerghi, I.P. Levkivskyi, E. Idrisov, E.V. Sukhorukov, L.I. Glazman, F. Pierre, Nature 536, 58 (2016). https://doi.org/10.1038/nature19072

    Article  ADS  Google Scholar 

  8. T.A. Fulton, P.L. Gammel, D.J. Bishop, L.N. Dunkleberger, G.J. Dolan, Phys. Rev. Lett. 63, 1307 (1989). https://doi.org/10.1103/PhysRevLett.63.1307

    Article  ADS  Google Scholar 

  9. P. Hadley, E. Delvigne, E.H. Visscher, S. Lähteenmäki, J.E. Mooij, Phys. Rev. B 58, 15317 (1998). https://doi.org/10.1103/PhysRevB.58.15317

    Article  ADS  Google Scholar 

  10. R.J. Fitzgerald, S.L. Pohlen, M. Tinkham, Phys. Rev. B 57, R11073 (1998). https://doi.org/10.1103/PhysRevB.57.R11073

    Article  ADS  Google Scholar 

  11. T.M. Klapwijk, G.E. Blonder, M. Tinkham, Phys. B 109, 1657 (1982)

    Article  Google Scholar 

  12. M. Octavio, M. Tinkham, G.E. Blonder, T.M. Klapwijk, Phys. Rev. B 27, 6739 (1983). https://doi.org/10.1103/PhysRevB.27.6739

    Article  ADS  Google Scholar 

  13. Y. Avishai, A. Golub, A.D. Zaikin, Europhys. Lett. 54, 640 (2001). https://doi.org/10.1209/epl/i2001-00340-1

    Article  ADS  Google Scholar 

  14. T.M. Eiles, J.M. Martinis, M.H. Devoret, Phys. Rev. Lett. 70, 1862 (1993). https://doi.org/10.1103/PhysRevLett.70.1862

    Article  ADS  Google Scholar 

  15. F.W.J. Hekking, L.I. Glazman, K.A. Matveev, R.I. Shekhter, Phys. Rev. Lett. 70, 4138 (1993). https://doi.org/10.1103/PhysRevLett.70.4138

    Article  ADS  Google Scholar 

  16. M.R. Buitelaar, W. Belzig, T. Nussbaumer, B. Babić, C. Bruder, C. Schönenberger, Phys. Rev. Lett. 91, 057005 (2003). https://doi.org/10.1103/PhysRevLett.91.057005

    Article  ADS  Google Scholar 

  17. J.C. Cuevas, A. Martín-Rodero, A.L. Yeyati, Phys. Rev. B 54, 7366 (1996). https://doi.org/10.1103/PhysRevB.54.7366

  18. V.F. Maisi, O.P. Saira, Y.A. Pashkin, J.S. Tsai, D.V. Averin, J.P. Pekola, Phys. Rev. Lett. 106, 217003 (2011). https://doi.org/10.1103/PhysRevLett.106.217003

    Article  ADS  Google Scholar 

  19. T. Greibe, M.P.V. Stenberg, C.M. Wilson, T. Bauch, V.S. Shumeiko, P. Delsing, Phys. Rev. Lett. 106, 097001 (2011). https://doi.org/10.1103/PhysRevLett.106.097001

    Article  ADS  Google Scholar 

  20. E. Scheer, P. Joyez, D. Esteve, C. Urbina, M.H. Devoret, Phys. Rev. Lett. 78, 3535 (1997). https://doi.org/10.1103/PhysRevLett.78.3535

    Article  ADS  Google Scholar 

  21. C. Schirm, M. Matt, F. Pauly, J.C. Cuevas, P. Nielaba, E. Scheer, Nat. Nanotechnol. 8, 645 (2013). https://doi.org/10.1038/nnano.2013.170

    Article  ADS  Google Scholar 

  22. A.I. Yanson, J.M. van Ruitenbeek, Phys. Rev. Lett. 79, 2157 (1997). https://doi.org/10.1103/PhysRevLett.79.2157

    Article  ADS  Google Scholar 

  23. M. Thalmann, H.-F. Pernau, C. Strunk, E. Scheer, T. Pietsch, Rev. Sci. Instrum. 88, 114703 (2017). https://doi.org/10.1063/1.4995076

