Counting Statistics of Single-Electron Transport

Part of the Lecture Notes in Physics book series (LNP, volume 911)

Abstract

Single-electron counting is a sensitive quantum measurement that allows the detection of individual electron flow in real time. The apparatus required for such measurements can be prepared using a fast charge sensor attached to a quantum dot. The scheme allows us to measure extremely small currents of the order of attoamperes with single-electron resolution and evaluate the statistical characteristics of the transport. A bidirectional counting scheme with a double quantum dot enables measurements in linear as well as nonlinear transport regimes, where both forward and backward transport processes are essential. Various statistical analyses, such as frequency spectrum, time-correlation, and full counting statistics, have been developed to characterize current fluctuations and understand correlated electron transport in nanostructures.

Keywords

Counting statistics Higher-order moments Quantum dots Single-electron transport Anti-bunching 

Notes

Acknowledgements

We thank J. C. H. Chen, M. Hashisaka, T. Hayashi, Y. Hirayama, K. Muraki, Y. Tokura, R. Tomita, M. Ueki, N. Watase, and M. Yamagushi for valuable discussions and supports. This work was supported by FIRST “Quantum Information Processing” project, JSPS Grants-in-Aid for Scientific Research (KAKENHI) Grant Numbers 21000004 and 26247051, and GCOE project “Nanoscience and Quantum Physics” at Tokyo Institute of Technology.

