Physical Review Letters -- July 26, 1999 -- Volume 83, Issue 4, pp. 808-811

How Long Does It Take for the Kondo Effect to Develop?

Peter Nordlander
Department of Physics and Rice Quantum Institute, Rice University, Houston, Texas 77251-1892
Michael Pustilnik and Yigal Meir
Physics Department, Ben Gurion University, Beer Sheva, 84105, Israel
Ned S. Wingreen
NEC Research Institute, 4 Independence Way, Princeton, New Jersey 08540
David C. Langreth
Department of Physics and Astronomy, Rutgers University, Piscataway, NJ 08854-8019

(Received 16 March 1999)

The time development of the Kondo effect is theoretically investigated by studying a quantum dot suddenly shifted into the Kondo regime by a change of voltage on a nearby gate. Using time-dependent versions of both the Anderson and Kondo Hamiltonians, it is shown that after a time t following the voltage shift, the form of the Kondo resonance matches the time-independent resonance at an effective temperature Teff = T/tanh(pi Tt/2). Relevance of the buildup of the Kondo resonance to the transport current through a quantum dot is demonstrated. ©1999 The American Physical Society

PII: S0031-9007(99)09685-4
PACS: 72.15.Qm, 73.50.Mx, 85.30.Vw

  Full Text:


Citation links [e.g., Phys. Rev. D 40, 2172 (1989)] go to online journal abstracts. Other links (see Reference Information) are available with your current login. Navigation of links may be more efficient using a second browser window.

  1. D. Goldhaber-Gordon et al., Nature (London) 391, 156 (1998);  [INSPEC]
    D. Goldhaber-Gordon et al., Phys. Rev. Lett. 81, 5225 (1998);
    S. M. Cronenwett, T. H. Oosterkamp, and L. P. Kouwenhoven, Science 281, 540 (1998);  [INSPEC]
    F. Simmel et al., ;  [LANL]
    T. Schmidt et al. (unpublished).
  2. L. I. Glazman and M. E. Raikh, Pis'ma Zh. Eksp. Teor. Fiz. 47, 378 (1988)  [INSPEC]
    [JETP Lett. 47, 452 (1988)];  [SPIN]
    T. K. Ng and P. A. Lee, Phys. Rev. Lett. 61, 1768 (1988);
    S. Hershfield, J. H. Davies, and J. W. Wilkins, Phys. Rev. Lett. 67, 3720 (1991).
  3. Y. Meir, N. S. Wingreen, and P. A. Lee, Phys. Rev. Lett. 70, 2601 (1993);
    N. S. Wingreen and Y. Meir, Phys. Rev. B 49, 11 040 (1994).
  4. L. P. Kouwenhoven et al., in Mesoscopic Electron Transport, edited by L. L. Sohn, L. P. Kouwenhoven, and G. Schön (Kluwer, Dordrecht, The Netherlands, 1997).
  5. A. Schiller and S. Hershfield, Phys. Rev. Lett. 77, 1821 (1996);
    T. K. Ng, Phys. Rev. Lett. 76, 487 (1996);
    Y. Goldin and Y. Avishai, Phys. Rev. Lett. 81, 5394 (1998).
  6. N. E. Bickers, Rev. Mod. Phys. 59, 845 (1987).  [SPIN]
  7. D. C. Langreth and P. Nordlander, Phys. Rev. B 43, 2541 (1991);
    H. Shao, D. C. Langreth, and P. Nordlander, Phys. Rev. B 49, 13 929 (1994).
  8. We define Gammadot(epsilon) = 2 pi [summation]k|Vk|2delta(epsilonepsilonk), a slowly varying quantity. The notation Gammadot with no energy specified will always refer to the value at the Fermi level.
  9. For U = [infinity], D[prime] ~= sqrt(D Gammadot/4), where 2D is the effective bandwidth. The calculations here used a parabolic band of total width 40 Gammadot.
  10. A.-P. Jauho, N. S. Wingreen, and Y. Meir, Phys. Rev. B 50, 5528 (1994).
  11. There are transients arising from the abrupt shift of epsilondot which are included inaccurately, because we neglect higher dot levels. However, all such transients decay rapidly for t > [h-bar]/Gammadot and hence are not visible on the scale of any of our figures. Such transients do not occur at all if tauepsilon, the rise time of epsilondot, is such that tauepsilon >> 1/Gammadot; and if tauepsilon << min(1/TK, 1/T), the appearance of our figures on their current scales (t >> tauepsilon) will be the same.
  12. J. R. Schrieffer and P. A. Wolff, Phys. Rev. 149, 491 (1966).
  13. A. A. Abrikosov, Physics 2, 5 (1965).
  14. G. Yuval and P. W. Anderson, Phys. Rev. B 1, 1522 (1970).  [INSPEC]
  15. By evaluating the conduction electron self-energy to order J3, we have directly confirmed the ~ 1/t cutoff for the Kondo peak in the spectral density.
  16. Y. Meir and N. S. Wingreen, Phys. Rev. Lett. 68, 2512 (1992).
  17. The difference between the dashed and solid curves at small tauon reflects the finite decay time of the Kondo resonance after the pulse is switched off.
  18. Y. Nakamura, Y. A. Pashkin, and J. S. Tsai, Nature (London) 398, 786 (1999);  [INSPEC]
    L. P. Kouwenhoven (private communication).