The Problem Of True Macroscopic Charge Quantization In The Coulomb Blockade

  • I. S. BurmistrovEmail author
  • A. M. M. Pruisken
Conference paper
Part of the NATO Science for Peace and Security Series B: Physics and Biophysics book series (NAPSB)

Based on the Ambegaokar-Eckern-Schön approach to the Coulomb blockade we develop a complete quantum theory of the single electron transistor. We identify a previously unrecognized physical observable in the problem that, unlike the usual average charge on the island, is robustly quantized for any finite value of the tunneling conductance as the temperature goes to the absolute zero. This novel quantity is fundamentally related to the non-symmetrized current noise of the system. Our results display all the super universal topological features of the θ-angle concept that previously arose in the theory of the quantum Hall effect.


Coulomb blockade charge quantization 


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  1. 1.
    V. Ambegaokar, U. Eckern, and G. Schön, Phys. Rev. Lett. 48, 1745 (1982)CrossRefADSGoogle Scholar
  2. 2.
    G. Schön and A.D. Zaikin, Phys. Rep. 198, 237 (1990)CrossRefADSGoogle Scholar
  3. 3.
    H. Grabert, M. Devoret. Single Charge Tunneling, ed. by H. Grabert and M.H. Devoret (Plenum, New York, 1992)Google Scholar
  4. 4.
    H. Grabert and H. Horner (eds.), Z. Phys. B 85, 317 (1991)CrossRefADSGoogle Scholar
  5. 5.
    L.I. Glazman and M. Pustilnik in: New Directions in Mesoscopic Physics Towards to Nanoscience, ed. by R. Fazio, G.F. Gantmakher and Y. Imry (Kluwer, Dordrecht, 2003)Google Scholar
  6. 6.
    P. Lafarge, H. Pothier, E.R. Williams, D. Esteve, C. Urbina, and M.H. Devoret, Z. Phys. B 85, 327 (1991)CrossRefADSGoogle Scholar
  7. 7.
    T.A. Fulton and G.J. Dolan, Phys. Rev. Lett. 59, 109 (1987)CrossRefADSGoogle Scholar
  8. 8.
    G. Falci, G. Schon, and G. Zimanyi, Phys. Rev. Lett. 74, 3257 (1995); Physica B 203, 409 (1994)CrossRefADSGoogle Scholar
  9. 9.
    I.S. Beloborodov, K.B. Efetov, A. Altland, and F.W.J. Hekking, Phys. Rev. B 63, 115109 (2001); K.B. Efetov, and A. Tschersich, Phys. Rev. B 67, 174205 (2003)CrossRefADSGoogle Scholar
  10. 10.
    H. Schoeller and G. Schön, Phys. Rev. B 50, 18436 (1994)CrossRefADSGoogle Scholar
  11. 11.
    A. Altland, L.I. Glazman, A. Kamenev, and J.S. Meyer, Ann. Phys. (N.Y.) 321, 2566 (2006)zbMATHCrossRefADSGoogle Scholar
  12. 12.
    K.A. Matveev, Sov. Phys. JETP 72, 892 (1991)Google Scholar
  13. 13.
    A.M.M. Pruisken and I.S. Burmistrov, Ann. of Phys. 316, 285 (2005)zbMATHCrossRefADSMathSciNetGoogle Scholar
  14. 14.
    R. Rajaraman, Instantons and solitons, (Amsterdam, North-Holland, 1982); A.M. Polyakov, Gauge fields and strings, (Harwood Academic Publishers, Shur, 1987)zbMATHGoogle Scholar
  15. 15.
