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Transport of Interacting Electrons Through a Quantum Dot in Nanowires

  • Igor V. Gornyi
  • Dmitri G. Polyakov
Chapter
Part of the Lecture Notes in Physics book series (LNP, volume 658)

Abstract

We generalize the fermionic renormalization group method to analytically describe transport through a double barrier structure in a one-dimensional system. Focusing on the case of weakly interacting electrons, we investigate thoroughly the dependence of the conductance on the strength and the shape of the double barrier for arbitrary temperature T, down to zero T. We systematically analyze the contributions to renormalized scattering amplitudes from characteristic scales absent in the case of a single impurity, without restricting the consideration to the model of a single resonant level. Both a sequential resonant tunneling for high T and a resonant transmission for T smaller than the resonance width are studied within the unified treatment of transport through strong barriers. For weak barriers, we show that two different regimes are possible. Moderately weak impurities get strong due to the renormalization, so that transport is described in terms of theory for initially strong barriers. The renormalization of very weak impurities does not yield any peak in the transmission probability; however, remarkably, the interaction gives rise to a sharp peak in the conductance.

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References

  1. 1. J. Sólyom: Adv. Phys. 28, 201 (1979); J. Voit: Rep. Prog. Phys. 58, 977 (1994)CrossRefGoogle Scholar
  2. 2. A.O. Gogolin, A.A. Nersesyan, A.M. Tsvelik: Bosonization and Strongly Correlated Systems (Cambridge University, Cambridge 1998)Google Scholar
  3. 3. C.L. Kane, M.P.A. Fisher: Phys. Rev. B 46, 15233 (1992)CrossRefGoogle Scholar
  4. 4. A. Furusaki, N. Nagaosa: Phys. Rev. B 47, 4631 (1993)CrossRefGoogle Scholar
  5. 5. M. Bockrath, D.H. Cobden, J. Lu, A.G. Rinzler, R.E. Smalley, L. Balents, P.L. McEuen: Nature 397, 598 (1999)CrossRefGoogle Scholar
  6. 6. Z. Yao, H. Postma, L. Balents, C. Dekker: Nature 402, 273 (1999)CrossRefGoogle Scholar
  7. 7. Z. Yao, C.L. Kane, C. Dekker: Phys. Rev. Lett. 84, 2941 (2000)CrossRefGoogle Scholar
  8. 8. J. Nygård, D.H. Cobden, P.E. Lindelof: Nature 408, 342 (2000)CrossRefGoogle Scholar
  9. 9. M. Bockrath, W. Liang, D. Bozovic, J.H. Hafner, C.M. Lieber, M. Tinkham, H. Park: Science 291, 283 (2001)CrossRefGoogle Scholar
  10. 10. R. Krupke, F. Hennrich, H.B. Weber, D. Beckmann, O. Hampe, S. Malik, M.M. Kappes, H. v. Löhneysen: Appl. Phys. A 76, 397 (2003)CrossRefGoogle Scholar
  11. 11. O.M. Auslaender, A. Yacoby, R. de Picciotto, K.W. Baldwin, L.N. Pfeiffer, K.W. West: Phys. Rev. Lett. 84, 1764 (2000)CrossRefGoogle Scholar
  12. 12. H.W.Ch. Postma, T. Teepen, Z. Yao, M. Grifoni, C. Dekker: Science 293, 76 (2001)CrossRefGoogle Scholar
  13. 13. A. Furusaki, N. Nagaosa: Phys. Rev. B 47, 3827 (1993)CrossRefGoogle Scholar
  14. 14. M. Sassetti, F. Napoli, U. Weiss: Phys. Rev. B 52, 11213 (1995)CrossRefGoogle Scholar
  15. 15. H. Maurey, T. Giamarchi: Europhys. Lett. 38, 681 (1997)CrossRefGoogle Scholar
  16. 16. A. Furusaki: Phys. Rev. B 57, 7141 (1998)CrossRefGoogle Scholar
  17. 17. A. Braggio, M. Grifoni, M. Sassetti, F. Napoli: Europhys. Lett. 50, 236 (2000)CrossRefGoogle Scholar
  18. 18. A. Komnik, A.O. Gogolin: Phys. Rev. Lett. 90, 246403 (2003)CrossRefGoogle Scholar
  19. 19. R. Egger, A.O. Gogolin: Phys. Rev. Lett. 79, 5082 (1997); Eur. Phys. J. B 3, 281 (1998); C.L. Kane, L. Balents, M.P.A. Fisher: Phys. Rev. Lett. 79, 5086 (1997).CrossRefGoogle Scholar
  20. 20. M.P.A. Fisher, L.I. Glazman: in Mesoscopic Electron Transport, ed. by L.L. Sohn, L.P. Kouwenhoven, G. Schön (Kluwer, Dordrecht 1997)Google Scholar
  21. 21. K.A. Matveev, D. Yue, L.I. Glazman: Phys. Rev. Lett. 71, 3351 (1993); D. Yue, L.I. Glazman, K.A. Matveev: Phys. Rev. B 49, 1966 (1994)CrossRefGoogle Scholar
  22. 22. C.L. Kane, K.A. Matveev, L.I. Glazman: Phys. Rev. B 49, 2253 (1994)CrossRefGoogle Scholar
  23. 23. S.-W. Tsai, D.L. Maslov, L.I. Glazman: Phys. Rev. B 65, 241102 (2002)CrossRefGoogle Scholar
  24. 24. Yu.V. Nazarov, L.I. Glazman: Phys. Rev. Lett. 91, 126804 (2003)CrossRefGoogle Scholar
  25. 25. A perturbative-in-α fermionic RG approach similar to that of Ref. [21] has been used as a basis for numerical simulations in V. Meden, W. Metzner, U. Schollwöck, O. Schneider, T. Stauber, K. Schönhammer: Eur. Phys. J. B 16, 631 (2000); V. Meden, W. Metzner, U. Schollwöck, K. Schönhammer: J. Low Temp. Phys. 126, 1147 (2002)CrossRefGoogle Scholar
  26. 26. M. Thorwart, M. Grifoni, G. Cuniberti, H.W.Ch. Postma, C. Dekker: Phys. Rev. Lett. 89, 196402 (2002); M. Thorwart, M. Grifoni: Chem. Phys. 281, 477 (2002)CrossRefGoogle Scholar
  27. 27. D. G. Polyakov, I. V. Gornyi: Phys. Rev. B 68, 035421 (2003)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Igor V. Gornyi
    • 1
    • 2
  • Dmitri G. Polyakov
    • 1
    • 2
  1. 1.Forschungszentrum Karlsruhe, Institut für Nanotechnologie (INT), Postfach 3640KarlsruheGermany
  2. 2.A.F. Ioffe Physico-Technical InstituteSt.PetersburgRussia

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