Skip to main content
SpringerLink
Log in

Tunable Josephson supercurrent through a two level quantum dot superconductor tunnel junction

  • Published:
Journal of Computational Electronics Aims and scope Submit manuscript

Abstract

The present paper deals with the study of Josephson supercurrent across a two level quantum dot (QD) sandwiched between the s-wave superconductors. The renormalized Anderson model used that includes the contribution towards attractive BCS type effective interaction in the superconducting leads responsible for s-wave pairing, electron tunneling energy term representing coupling of superconducting leads with the dot energy levels responsible for Josephson Cooper pair tunneling between two superconductors. The Green’s function meanfield technique is employed within the framework of Ambegaokar–Baratoff approach to analyze the Josephson supercurrent across such a junction. It is pointed out that the Josephson supercurrent is suppressed when additional QD level(s) are switched on.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Reed, M.A.: Quantum dots. Sci. Am. 268, 98–103 (1993)

    Article  Google Scholar 

  2. Kouwenhoven, L.P., Austing, D.G., Tarucha, S.: Few-electron quantum dots. Rep. Prog. Phys. 64, 701 (2001)

    Article  Google Scholar 

  3. Takesue, I., Haruyama, J., Kobayashi, N., Chiashi, S., Maruyama, S., Sugai, T., Shinohara, H.: Superconductivity in entirely end-bonded multiwalled carbon nanotubes. Phys. Rev. Lett. 96, 057001 (2006)

    Article  Google Scholar 

  4. Levy Yeyati, A., Cuevas, J.C., López-Dávalos, A., Martín-Rodero, A.: Resonant tunneling through a small quantum dot coupled to superconducting leads. Phys. Rev. B 55, R6137(R) (1997)

    Article  Google Scholar 

  5. Dhyani, A., Tewari, B.S., Ajay, : Interplay of the single particle and Josephson Cooper pair tunneling on supercurrent across the superconducting quantum dot junction. Phys. E 41, 1179–1183 (2009)

    Article  Google Scholar 

  6. Dhyani, A., Tewari, B.S., Ajay, : Study of the Josephson supercurrent through nanoscopic superconducting–quantum dot tunnel junction. Phys. E 42, 162–166 (2009)

    Article  Google Scholar 

  7. Quay, C.H.L., Cumings, J., Gamble, S.J., de Picciotto, R., Kataura, H., Goldhaber- Gordon, D.: Magnetic field dependence of the spin-12 and spin-1 Kondo effects in a quantum dot. Phys. Rev. B 76, 245311 (2007)

    Article  Google Scholar 

  8. Roch, N., Florens, S., Bouchiat, V., Wernsdorfer, W., Balestro, F.: Quantum phase transition in a single-molecule quantum dot. Nature 453, 633–637 (2008)

    Article  Google Scholar 

  9. Jørgensen, H.I., Novotny, T., Grove-Rasmussen, K., Flensberg, K., Lindel, P.E.: Critical current 0-p transition in Josephson quantum dot junction. Nano Lett. 7, 2441 (2007)

    Article  Google Scholar 

  10. van Dam, J.A., Nazarov, Y.V., Bakkers, E.P.A.M., De Franceschi, S., Kouwenhoven, L.P.: Supercurrent reversal in quantum dots. Nature 442, 667 (2006)

    Article  Google Scholar 

  11. Pala, M.G., Governale, M., König, J.: Nonequilibrium Josephson and Andreev current through interacting quantum dots. N. J. Phys. 9, 278 (2007)

    Article  Google Scholar 

  12. Li, W., Zhu, Y., Lin, T-h: Analytical result on the supercurrent through a superconductor/quantum-dot/superconductor junction. Commun. Theo. Phys. 38, 103–106 (2002)

    Article  Google Scholar 

  13. Avishai, Y., Golub, A., Zaikin, A.D.: Superconductor–quantum dot–superconductor junction in the Kondo regime. Phys. Rev. B 67, 041301(R) (2003)

    Article  Google Scholar 

  14. Glazman, L.I., Matveev, K.A.: Resonant Josephson current through Kondo impurities in a tunnel barrier. JETP Lett. 49, 659–662 (1989)

    Google Scholar 

  15. Spivak, B.I., Kivelson, S.A.: Negative local superfluid densities: the difference between dirty superconductors and dirty Bose liquids. Phys. Rev. B 43, 3740–3743 (1991)

    Article  Google Scholar 

  16. Rozhokov, A.V., Arovas, D.P., Guinea, F.: Josephson coupling through a quantum dot. Phys. Rev. B 64, 233301 (2001)

    Article  Google Scholar 

  17. Tanaka, Y., Kawakami, N., Oguri, A.: Numerical renormalization group approach to a quantum dot coupled to normal and superconducting leads. J. Phys. Soc. Jpn. 76, 074701 (2007)

    Article  Google Scholar 

  18. Oguri, A., Tanaka, Y., Hewson, A.C.: Quantum phase transition in a minimal model for the Kondo effect in a Josephson Junction. J. Phys. Soc. Jpn. 73, 2494–2504 (2004)

    Article  MATH  Google Scholar 

  19. Karrasch, C., Oguri, A., Meden, V.: Josephson current through a single Anderson impurity coupled to BCS leads. Phys. Rev. B 9, 024517 (2008)

