Skip to main content
Log in

Quantum transport of double quantum dots coupled to an oscillator in arbitrary strong coupling regime

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

Abstract

In this paper, we investigate the quantum transport of a double quantum dot coupled with a nanomechanical resonator at arbitrary strong electron-phonon coupling regimes. We employ the generalized quantum master equation to study full counting statistics of currents. We demonstrate the coherent phonon states method can be applied to decouple the electron-phonon interaction non-perturbatively. With the help of this non-perturbative treatment of electron-phonon couplings, we find that the phonon-assisted resonant tunneling emerges when the excess energy from the left quantum dot to the right one can excite integer number of phonons and multi-phonon excitations can enhance the transport in strong electron-phonon coupling regime. Moreover, we find that as the electron-phonon coupling increases, it first plays a constructive role to assist the transport, and then plays the role of scattering and strongly represses the transport.

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. T.A. Fulton, G.J. Dolan, Phys. Rev. Lett. 59, 109 (1987)

    Article  ADS  Google Scholar 

  2. H. Grabert, M.H. Devoret, Single Charge Tunneling (Plenum, New York, 1992)

  3. R. Ashoori, Nature 379, 413 (1996)

    Article  ADS  Google Scholar 

  4. C. Joachim, J.K. Gimzewski, A. Aviram, Nature 408, 541 (2000)

    Article  ADS  Google Scholar 

  5. H. Park, J. Park, A.K.L. Lim, E.H. Anderson, A.P. Alivisatos, P.L. McEuen, Nature 407, 57 (2000)

    Article  ADS  Google Scholar 

  6. A. Aviram, M.A. Ratner, Chem. Phys. Lett. 29, 277 (1974)

    Article  ADS  Google Scholar 

  7. C. Joachim, J.K. Gimzewski, R.R. Schlittler, C. Chavy, Phys. Rev. Lett. 74, 2102 (1995)

    Article  ADS  Google Scholar 

  8. L.A. Bumm et al., Science 271, 1705 (1996)

    Article  ADS  Google Scholar 

  9. M.A. Reed, C. Zhou, C.J. Muller, P. Burgin, J.M. Tour, Science 278, 252 (1997)

    Article  Google Scholar 

  10. H.G. Craighead, Science 290, 1532 (2000)

    Article  ADS  Google Scholar 

  11. A.N. Cleland, Foundations of Nanomechanics (Springer, Berlin, 2003)

  12. M. Blencowe, Phys. Rep. 395, 159 (2004)

    Article  ADS  Google Scholar 

  13. W.G. van der Wiel, S.D. Franceschi, J.M. Elzerman, T. Fujisawa, S. Tarucha, L.P. Kouwenhowen, Rev. Mod. Phys. 75, 1 (2003)

    Article  Google Scholar 

  14. Y. Nakamura et al., Nature 398, 786 (1999)

    Article  ADS  Google Scholar 

  15. D. Vion et al., Science 296, 886 (2002)

    Article  ADS  Google Scholar 

  16. I. Chiorescu et al., Science 299, 1869 (2003)

    Article  ADS  Google Scholar 

  17. Y.A. Pashkin et al., Nature 421, 823 (2003)

    Article  ADS  Google Scholar 

  18. T. Fujisawa et al., Science 282, 932 (1998)

    Article  ADS  Google Scholar 

  19. T. Brandes, B. Kramer, Phys. Rev. Lett. 83, 3021 (1999)

    Article  ADS  Google Scholar 

  20. R.S. Knobel, A.N. Cleland, Nature 424, 291 (2003)

    Article  ADS  Google Scholar 

  21. M.D. LaHaye et al., Science 304, 74 (2004)

    Article  ADS  Google Scholar 

  22. A. Naik et al., Nature 443, 193 (2006)

    Article  ADS  Google Scholar 

  23. A.A. Clerk, S. Bennett, New J. Phys. 7, 238 (2005)

    Article  ADS  Google Scholar 

  24. G. Kießlich, E. Schöll, T. Brandes, F. Hohls, R.J. Haug, Phys. Rev. Lett. 99, 206602 (2007)

    Article  ADS  Google Scholar 

  25. R. Sánchez, S. Kohler, P. Hänggi, G. Platero, Phys. Rev. B 77, 035409 (2008)

    Article  ADS  Google Scholar 

  26. Y.M. Blanter, M. Büttiker, Phys. Rep. 336, 1 (2000)

    Article  ADS  Google Scholar 

  27. Quantum Noise in Mesoscopic Physics, edited by Y.V. Nazarov (Kluwer, Dordrecht, 2003)

  28. L.S. Levitov, G.B. Lesovik, JETP Lett. 58, 230 (1993)

    ADS  Google Scholar 

  29. L.S. Levitov, H. Lee, G.B. Lesovik, J. Math. Phys. 37, 4845 (1996)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  30. H.B. Sun, G.J. Milburn, Phys. Rev. B. 59, 10748 (1999)