  24. Y. Nakamura, C.D. Chen, J.S. Tsai, Phys. Rev. B 53, 8234 (1996). https://doi.org/10.1103/PhysRevB.53.8234

    Article  ADS  Google Scholar 

  25. G. Schön, in Quantum Transport and Dissipation, 1st edn., ed. by T. Dittrich (Wiley-VCH, Weinheim, 1998), p. 149

  26. V.Y. Aleshkini, D.V. Averin, Phys. B 165, 949 (1990). https://doi.org/10.1016/S0921-4526(09)80060-4

    Article  ADS  Google Scholar 

  27. D. Averin, V.Y. Aleshkin, JETP Lett. 50, 9 (1989)

    Google Scholar 

  28. S.L. Pohlen, R.J. Fitzgerald, M. Tinkham, Phys. B 284, 1812 (2000). https://doi.org/10.1016/S0921-4526(99)03027-6

    Article  ADS  Google Scholar 

  29. J. Siewert, Europhys. Lett. 46, 768 (1999). https://doi.org/10.1209/epl/i1999-00121-4

    Article  ADS  Google Scholar 

  30. S. Rajauria, P. Gandit, T. Fournier, F.W.J. Hekking, B. Pannetier, H. Courtois, Phys. Rev. Lett. 100, 207002 (2008). https://doi.org/10.1103/PhysRevLett.100.207002

    Article  ADS  Google Scholar 

  31. S.L. Pohlen, The Superconducting Single-Electron Transistor. Ph.D. Thesis, Harvard University (1999)

  32. J.C. Cuevas, W. Belzig, Phys. Rev. Lett. 91, 187001 (2003). https://doi.org/10.1103/PhysRevLett.91.187001

    Article  ADS  Google Scholar 

  33. J.M. Hergenrother, M.T. Tuominen, T.S. Tighe, M. Tinkham, I.E.E.E. Trans, Appl. Supercond. 3, 1980 (1993). https://doi.org/10.1109/77.233570

    Article  ADS  Google Scholar 

  34. A. Pourkabirian, V. Gustafsson, M.G. Johansson, J. Clarke, P. Delsing, Phys. Rev. Lett. 113, 256801 (2014). https://doi.org/10.1103/PhysRevLett.113.256801

    Article  ADS  Google Scholar 

  35. E.B. Foxman, P.L. McEuen, U. Meirav, N.S. Wingreen, Y. Meir, P.A. Belk, N.R. Belk, M.A. Kastner, S.J. Wind, Phys. Rev. B 47, 10020 (1993). https://doi.org/10.1103/PhysRevB.47.10020

    Article  ADS  Google Scholar 

  36. L.W. Molenkamp, K. Flensberg, M. Kemerink, Phys. Rev. Lett. 75, 4282 (1995). https://doi.org/10.1103/PhysRevLett.75.4282

    Article  ADS  Google Scholar 

  37. D.V. Averin, A.N. Korotkov, A.J. Manninen, J.P. Pekola, Phys. Rev. Lett. 78, 4821 (1997). https://doi.org/10.1103/PhysRevLett.78.4821

    Article  ADS  Google Scholar 

  38. G. Falci, G. Schön, G.T. Zimanyi, Phys. Rev. Lett. 74, 3257 (1995). https://doi.org/10.1103/PhysRevLett.74.3257

    Article  ADS  Google Scholar 

  39. K. Flensberg, Phys. Rev. B 48, 11156 (1993). https://doi.org/10.1103/PhysRevB.48.11156

    Article  ADS  Google Scholar 

  40. K. Flensberg, Phys. B 203, 432 (1994). https://doi.org/10.1016/0921-4526(94)90092-2

    Article  ADS  Google Scholar 

  41. Y.V. Nazarov, Phys. Rev. Lett. 82, 1245 (1999). https://doi.org/10.1103/PhysRevLett.82.1245

    Article  ADS  Google Scholar 

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Acknowledgements

The authors like to thank Jens Siewert and Wolfgang Belzig for useful discussion. We also thank Olivier Schecker, Ursula Schröter, and Paramita Kar Choudhury for their contributions in the early state of the project.

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  1. Department of Physics, University of Konstanz, Universitätsstr. 10, 78464, Konstanz, Germany

    Thomas Lorenz, Susanne Sprenger & Elke Scheer

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Correspondence to Thomas Lorenz.

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Lorenz, T., Sprenger, S. & Scheer, E. Coulomb Blockade and Multiple Andreev Reflection in a Superconducting Single-Electron Transistor. J Low Temp Phys 191, 301–315 (2018). https://doi.org/10.1007/s10909-017-1837-4

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