Skip to main content

Correlation Effects on Electronic Transport through Dots and Wires

  • Chapter

Part of the Advances in Solid State Physics book series (ASSP,volume 46)

Abstract

We investigate how two-particle interactions affect the electronic transport through meso- and nanoscopic systems of two different types: quantum dots with local Coulomb correlations and quasi one-dimensional quantum wires of interacting electrons. A recently developed functional renormalization group scheme is used that allows to investigate systems of complex geometry. Considering simple setups we show that the method includes the essential aspects of Luttinger liquid physics (one-dimensional wires) as well as of the physics of local correlations, with the Kondo effect being an important example. For more complex systems of coupled dots and Y-junctions of interacting wires we find surprising new correlation effects.

Keywords

  • Quantum Wire
  • Luttinger Liquid
  • Single Impurity
  • Hubbard Band
  • Functional Renormalization Group

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

In memory of Xavier Barnabé-Thériault, who passed away in a tragic accident on August 15, 2004.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-3-540-38235-5_14
  • Chapter length: 13 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   189.00
Price excludes VAT (USA)
  • ISBN: 978-3-540-38235-5
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   249.99
Price excludes VAT (USA)
Hardcover Book
USD   249.99
Price excludes VAT (USA)

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. C. Hewson, The Kondo Problem to Heavy Fermions, (Cambridge University Press, Cambridge, UK, 1993)

    CrossRef  Google Scholar 

  2. L. Glazman and M. Raikh, JETP Lett. 47, 452 (1988)

    ADS  Google Scholar 

  3. T. Ng and P. Lee, Phys. Rev. Lett. 61, 1768 (1988)

    CrossRef  ADS  Google Scholar 

  4. K. Schönhammer in D. Baeriswyl (Ed.): Interacting Electrons in Low Dimensions, (Kluwer Academic Publishers, 2005)

    Google Scholar 

  5. A. W. Holleitner et al., Phys. Rev. Lett. 87, 256802 (2001); Science 297, 70 (2002)

    CrossRef  ADS  Google Scholar 

  6. N. J. Craig et al., Science 304, 565 (2004)

    CrossRef  ADS  Google Scholar 

  7. M. Terrones et al., Phys. Rev. Lett. 89, 075505 (2002)

    CrossRef  ADS  Google Scholar 

  8. M. Salmhofer, Renormalization, (Springer, Berlin, 1998)

    Google Scholar 

  9. A. M. Tsvelik and P. B. Wiegmann, Adv. Phys. 32, 453 (1983)

    CrossRef  ADS  Google Scholar 

  10. T. A. Costi, A. C. Hewson, and V. Zlatic, J. Phys.: Condens. Matter 6, 2519 (1994)

    CrossRef  ADS  Google Scholar 

  11. U. Gerland, J. von Delft, T.A. Costi, and Y. Oreg, Phys. Rev. Lett. 84, 3710 (2000)

    CrossRef  ADS  Google Scholar 

  12. Y. Meir and N. S. Wingreen, Phys. Rev. Lett. 68, 2512 (1992)

    CrossRef  ADS  Google Scholar 

  13. D. Goldhaber-Gordon et al., Nature 391, 156 (1998)

    CrossRef  ADS  Google Scholar 

  14. W. van der Wiel et al., Science 289, 2105 (2000)

    CrossRef  ADS  Google Scholar 

  15. A. Luther and I. Peschel, Phys. Rev. B 9, 2911 (1974)

    CrossRef  ADS  Google Scholar 

  16. D. C. Mattis, J. Math. Phys. 15, 609 (1974)

    CrossRef  ADS  Google Scholar 

  17. W. Apel and T.M. Rice, Phys. Rev. B 26, 7063 (1982)

    CrossRef  ADS  Google Scholar 

  18. T. Giamarchi and H. J. Schulz, Phys. Rev. B 37, 325 (1988)

    CrossRef  ADS  Google Scholar 

  19. C. L. Kane and M. P. A. Fisher, Phys. Rev. Lett. 68, 1220 (1992); Phys. Rev. B 46, 15233 (1992)

    CrossRef  ADS  Google Scholar 

  20. A. Furusaki and N. Nagaosa, Phys. Rev. B 47, 4631 (1993)

    CrossRef  ADS  Google Scholar 

  21. P. Fendley, A. W. W. Ludwig, and H. Saleur, Phys. Rev. Lett. 74, 3005 (1995)

    CrossRef  ADS  Google Scholar 

  22. A. Furusaki and N. Nagaosa, Phys. Rev. B 54, R5239 (1996)

    CrossRef  ADS  Google Scholar 

  23. M. Bockrath et al., Nature 397, 598 (1999)

    CrossRef  ADS  Google Scholar 

  24. Z. Yao, H. Postma, L. Balents, and C. Dekker, Nature 402, 273 (1999)

    CrossRef  ADS  Google Scholar 

  25. O. Auslaender et al., Phys. Rev. Lett. 84, 1764 (2000)

    CrossRef  ADS  Google Scholar 

  26. R. de Picciotto et al., Nature 411, 51 (2001)

    CrossRef  ADS  Google Scholar 

  27. R. Hedden, V. Meden, Th. Pruschke, and K. Schönhammer, J. Phys.: Condens. Matter 16, 5279 (2004)

    CrossRef  ADS  Google Scholar 

  28. T. Enss et al., Phys. Rev. B 71, 155401 (2005)

    CrossRef  ADS  Google Scholar 

  29. V. Meden, lecture notes on the “Functional renormalization group”, http://www.theorie.physik.uni-goettingen.de/~meden/funRG/

    Google Scholar 

  30. S. Andergassen et al., Phys. Rev. B 70, 075102 (2004)

    CrossRef  ADS  Google Scholar 

  31. C. Karrasch, T. Enss, and V. Meden, cond-mat/0603510

    Google Scholar 

  32. T. A. Costi, Phys. Rev. B 64, 241310(R) (2001)

    CrossRef  ADS  Google Scholar 

  33. S. Andergassen et al., Phys. Rev. B 73, 045125 (2006)

    CrossRef  ADS  Google Scholar 

  34. F. D. M. Haldane, Phys. Rev. Lett. 45, 1358 (1980)

    CrossRef  ADS  MathSciNet  Google Scholar 

  35. V. Meden, W. Metzner, U. Schollwöck, and K. Schönhammer, J. Low Temp. Physics 126, 1147 (2002)

    CrossRef  Google Scholar 

  36. V. Meden and F. Marquardt, Phys. Rev. Lett. 96, 146801 (2006)

    CrossRef  ADS  Google Scholar 

  37. X. Barnabé-Thériault, A. Sedeki, V. Meden, and K. Schönhammer, Phys. Rev. Lett. 94, 136405 (2005)

    CrossRef  ADS  Google Scholar 

  38. C. Chamon, M. Oshikawa, and I. Affleck, Phys. Rev. Lett. 91, 206403 (2003)

    CrossRef  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and Permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Meden, V. (2008). Correlation Effects on Electronic Transport through Dots and Wires. In: Advances in Solid State Physics. Advances in Solid State Physics, vol 46. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-38235-5_14

Download citation