Advances in Solid State Physics pp 163-173

Part of the Advances in Solid State Physics book series (ASSP, volume 42) | Cite as

Full Counting Statistics of Mesoscopic Electron Transport

  • Wolfgang Belzig
Chapter

Abstract

Full Counting Statistics is the theory of quantum statistical properties of transport phenomena. It can be accessed by a modification of the standard Keldysh-Green’s function technique, and is concisely formulated in terms of a circuit theory of mesoscopic electron transport. We summarize the basics of the theoretical methods and discuss two examples: a single-channel quantum contact and a double tunnel junction. For both examples we compare the transport statistics for the cases of normal electrons and Andreev reflection.

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References

  1. 1.
    Ya. M. Blanter and M. Büttiker, Phys. Rep. 336, 1 (2000).CrossRefGoogle Scholar
  2. 2.
    X. Jehl et al., Phys. Rev. Lett. 83, 1660 (1999); X. Jehl et al., Nature 405, 50 (2000); A. A. Kozhevnikov, R. J. Schoelkopf, and D. E. Prober, Phys. Rev. Lett 83, 1660 (2000); P. Dieleman et al.; Phys. Rev. Lett. 79, 3486 (1997); T. Hoss et al., Phys. Rev. B 62, 4079 (2000).CrossRefGoogle Scholar
  3. 3.
    L. S. Levitov and G. B. Lesovik, JETP Lett. 58, 230 (1993).Google Scholar
  4. 4.
    L. S. Levitov, H. W. Lee, and G. B. Lesovik, J. Math. Phys. 37, 4845 (1996).CrossRefGoogle Scholar
  5. 5.
    H. Lee, L. S. Levitov, and A. Yu. Yakovets, Phys. Rev. B 51, 4079 (1996).CrossRefGoogle Scholar
  6. 6.
    Yu. V. Nazarov, Ann. Phys. (Leipzig) 8, SI-193 (1999).Google Scholar
  7. 7.
    W. Belzig and Yu. V. Nazarov, Phys. Rev. Lett. 87, 067006 (2001).CrossRefGoogle Scholar
  8. 8.
    W. Belzig and Yu. V. Nazarov, Phys. Rev. Lett. 87, 197006 (2001).CrossRefGoogle Scholar
  9. 9.
    J. Rammer and H. Smith, Rev. Mod. Phys. 58, 323 (1986).CrossRefGoogle Scholar
  10. 10.
    Yu. V. Nazarov and M. Kindermann, cond-mat/0107133.Google Scholar
  11. 11.
    G. Eilenberger, Z. Phys. 214, 195 (1968); A. I. Larkin and Yu. N. Ovchinnikov, Sov. Phys. JETP 26, 1200(1968); K. D. Usadel, Phys. Rev. Lett. 25, 507 (1970).CrossRefGoogle Scholar
  12. 12.
    Yu. V. Nazarov, Phys. Rev. Lett. 73, 134 (1994).CrossRefGoogle Scholar
  13. 13.
    Yu. V. Nazarov, Superlattices Microst. 25, 1221 (1999).CrossRefGoogle Scholar
  14. 14.
    Yu. V. Nazarov and D. Bagrets, cond-mat/0112223.Google Scholar
  15. 15.
    J. Börlin, W. Belzig, and C. Bruder, cond-mat/0201579.Google Scholar
  16. 16.
    B. A. Muzykantskii and D. E. Khmelnitskii, Phys. Rev. B 50, 3982 (1994).CrossRefGoogle Scholar
  17. 17.
    V. A. Khlus, Sov. Phys. JETP 66, 1243 (1987); M. J. M. de Jong and C. W. J. Beenakker, Phys. Rev. B 49, 16070 (1994); K. E. Nagaev and M. Büttiker, ibid. 63, 081301 (R) (2001).Google Scholar
  18. 18.
    J. Börlin, Diploma thesis (University of Basel), 2002).Google Scholar
  19. 19.
    M. J. M. de Jong, Phys. Rev. B 54, 8144 (1996).CrossRefGoogle Scholar
  20. 20.
    F. Taddei and R. Fazio, Phys. Rev. B 65, 075317 (2002).CrossRefGoogle Scholar
  21. 21.
    A. Andreev and A. Kamenev, Phys. Rev. Lett. 85, 1294 (2000); Yu. Makhlin and A. Mirlin, ibid. 87, 276803 (2001); L. S. Levitov, cond-mat/0103617. 172CrossRefGoogle Scholar
  22. 22.
    C. W. J. Beenakker and H. Schomerus, Phys. Rev. Lett. 86, 700 (2001).CrossRefGoogle Scholar
  23. 23.
    M. Kindermann, Yu. V. Nazarov, and C. W. J. Beenakker, Phys. Rev. Lett. 88, 063601 (2002).CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Wolfgang Belzig
    • 1
  1. 1.Departement für Physik und AstronomieUniversität BaselBaselSwitzerland

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