Skip to main content
Log in

Power-law behavior in electron transport through a quantum dot with Luttinger liquid leads

  • Regular Article
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

The electron transport of a system consisting of a Kondo dot and two Luttinger liquid (LL) leads is theoretically studied by use of nonequilibrium Green function approach. In the Kondo regime, the zero bias anomaly appears and the density of states of the dot obeys a power-law scaling at positive energy part with an exponent β/2 = 1/g − 1, where g reflects the electron interaction in the LL leads. The differential conductance shows a power-law scaling both in bias voltage and in temperature, with the exponent being β. The power-law temperature dependence of the peak conductance is observed in different temperature regimes. These features are ascribed to the LL correlation in the leads. Our work describes both the zero bias anomaly and power-law scalings within one theoretical frame.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. L.I. Glazman, M.E. Raikh, J. Exp. Theor. Phys. Lett. 47, 452 (1988)

    Google Scholar 

  2. T.K. Ng, P.A. Lee, Phys. Rev. Lett. 61, 1768 (1988)

    Article  ADS  Google Scholar 

  3. S.M. Cronenwett, T.H. Oosterkamp, L.P. Kouwenhoven, Science 281, 540 (1998)

    Article  ADS  Google Scholar 

  4. S. Hershfield, J.H. Davis, J.W. Wilkins, Phys. Rev. Lett. 67, 3720 (1991)

    Article  ADS  Google Scholar 

  5. S. Hershfield, J.H. Davis, J.W. Wilkins, Phys. Rev. B 46, 7046 (1992)

    Article  ADS  Google Scholar 

  6. L.P. Kouwenhoven, L. Glazman, Phys. World 14, 33 (2001)

    Google Scholar 

  7. S. Tomonaga, Prog. Theor. Phys. 5, 544 (1950)

    Article  ADS  MathSciNet  Google Scholar 

  8. J.M. Luttinger, J. Math. Phys. 4, 1154 (1963)

    Article  ADS  MathSciNet  Google Scholar 

  9. F.D.M. Haldane, Phys. Rev. Lett. 47, 1840 (1981)

    Article  ADS  Google Scholar 

  10. J. Voit, Rep. Prog. Phys. 57, 977 (1994)

    Google Scholar 

  11. D.-H. Lee, J. Toner, Phys. Rev. Lett. 69, 3378 (1992)

    Article  ADS  Google Scholar 

  12. A. Furusaki, N. Nagaosa, Phys. Rev. Lett. 72, 892 (1994)

    Article  ADS  Google Scholar 

  13. R. Egger, A. Komnik, Phys. Rev. B 57, 10620 (1998)

    Article  ADS  Google Scholar 

  14. M. Fabrizio, A.O. Gogolin, Phys. Rev. B 51, 17827 (1995)

    Article  ADS  Google Scholar 

  15. R.M. Potok, I.G. Rau, H. Shtrikman, Y. Oreg, D. Goldhaber-Gordon, Nature 446, 167 (2007)

    Article  ADS  Google Scholar 

  16. B. Gao, A. Komnik, R. Egger, D.C. Glattli, A. Bachtold, Phys. Rev. Lett. 92, 216804 (2004)

    Article  ADS  Google Scholar 

  17. Y. Gong, M. Long, G. Liu, S. Gao, C. Zhu, X. Wei, X. Geng, M. Sun, C. Yang, L. Lu, L. Liu, Phys. Rev. B 87, 165404 (2013)

    Article  ADS  Google Scholar 

  18. A. Bachtold, M. de Jonge, K. Grove-Rasmussen, P.L. McEuen, M. Buitelaar, C. Schonenberger, Phys. Rev. Lett. 87, 166801 (2001)

