, Volume 64, Issue 6, pp 1039–1049 | Cite as

Keldysh proximity action for disordered superconductors

  • M V Feigel’man
  • A I Larkin
  • M A Skvortsov


We review a novel approach to the superconductive proximity effect in disordered normal-superconducting (N-S) structures. The method is based on the multicharge Keldysh action and is suitable for the treatment of interaction and fluctuation effects. As an application of the formalism, we study the subgap conductance and noise in two-dimensional N-S systems in the presence of the electron-electron interaction in the Cooper channel. It is shown that singular nature of the interaction correction at large scales leads to a nonmonotonuos temperature, voltage and magnetic field dependence of the Andreev conductance.


Superconductivity nanostructures noise 


74.45.+c 74.78.Na 73.50.Bk 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    A F Andreev,Zh. Eksp. Teor. Fiz. 46, 1823 (1964) [Sov. Phys. JETP 19, 1228 (1964)]Google Scholar
  2. [2]
    A F Volkov, A V Zaitsev and T M Klapwijk,Physica C210, 21 (1993)ADSGoogle Scholar
  3. [3]
    Yu V Nazarov,Phys. Rev. Lett. 73, 134 (1994)CrossRefADSGoogle Scholar
  4. [4]
    Yu V Nazarov,Phys. Rev. Lett. 73, 1420 (1994)CrossRefADSGoogle Scholar
  5. [5]
    C W J Beenakker,Rev. Mod. Phys. 69, 731 (1997)CrossRefADSGoogle Scholar
  6. [6]
    B Pannetier and H Courtois, cond-mat/9912024Google Scholar
  7. [7]
    A I Larkin and Yu N Ovchinnikov, inNonequilibrium superconductivity edited by D N Langenberg and A I Larkin (Elsevier, New York, 1986)Google Scholar
  8. [8a]
    C J Lambert,J. Phys. Condens. Matter 3, 6579 (1991)CrossRefADSGoogle Scholar
  9. [8b]
    C W J Beenakker,Phys. Rev. B46, 12841 (1992)ADSGoogle Scholar
  10. [9]
    B L Altshuler and A G Aronov, inElectron-electron interactions in disordered conductors edited by A J Efros and M Pollack (Elsevier Science Publishers, North-Holland, 1985)Google Scholar
  11. [10]
    F Zhou, B Z Spivak and A Yu Zyuzin,Phys. Rev. B52, 4467 (1995)ADSGoogle Scholar
  12. [11]
    T H Stoof and Yu V Nazarov,Phys. Rev. B53, 14496 (1996)ADSGoogle Scholar
  13. [12]
    M A Skvortsov, A I Larkin and M V Feigel’man,Phys. Rev. B63, 134507 (2001)ADSGoogle Scholar
  14. [13]
    M V Feigel’man, A I Larkin and M A Skvortsov,Phys. Rev. B61, 12361 (2000)ADSGoogle Scholar
  15. [14]
    L S Levitov and G B Lesovik,Pis’ma Zh. Eksp. Teor. Phys. 58, 225 (1993) [JETP Lett. 58, 230 (1993)]Google Scholar
  16. [15]
    H Lee, L S Levitov and A Yu Yakovets, Phys. Rev.B51, 4079 (1995)ADSCrossRefGoogle Scholar
  17. [16]
    A M Finkelstein,Pis’ma ZhETF 45, 37 (1987) [JETP Lett. 45, 46 (1987)]ADSGoogle Scholar
  18. [17]
    A M Finkelstein,Physica B197, 636 (1994)ADSGoogle Scholar
  19. [18]
    A M Finkelstein, Electron liquid in disordered conductors, inSoviet scientific reviews, edited by I M Khalatnikov (Harwood Academic Publishers, London, 1990) Vol. 14Google Scholar
  20. [19]
    M V Feigel’man, A I Larkin and M A Skvortsov,Phys. Rev. Lett. 86, 1869 (2001)CrossRefADSGoogle Scholar
  21. [20]
    C W J Beenakker, B Rejaei and J A Melsen,Phys. Rev. Lett. 72, 2470 (1994)CrossRefADSGoogle Scholar
  22. [21]
    M V Feigel’man, A I Larkin and M A Skvortsov, cond-mat/0010402Google Scholar
  23. [22]
    Ya M Blanter and M Büttiker, Phys. Rep.336, 1 (2000)CrossRefADSGoogle Scholar
  24. [23]
    Yu V Nazarov, inQuantum dynamics of submicron structures edited by H Cerdeira, B Kramer and G Schoen (Kluwer, 1995), cond-mat/9410011Google Scholar
  25. [24]
    S N Artemenko, A F Volkov and A V Zaitsev,Solid State Commun. 30, 771 (1995)CrossRefGoogle Scholar
  26. [25]
    M J M de Jong and C W J Beenakker,Phys. Rev. B49, 16070 (1994)ADSGoogle Scholar
  27. [26a]
    C W J Beenakker and M Büttiker,Phys. Rev. B46, 1889 (1992)ADSGoogle Scholar
  28. [26b]
    K E Nagaev,Phys. Lett. A169, 103 (1992)ADSGoogle Scholar

Copyright information

© Indian Academy of Sciences 2005

Authors and Affiliations

  • M V Feigel’man
    • 1
  • A I Larkin
    • 1
  • M A Skvortsov
    • 1
  1. 1.L. D. Landau Institute for Theoretical PhysicsMoscowRussia

Personalised recommendations