    I.S. Burmistrov, and A.M.M. Pruisken, arXiv: cond-mat/0702400Google Scholar
  16. 16.
    S.E. Korshunov, JETP Lett. 45, 434 (1987)ADSMathSciNetGoogle Scholar
  17. 17.
    S.A. Bulgadaev, Phys. Lett. A 125, 299 (1987)CrossRefADSGoogle Scholar
  18. 18.
    I.S. Burmistrov, and A.M.M. Pruisken, in preparationGoogle Scholar
  19. 19.
    E. Ben-Jacob, E. Mottola, and G. Schön, Phys. Rev. Lett. 51, 2064 (1983)CrossRefADSGoogle Scholar
  20. 20.
    C. Wallisser, B. Limbach, P. vom Stein, R. Schäfer, C. Theis, G. Göppert, and H. Grabert, Phys. Rev. B 66, 125314 (2002)CrossRefADSGoogle Scholar
  21. 21.
    F. Guinea and G. Schön, Europhys. Lett. 1, 585 (1986)CrossRefADSGoogle Scholar
  22. 22.
    S.A. Bulgadaev, JETP Lett. 45, 622 (1987)ADSGoogle Scholar
  23. 23.
    W. Hofstetter and W. Zwerger, Phys. Rev. Lett. 78, 3737 (1997)CrossRefADSGoogle Scholar
  24. 24.
    I.S. Beloborodov, A.V. Andreev, and A.I. Larkin, Phys. Rev. B 68, 024204 (2003)CrossRefADSGoogle Scholar
  25. 25.
    S.V. Panyukov and A.D. Zaikin, Phys. Rev. Lett. 67, 3168 (1991)CrossRefADSGoogle Scholar
  26. 26.
    X. Wang and H. Grabert, Phys. Rev. B 53, 12621 (1996)CrossRefADSGoogle Scholar
  27. 27.
    D.E. Khmelniskii, Phys. Lett. A 106, 182 (1984)CrossRefADSGoogle Scholar
  28. 28.
    A.D. Mirlin, D.G. Polyakov, and P. Wölfe, Phys. Rev. Lett. 80, 2429 (1998); F. Evers, A.D. Mirlin, D.G. Polyakov, and P. Wölfe, Phys. Rev. B 60, 8951 (1999)CrossRefADSGoogle Scholar
  29. 29.
    A.M.M. Pruisken and I.S. Burmistrov, Phys. Rev. Lett. 95, 189701 (2005)CrossRefADSGoogle Scholar
  30. 30.
    S.S. Murzin, A.G.M. Jansen, and I. Claus, Phys. Rev. Lett. 92, 016802 (2004); S.S. Murzin and A.G.M. Jansen, Phys. Rev. Lett. 95, 189702 (2005)CrossRefADSGoogle Scholar
  31. 31.
    A.A. Abrikosov, Physics 2, 21 (1965)Google Scholar
  32. 32.
    see, e.g., Yu.A. Izyumov and Yu. N. Skryabin, Statistical mechanics of magneto-ordered systems, (Moskva, Nauka, 1987) (in Russian)Google Scholar
  33. 33.
    A.I. Larkin and V.I. Melnikov, Sov. Phys. JETP 34, 656 (1972)ADSGoogle Scholar
  34. 34.
    L. Zhu and Q. Si, Phys. Rev. B 66, 024426 (2002); G. Zaránd and E. Demler, Phys. Rev. B 66, 024427 (2002)CrossRefADSGoogle Scholar
  35. 35.
    G. Gröppert, H. Grabert, Eur. Phys. J. B 16, 687 (2000)CrossRefADSGoogle Scholar
  36. 36.
    A.M.M. Pruisken, I.S. Burmistrov and R. Shankar, cond-mat/0602653 (unpublished)Google Scholar
  37. 37.
    A.M.M. Pruisken, R. Shankar and N. Surendran, Phys. Rev. B 72, 035329 (2005)CrossRefADSGoogle Scholar

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© Springer Science + Business Media B.V 2008

Authors and Affiliations

  1. 1.L.D. Landau Institute for Theoretical PhysicsMoscowRussia
  2. 2.Institute for Theoretical PhysicsUniversity of AmsterdamAmsterdamThe Netherlands

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