    Article  Google Scholar 

  20. Bauer, J., Oguri, A., Hewson, A.C.: Spectral properties of locally correlated electrons in a Bardeen–Cooper–Schrieffer superconductor. J. Phys. 19, 486211 (2007)

    Google Scholar 

  21. Avishai, Y., Golub, A.: Josephson current in unconventional superconductors through an Anderson impurity. Phys. Rev. B 61, 11293 (2000)

    Article  Google Scholar 

  22. Golubov, A.A., Kupriyanov, M.Y., ll’Ichev, E.: The current–phase relation in Josephson junctions. Rev. Mod. Phys. 76, 411 (2004)

    Article  Google Scholar 

  23. Tanaka, Y., Kashiwaya, S.: Theory of Josephson effects in anisotropic superconductors. Phys. Rev. B. 56, 892 (1997)

    Article  Google Scholar 

  24. Ralph, D.C., Black, C.T., Tinkham, M.: Spectroscopic measurements of discrete electronic states in single metal particles. Phys. Rev. Lett. 74, 3241 (1995)

    Article  Google Scholar 

  25. Pan, H., Lin, T.-H.: Spin-flip effects on the supercurrent through mesoscopic superconducting junctions. J. Phys. 17, 5207–5214 (2005)

  26. Torre’s, J., Martin, T.: Positive and negative Hanbury–Brown and Twiss correlations in normal metal-superconducting devices. Eur. Phys. J. B. 12, 319–322 (1999)

    Article  Google Scholar 

  27. Deutscher, G., Feinberg, D.: Coupling superconducting-ferromagnetic point contacts by Andreev reflections. Appl. Phys. Lett. 76, 487 (2000)

    Article  Google Scholar 

  28. Dell’ Anne, L., Zazunov, A., Egger, R., Martin, T.: Josephson current through a quantum dot with spin-orbit coupling. Phys. Rev. B 75, 085305 (2007)

    Article  Google Scholar 

  29. Brunetti, A., Zazunov, A., Kundu, A., Egger, R.: Anomalous Josephson current, incipient time-reversal symmetry breaking, and Majorana bound states in interacting multilevel dots. Phys. Rev. B 88, 144515 (2013)

    Article  Google Scholar 

  30. Ambegaokar, V., Baratoff, A.: Tunneling between superconductors. Phys. Rev. Lett. 10, 486 (1963)

    Article  Google Scholar 

  31. Singh, M.P., Ajay, Gupta, B.R.K.: Temperature dependence of the supercurrent density in bilayer cuprate superconductors. Phys. C 383, 388–394 (2003)

    Article  Google Scholar 

  32. Zubarev, D.N.: Double-time green function in statistical physics. Sov. Phys. Usp. 3, 320–345 (1960)

    Article  MathSciNet  Google Scholar 

  33. Domański, T., Donabidowicz, A., Wysokiński, K.I.: Influence of pair coherence on charge tunneling through a quantum dot connected to a superconducting lead. Phys. Rev. B 76, 104514 (2007)

    Article  Google Scholar 

  34. Payette, C., et al.: Coherent three-level mixing in an electronic quantum dot. Phys. Rev. Lett. 102, 026808 (2009)

    Article  Google Scholar 

  35. Reimann, S.M., Manninen, M.: Electronic structure of quantum dots. Rev. Mod. Phys. 74, 1283 (2002)

    Article  Google Scholar 

  36. Nilsson, H.A., Karlström, O., Larsson, M., Caroff, P., Pedersen, J.N., Samuelson, L., Wacker, A., Wernersson, L.-E., Xu, H.Q.: Correlation-induced conductance suppression at level degeneracy in a quantum dot. Phys. Rev. Lett. 104, 186804 (2010)

    Article  Google Scholar 

  37. Pototzky, K.J., Gross, E.K.U.: How to interpret the spectral density of the Keldysh nonequilibrium Green’s function. arXiv:1405.5984v1[cond-mat.mes-hall] (23 May 2014)

  38. Lee, W.-C., Park, W. K., Arham, H. Z.: Theory of point contact spectroscopy in correlated materials. arXiv:1405.6357v1 [cond-mat.mes-hall] 25 May 2014

Download references

Author information

Authors and Affiliations

  1. Department of Physics, College of Engineering, University of Petroleum and Energy Studies (UPES), Energy Acres, VPO Bidholi, PO Prem Nagar, Dehradun, 248007, Uttarakhand, India

    A. Dhyani & B. S. Tewari

  2. Department of Applied Science and Engineering, Indian Institute of Technology Roorkee, Saharanpur Campus, Saharanpur, 247001, U.P., India

    Rajendra Kumar &  Ajay

Authors
  1. A. Dhyani
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rajendra Kumar
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. B. S. Tewari
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ajay
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to B. S. Tewari.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dhyani, A., Kumar, R., Tewari, B.S. et al. Tunable Josephson supercurrent through a two level quantum dot superconductor tunnel junction. J Comput Electron 14, 139–145 (2015). https://doi.org/10.1007/s10825-014-0631-7

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10825-014-0631-7

Keywords

Search

Navigation