References

  1. 1.
    Yu.V. Nazarov, Y.M. Blanter, Quantum Transport: Introduction to Nanoscience (Cambridge University Press, Cambridge/New York, 2009)CrossRefGoogle Scholar
  2. 2.
    H. Grabert, M.H. Devoret (eds.), Single Charge Tunneling, Coulomb Blockade Phenomena in Nanostuctures. NATO ASI Series B, vol. 0294, (Plenum Press, New York, 1991)Google Scholar
  3. 3.
    Yu.V. Nazarov (ed.), Quantum Noise in Mesoscopic Physics. NATO Science Series II, vol. 97 (Kluwer, Dordrecht, 2003)Google Scholar
  4. 4.
    Ya.M. Blanter, M. Büttiker, Phys. Rep. 336, 1 (2000)Google Scholar
  5. 5.
    P. Dutta, P.M. Horn, Rev. Mod. Phys. 53, 497 (1981)ADSCrossRefGoogle Scholar
  6. 6.
    M.J. Kirton, M.J. Uren, Adv. Phys. 38, 367 (1989)ADSCrossRefGoogle Scholar
  7. 7.
    H. Birk, M.J.M. de Jong, C. Schönenberger, Phys. Rev. Lett. 75, 1610 (1995)ADSCrossRefGoogle Scholar
  8. 8.
    L. Saminadayar, D.C. Glattli, Y. Jin, B. Etienne, Phys. Rev. Lett. 79, 2526 (1997)ADSCrossRefGoogle Scholar
  9. 9.
    R. de-Picciotto, M. Reznikov, M. Heiblum, V. Umansky, G. Bunin, D. Mahalu, Nature 389, 162 (1997)Google Scholar
  10. 10.
    R. Loudon, The Quantum Theory of Light (Oxford University Press, New York, 1973)Google Scholar
  11. 11.
    Yu. Bomze, G. Gershon, D. Shovkun, L.S. Levitov, M. Reznikov, Phys. Rev. Lett. 95, 176601 (2005)ADSCrossRefGoogle Scholar
  12. 12.
    G. Gershon, Y. Bomze, E.V. Sukhorukov, M. Reznikov, Phys. Rev. Lett. 101, 016803 (2008)ADSCrossRefGoogle Scholar
  13. 13.
    B. Reulet, J. Senzier, D.E. Prober, Phys. Rev. Lett. 91, 196601 (2003)ADSCrossRefGoogle Scholar
  14. 14.
    J. Gabelli, B. Reulet, J. Stat. Mech. 2009, P01049 (2009)CrossRefGoogle Scholar
  15. 15.
    C.W.J. Beenakker, M. Kindermann, Yu.V. Nazarov, Phys. Rev. Lett. 90, 176802 (2003)ADSCrossRefGoogle Scholar
  16. 16.
    T. Fujisawa, T. Hayashi, Y. Hirayama, H.D. Cheong, Y.H. Jeong, Appl. Phys. Lett. 84, 2343 (2004)ADSCrossRefGoogle Scholar
  17. 17.
    W. Lu, Z. Ji, L. Pfeiffer, K.W. West, A.J. Rimberg, Nature 423, 422 (2003)ADSCrossRefGoogle Scholar
  18. 18.
    J. Bylander, T. Duty, P. Delsing, Nature 434, 361 (2005)ADSCrossRefGoogle Scholar
  19. 19.
    S. Gustavsson, R. Leturcq, B. Simoviv, R. Schleser, T. Ihn, P. Studerus, K. Ensslin D.C. Driscoll, A.C. Gossard, Phys. Rev. Lett. 96, 076605 (2006)ADSCrossRefGoogle Scholar
  20. 20.
    S. Gustavsson, R. Leturcq, M. Studer, I. Shorubalko, T. Ihn, K. Ensslin, D.C. Driscoll, A.C. Gossard, Surf. Sci. Rep. 64, 191 (2009)ADSCrossRefGoogle Scholar
  21. 21.
    T. Fujisawa, T. Hayashi, R. Tomita, Y. Hirayama, Science 312, 1634 (2006)ADSCrossRefGoogle Scholar
  22. 22.
    M. Field, C.G. Smith, M. Pepper, D.A. Ritchie, J.E.F. Frost, G.A.C. Jones, D.G. Hasko, Phys. Rev. Lett. 70, 1311 (1993)ADSCrossRefGoogle Scholar
  23. 23.
    R.J. Schoelkopf, P. Wahlgren, A.A. Kozhevnikov, P. Delsing, D.E. Prober, Science 280, 1238 (1998)ADSCrossRefGoogle Scholar
  24. 24.
    I.T. Vink, T. Nooitgedagt, R.N. Schouten, L.M.K. Vandersypen, W. Wegscheider, Appl. Phys. Lett. 91, 123512 (2007)ADSCrossRefGoogle Scholar
  25. 25.
    G. Shinkai, T. Hayashi, T. Ota, T. Fujisawa, Phys. Rev. Lett. 103, 056802 (2009)ADSCrossRefGoogle Scholar
  26. 26.
    B.J. van Wees, H. van Houten, C.W.J. Beenakker, J.G. Williamson, L.P. Kouwenhoven, D. van der Marel, C.T. Foxon, Phys. Rev. Lett. 60 (1988) 848ADSCrossRefGoogle Scholar
  27. 27.
    N. Watase, M. Hashisaka, K. Muraki, T. Fujisawa, Jpn. J. Appl. Phys. 53, 04EJ01 (2014)Google Scholar
  28. 28.
    O. Naaman, J. Aumentado, Phys. Rev. Lett. 96, 100201 (2006)ADSCrossRefGoogle Scholar
  29. 29.
    O. Naaman, J. Aumentado, Phys. Rev. B 73, 172504 (2006)ADSCrossRefGoogle Scholar
  30. 30.
    O.H. Schmitt, J. Sci. Instr. 15, 24 (1938)ADSCrossRefGoogle Scholar
