Physical Review B (Condensed Matter and Materials Physics) -- January 15, 2000 -- Volume 61, Issue 3, pp. 2146-2150

Kondo physics in the single-electron transistor with ac driving

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

(Received 20 September 1999)

Using a time-dependent Anderson Hamiltonian, a quantum dot with an ac voltage applied to a nearby gate is investigated. A rich dependence of the linear response conductance on the external frequency and driving amplitude is demonstrated. At low frequencies a sufficiently strong ac potential produces sidebands of the Kondo peak in the spectral density of the dot, and a slow, roughly logarithmic decrease in conductance over several decades of frequency. At intermediate frequencies, the conductance of the dot displays an oscillatory behavior due to the appearance of Kondo resonances of the satellites of the dot level. At high frequencies, the conductance of the dot can vary rapidly due to the interplay between photon-assisted tunneling and the Kondo resonance. ©2000 The American Physical Society

PACS: 72.15.Qm, 73.50.Mx, 85.30.Vw 

  Full Text:

References

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. L.I. Glazman and M.E. Raikh, Pis'ma Zh. Éksp. Teor. Fiz. 47, 378 (1988) [ 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, 67, 3720 (1991).
  2. 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).
  3. D. Goldhaber-Gordon et al., Nature (London) 391, 156 (1998);  [INSPEC]
    Phys. Rev. Lett. 81, 5225 (1998);
    S.M. Cronenwett, T.H. Oosterkamp, and L.P. Kouwenhoven, Science 281, 540 (1998);  [INSPEC]
    T. Schmid et al., Phys. Rev. B 256, 182 (1998);
    F. Simmel et al., Phys. Rev. Lett. 83, 804 (1999).
  4. L.P. Kouwenhoven et al., in Mesoscopic Electron Transport, edited by L.L. Sohn, L.P. Kouwenhoven, and G. Schön (Kluwer, Netherlands, 1997).
  5. M.H. Hettler and H. Schoeller, Phys. Rev. Lett. 74, 4907 (1995).
  6. A. Schiller and S. Hershfield, Phys. Rev. Lett. 77, 1821 (1996).
  7. T.K. Ng, Phys. Rev. Lett. 76, 487 (1996);
    Y. Goldin and Y. Avishai, 81, 5394 (1998);
    R. Lopez et al., 81, 4688 (1998).
  8. Gammadot(epsilon)[equivalent]2pi[summation]k|Vk|2delta(epsilon–epsilonk) is slowly varying. Gammadot with no energy specified refers to the Fermi level value.
  9. N.E. Bickers, Rev. Mod. Phys. 59, 845 (1987).  [SPIN]
  10. D.C. Langreth and P. Nordlander, Phys. Rev. B 43, 2541 (1991).
  11. H. Shao, D.C. Langreth, and P. Nordlander, Phys. Rev. B 49, 13 929 (1994).
  12. Y. Meir and N.S. Wingreen, Phys. Rev. Lett. 68, 2512 (1992).
  13. A.-P. Jauho, N.S. Wingreen, and Y. Meir, Phys. Rev. B 50, 5528 (1994).
  14. For the Hamiltonian (1) the time average dot(epsilon,t)>[equivalent]–Im<Adot(epsilon,t)>/pi, where Adot(epsilon,t) is the retarded and hence causal function defined in Ref. 13, Eq. (28).
  15. Hence in an experiment one may also expect peaks spaced by [h-bar]Omega in the differential conductance.
  16. A. Kaminski, Yu.V. Nazarov, and L.I. Glazman, Phys. Rev. Lett. 83, 384 (1999).
  17. P.K. Tien and J.P. Gordon, Phys. Rev. 129, 647 (1963).
  18. In contrast, an ac bias voltage of order TK/e can produce significant effects such as Kondo sidebands, cf. Refs. 6,7.
  19. J.R. Schrieffer and P.A. Wolff, Phys. Rev. 149, 491 (1966).
  20. To derive Eq. (6), we note that the full retarded propagators g for the lead electrons are given in terms of their bare values g0 by g = g0 + g0Tg0 with matrix multiplication implied in the time and lead quantum number k. The transition matrix T is given by Tkk[prime] = VkVk[prime]*Adot, where Adot is the corresponding propagator for the dot. The above two relations may be obtained directly from Eq. (1) for arbitrary U (via the equations of motion for the c's, for example). The total transition rate is then just –2 Im Tkk from the optical theorem, which then implies for the time averaged rate wleads(epsilon) = –2|Vk|2Im<Adot(epsilon,t)>. Finally, using the relation between A and rhodot given in Ref. 14 and the definition of Gammadot(epsilon) given in Ref. 8, we arrive at Eq. (6).
  21. A.A. Abrikosov, Physics (N.Y.) 2, 5 (1965).