    Article  ADS  Google Scholar 

  19. E. Graugnard, P.J. de Pablo, B. Walsh, A.W. Ghosh, S. Datta, R. Reifenberger, Phys. Rev. B 64, 125407 (2001)

    Article  ADS  Google Scholar 

  20. K. Liu, Ph. Avouris, R. Martel, W.K. Hsu, Phys. Rev. B 63, 161404 (2001)

    Article  ADS  Google Scholar 

  21. J. Hager, R. Matzdorf, J. He, R. Jin, D. Mandrus, M.A. Cazalilla, E.W. Plummer, Phys. Rev. Lett. 95, 186402 (2005)

    Article  ADS  Google Scholar 

  22. Th. Hunger, B. Lengeler, J. Appenzeller, Phys. Rev. B 69, 195406 (2004)

    Article  ADS  Google Scholar 

  23. Y. Tserkovnyak, B.I. Halperin, O.M. Auslaender, A. Yacoby, Phys. Rev. B 68, 125312 (2003)

    Article  ADS  Google Scholar 

  24. X. Hoffer, Ch. Klinke, J.-M. Bonard, L. Gravier, Europhys. Lett. 67, 103 (2004)

    Article  ADS  Google Scholar 

  25. L. Bitton, D.B. Gutman, R. Berkovits, A. Frydman, Phys. Rev. Lett. 106, 016803 (2011)

    Article  ADS  Google Scholar 

  26. H. Yan, R. Xu, X. Hong, Y. Sun, L. Feng, J.-C. Nie, L. He, AIP Adv. 2, 032143 (2012)

    Article  ADS  Google Scholar 

  27. P. Jiang, C.-C. Chien, I. Yang, W. Kang, K.W. Baldwin, L.N. Pfeiffer, K.W. West, Phys. Rev. Lett. 105, 246801 (2010)

    Article  ADS  Google Scholar 

  28. C. Blumenstein, J. Schäfer, S. Mietke, S. Meyer, A. Dollinger, M. Lochner, X.Y. Cui, L. Patthey, R. Matzdorf, R. Claessen, Nat. Phys. 7, 776 (2011)

    Article  Google Scholar 

  29. K.-H. Yang, Y. Chen, H.-Y Wang, B.-Y. Liu, Phys. Lett. A 377, 687 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  30. K.-H. Yang, B.-Y. Liu, H.-Y. Wang, X. He, Solid State Commun. 178, 50 (2014)

    Article  ADS  Google Scholar 

  31. K.-H. Yang, B.-Y. Liu, H.-Y. Wang, X. He, Europhys. Lett. 104, 37009 (2013)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  33. M. Bockrath, D.H. Cobden, J. Lu, A.G. Rinzler, R.E. Smalley, L. Balents, P.L. McEuen, Nature 397, 598 (1999)

    Article  ADS  Google Scholar 

  34. A. Kanda, K. Tsukagoshi, Y. Aoyagi, Y. Ootuka, Phys. Rev. Lett. 92, 036801 (2004)

    Article  ADS  Google Scholar 

  35. H.W.Ch. Postma, T. Teepen, Z. Yao, M. Grifoni, C. Dekker, Science 293, 76 (2001)

    Article  ADS  Google Scholar 

  36. C. Kane, L. Balents, M.P.A. Fisher, Phys. Rev. Lett. 79, 5086 (1997)

    Article  ADS  Google Scholar 

  37. C.L. Kane, M.P.A. Fisher, Phys. Rev. B 46, 15233 (1992)

    Article  ADS  Google Scholar 

  38. C.L. Kane, L. Balents, M.P.A. Fisher, Phys. Rev. Lett. 79, 5082 (1997)

    Article  ADS  Google Scholar 

  39. R. Egger, Phys. Rev. Lett. 83, 5547 (1999)

    Article  ADS  Google Scholar 

  40. R. Egger, A.O. Gogolin, Chem. Phys. 281, 447 (2002)

    Article  ADS  Google Scholar 

  41. R. Tarkiainen, M. Ahlskog, J. Penttila, L. Roschier, P. Hakonen, M. Paalanen, E. Sonin, Phys. Rev. B 64, 195412 (2001)

    Article  ADS  Google Scholar 

  42. A. Furusaki, Phys. Rev. B 57, 7141 (1998)

    Article  ADS  Google Scholar 

  43. M. Thorwart, R. Egger, M. Grifoni, Phys. Rev. B 72, 035330 (2005)

    Article  ADS  Google Scholar 

  44. H. Haug, A.P. Jauho, Quantum Kinetics in Transort and Optics of Semiconductors (Springer, New York, 1998)

  45. D.C. Langreth, Linear and Nonlinear Electron Transport in Solids (Plenum, New York, 1976)

  46. S. Takei, Y.B. Kim, A. Mitra, Phys. Rev. B 72, 075337 (2005)

    Article  ADS  Google Scholar 

  47. C. Lacroix, J. Phys. F 11, 2389 (1981)

    Article  ADS  Google Scholar 

  48. K. Kang, B.I. Min, Phys. Rev. B 52, 10689 (1995)

    Article  ADS  Google Scholar 

  49. C.L. Kane, M.P.A. Fisher, Phys. Rev. Lett. 76, 3192 (1996)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Kai-Hua Yang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, KH., He, X., Wang, HY. et al. Power-law behavior in electron transport through a quantum dot with Luttinger liquid leads. Eur. Phys. J. B 87, 172 (2014). https://doi.org/10.1140/epjb/e2014-50093-5

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/e2014-50093-5

Keywords

Navigation