  31. 31.
    N.G. van Kampen, Stochastic Processes in Physics and Chemistry (Elsevier, Amsterdam, 1992)Google Scholar
  32. 32.
    M. Yamagishi, N. Watase, M. Hashisaka, K. Muraki, T. Fujisawa, Phys. Rev. B 90, 035306 (2014)ADSCrossRefGoogle Scholar
  33. 33.
    R. Hanson, B. Witkamp, L.M.K. Vandersypen, L.H.W. van Beveren, J.M. Elzerman, L.P. Kouwenhoven, Phys. Rev. Lett. 91, 196802 (2003)ADSCrossRefGoogle Scholar
  34. 34.
    R. Hanson, L.M.K. Vander-sypen, L.H.W. van Beveren, J.M. Elzerman, I.T. Vink, L.P. Kouwenhoven, Phys. Rev. B 70, 241304 (2004)ADSCrossRefGoogle Scholar
  35. 35.
    B. Jouault, M. Gryglas, M. Baj, A. Cavanna, U. Gennser, G. Faini, D.K. Maude, Phys. Rev. B 79, 041307 (2009)ADSCrossRefGoogle Scholar
  36. 36.
    T. Fujisawa, T. Hayashi, S. Sasaki, Rep. Prog. Phys. 69, 759 (2006)ADSCrossRefGoogle Scholar
  37. 37.
    S. Amasha, K. MacLean, I.P. Radu, D.M. Zumbühl, M.A. Kastner, M.P. Hanson, A.C. Gossard, Phys. Rev. B 78, 041306 (2008)ADSCrossRefGoogle Scholar
  38. 38.
    M.G. House, M. Xiao, G. Guo, H. Li, G. Cao, M.M. Rosenthal, H. Jiang, Phys. Rev. Lett. 111, 126803 (2013)ADSCrossRefGoogle Scholar
  39. 39.
    C.-K. Wang, K.F. Berggren, Phys. Rev. B 54, R14257 (1996)ADSCrossRefGoogle Scholar
  40. 40.
    A. Lassl, P. Schlagheck, K. Richter, Phys. Rev. B 75, 045346 (2007)ADSCrossRefGoogle Scholar
  41. 41.
    H. Lind, I.I. Yakimenko, K.F. Berggren, Phys. Rev. B 83, 075308 (2011)ADSCrossRefGoogle Scholar
  42. 42.
    P. Stano, P. Jacquod, Phys. Rev. B 82, 125309 (2010)ADSCrossRefGoogle Scholar
  43. 43.
    A. Di Lorenzo, Y.V. Nazarov, Phys. Rev. Lett. 93, 046601 (2004)ADSCrossRefGoogle Scholar
  44. 44.
    T.L. Schmidt, A. Komnik, A.O. Gogolin, Phys. Rev. B 76, 241307 (2007)ADSCrossRefGoogle Scholar
  45. 45.
    T. Fujisawa, T.H. Oosterkamp, W.G. van der Wiel, B.W. Broer, R. Aguado, S. Tarucha, L.P. Kouwenhoven, Science 282, 932 (1998)ADSCrossRefGoogle Scholar
  46. 46.
    T. Hayashi, T. Fujisawa, H.D. Cheong, Y.H. Jeong, Y. Hirayama, Phys. Rev. Lett. 91, 226804 (2003)ADSCrossRefGoogle Scholar
  47. 47.
    J.R. Petta, A.C. Johnson, J.M. Taylor, E.A. Laird, A. Yacoby, M.D. Lukin, C.M. Marcus, M.P. Hanson, A.C. Gossard, Science 309, 2180 (2005)ADSCrossRefGoogle Scholar
  48. 48.
    C.W.J. Beenakker, D.P. DiVincenzo, C. Emary, M. Kindermann, Phys. Rev. Lett. 93, 020501 (2004)ADSCrossRefGoogle Scholar
  49. 49.
    W.G. van der Wiel, S. De Franceschi, J.M. Elzerman, T. Fujisawa, S. Tarucha, L.P. Kouwenhoven, Rev. Mod. Phys. 75, 1 (2003)CrossRefGoogle Scholar
  50. 50.
    D.H. Cobden, B.A. Muzykantskii, Phys. Rev. Lett. 75, 4274 (1995)ADSCrossRefGoogle Scholar
  51. 51.
    D.H. Cobden, M. Bockrath, P.L. McEuen, A.G. Rinzler, R.E. Smalley, Phys. Rev. Lett. 81, 681 (1998)ADSCrossRefGoogle Scholar
  52. 52.
    S. Hershfield, J.H. Davies, P. Hyldgaard, C.J. Stanton, J.W. Wilkins, Phys. Rev. B 47, 1967 (1993)ADSCrossRefGoogle Scholar
  53. 53.
    D.A. Bagrets, Yu.V. Nazarov, Phys. Rev. B 67, 085316 (2003)ADSCrossRefGoogle Scholar
  54. 54.
    L.S. Levitov, H. Lee, G.B. Lesovik, J. Math. Phys. 37, 4845 (1996)ADSMathSciNetCrossRefMATHGoogle Scholar
  55. 55.
    M. Ueda, Phys. Rev. A 40, 1096 (1989)ADSMathSciNetCrossRefGoogle Scholar
  56. 56.
    L.S. Levitov, M. Reznikov, Phys. Rev. B 70, 115305 (2004)ADSCrossRefGoogle Scholar
  57. 57.
    G. Kießlich, P. Samuelsson, A. Wacker, E. Schöll, Phys. Rev. B 73, 033312 (2006)ADSCrossRefGoogle Scholar
  58. 58.
    P. Samuelsson, E.V. Sukhorukov, M. Büttiker, Phys. Rev. Lett. 92, 026805 (2004)ADSCrossRefGoogle Scholar

Copyright information

© Springer Japan 2016

Authors and Affiliations

  1. 1.Department of PhysicsTokyo Institute of TechnologyTokyoJapan

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