    Article  Google Scholar 

  31. D.A. Bagrets, Y.V. Nazarov, Phys. Rev. B 67, 085316 (2003)

    Article  ADS  Google Scholar 

  32. R. Aguado, T. Brandes, Phys. Rev. Lett. 92, 206601 (2004)

    Article  ADS  Google Scholar 

  33. D.A. Bagrets, Y.V. Nazarov, Phys. Rev. Lett. 94, 056801 (2005)

    Article  ADS  Google Scholar 

  34. J. Ren, P. Hänggi, B. Li, Phys. Rev. Lett. 104, 170601 (2010)

    Article  ADS  Google Scholar 

  35. L. Wei, J. ZhingQing, L. Pfeiffer, K.W. West, A.J. Rimberg, Nature 423, 422 (2003)

    Article  ADS  Google Scholar 

  36. J. Bylander, T. Duty, P. Delsing, Nature 434, 361 (2005)

    Article  ADS  Google Scholar 

  37. S. Gustavsson, R. Leturcq, B. Simovič, R. Schleser, T. Ihn, P. Studerus, K. Ensslin, D.C. Driscoll, A.C. Gossard, Phys. Rev. Lett. 96, 076605 (2006)

    Article  ADS  Google Scholar 

  38. M. Campisi, P. Hänggi, P. Talkner, Rev. Mod. Phys. 83, 771 (2011)

    Article  ADS  Google Scholar 

  39. C. Flindt, T. Novotný, A. Braggio, M. Sassetti, A.-P. Jauho, Phys. Rev. Lett. 100, 150601 (2008)

    Article  ADS  Google Scholar 

  40. C. Flindt, T. Novotný, A.-P. Jauho, Europhys. Lett. 69, 475 (2005)

    Article  ADS  Google Scholar 

  41. S.R.S. Varadhan, Commun. Pure Appl. Math. 19, 261 (1966)

    Article  MathSciNet  MATH  Google Scholar 

  42. A. Dembo, O. Zeitouni, Large Deviations: Techniques and Applications, 2nd edn. (Springer, 1998)

  43. H. Touchette, Phys. Rep. 478, 1 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  44. E.K. Irish, Phys. Rev. Lett. 99, 173601 (2007)

    Article  ADS  Google Scholar 

  45. M.J. Hwang, M.S. Choi, Phys. Rev. A 82, 025802 (2010)

    Article  ADS  Google Scholar 

  46. Q.H. Chen, Y.Y. Zhang, T. Liu, K.L. Wang, Phys. Rev. A 78, 051801 (2008)

    Article  ADS  Google Scholar 

  47. Q.H. Chen, T. Liu, Y.Y. Zhang, K.L. Wang, Phys. Rev. A 82, 053841 (2010)

    Article  ADS  Google Scholar 

  48. Y.Y. Zhang, Q.H. Chen, K.L. Wang, Phys. Rev. B 81, 121105 (2010)

    Article  ADS  Google Scholar 

  49. N. Lambert, F. Nori, Phys. Rev. B 78, 214302 (2008)

    Article  ADS  Google Scholar 

  50. H. Park, J. Park, A.K.L. Lim, E.H. Anderson, A.P. Alivisatos, P.L. McEuen, Nature 407, 57 (2000)

    Article  ADS  Google Scholar 

  51. B.J. LeRoy, S.G. Lemay, J. Kong, C. Dekker, Nature 432, 371 (2004)

    Article  ADS  Google Scholar 

  52. S. Sapmaz, P. Jarillo-Herrero, Ya.M. Blanter, C. Dekker, H.S.J. van der Zant, Phys. Rev. Lett. 96, 026801 (2006)

    Article  ADS  Google Scholar 

  53. T. Niemczyk, F. Deppe, H. Huebl, E.P. Menzel, F. Hocke, M.J. Schwarz, J.J. Garcia-Ripoll, D. Zueco, T. Hümmer, E. Solano, A. Marx, R. Gross, Nature 6, 772 (2010)

    Google Scholar 

  54. M. Esposito, U. Harbola, S. Mukamel, Rev. Mod. Phys. 81, 1665 (2009)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  55. T. Brandes, N. Lambert, Phys. Rev. B 67, 125323 (2003)

    Article  ADS  Google Scholar 

  56. G.D. Mahan, Many-Particle Physics Plenum Press (New York, 1990)

  57. A.D. Armour, A. MacKinnon, Phys. Rev. B 66, 035333 (2002)

    Article  ADS  Google Scholar 

  58. F. Domínguez, S. Kohler, G. Platero, Phys. Rev. B 83, 235319 (2011)

    Article  ADS  Google Scholar 

  59. M. Galperin, M.A. Ratner, A. Nitzan, A. Troisi, Science 319, 1056 (2008)

    Article  ADS  Google Scholar 

  60. T.H. Stoof, Y.V. Nazarov, Phys. Rev. B 53, 1050 (1996)

    Article  ADS  Google Scholar 

  61. B. Elattari, S.A. Gurvitz, Phys. Lett. A 292, 289 (2002)

    Article  ADS  Google Scholar 

  62. T. Brandes, Phys. Rep. 408, 315 (2005)

    Article  ADS  Google Scholar 

  63. H. Haug, A.P. Jauho, Quantum Kinetics in Transport and Optics of Semiconductors (Springer-Verlag, Berlin, 2008)

  64. J. Koch, F. von Oppen, Phys. Rev. Lett. 94, 206804 (2005).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to J. Ren, B. W. Li or Q. H. Chen.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wang, C., Ren, J., Li, B.W. et al. Quantum transport of double quantum dots coupled to an oscillator in arbitrary strong coupling regime. Eur. Phys. J. B 85, 110 (2012). https://doi.org/10.1140/epjb/e2012-30027-1

Download citation

  • Received:

  • Revised:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/e2012-30027-1

Keywords

Navigation