Letter | Published:

Non-equilibrium singlet–triplet Kondo effect in carbon nanotubes

Nature Physics volume 2, pages 460464 (2006) | Download Citation

Subjects

Abstract

The Kondo effect is a many-body phenomenon arising due to conduction electrons scattering off a localized spin1. Coherent spin-flip scattering off such a quantum impurity correlates the conduction electrons, and at low temperature this leads to a zero-bias conductance anomaly2,3. This has become a common signature in bias spectroscopy of single-electron transistors, observed in GaAs quantum dots4,5,6,7,8,9 as well as in various single-molecule transistors10,11,12,13,14,15. Although the zero-bias Kondo effect is well established, the extent to which Kondo correlations persist in non-equilibrium situations where inelastic processes induce decoherence remains uncertain. Here we report on a pronounced conductance peak observed at finite bias voltage in a carbon-nanotube quantum dot in the spin-singlet ground state. We explain this finite-bias conductance anomaly by a non-equilibrium Kondo effect involving excitations into a spin-triplet state. Excellent agreement between calculated and measured nonlinear conductance is obtained, thus strongly supporting the correlated nature of this non-equilibrium resonance.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

References

  1. 1.

    The Kondo Problem to Heavy Fermions (Cambridge Univ. Press, Cambridge, 1993).

  2. 2.

    & Resonant Kondo transparency of a barrier with quasilocal impurity states. JETP Lett. 47, 452–455 (1988).

  3. 3.

    & On-site Coulomb repulsion and resonant tunnelling. Phys. Rev. Lett. 61, 1768–1771 (1988).

  4. 4.

    et al. Kondo effect in a single-electron transistor. Nature 391, 156–159 (1998).

  5. 5.

    , & A tunable Kondo effect in quantum dots. Science 281, 540–544 (1998).

  6. 6.

    et al. The Kondo effect in the unitary limit. Science 289, 2105–2108 (2000).

  7. 7.

    et al. Kondo effect in an integer-spin quantum dot. Nature 405, 764–767 (2000).

  8. 8.

    , , & Singlet-triplet transition in a single-electron transistor at zero magnetic field. Phys. Rev. B 67, 113309 (2003).

  9. 9.

    , , & Cotunnelling spectroscopy in few-electron quantum dots. Phys. Rev. Lett. 93, 256801 (2004).

  10. 10.

    et al. Coulomb blockade and the Kondo effect in single-atom transistors. Nature 417, 722–725 (2002).

  11. 11.

    , & Kondo physics in carbon nanotubes. Nature 408, 342–346 (2000).

  12. 12.

    , , , & Kondo resonance in a single-molecule transistor. Nature 417, 725–729 (2002).

  13. 13.

    et al. Inelastic electron tunnelling via molecular vibrations in single molecule transistors. Phys. Rev. Lett. 93, 266802 (2004).

  14. 14.

    , & Kondo effect in carbon nanotubes at half filling. Phys. Rev. B 70, 235419 (2004).

  15. 15.

    et al. Orbital Kondo effect in carbon nanotubes. Nature 434, 484–488 (2005).

  16. 16.

    ‘s-d’ exchange model of zero-bias tunnelling anomalies. Phys. Rev. Lett. 17, 91–95 (1966).

  17. 17.

    , & Nonequilibrium transport through a Kondo dot in a magnetic field: perturbation theory. Phys. Rev. B 69, 155330 (2004).

  18. 18.

    , & Resonance kondo tunnelling through a double quantum dot at finite bias. Phys. Rev. B 68, 155323 (2003).

  19. 19.

    , & Shell filling and exchange coupling in metallic single-walled carbon nanotubes. Phys. Rev. Lett. 88, 126801 (2002).

  20. 20.

    , & The Kondo effect in an artificial quantum dot molecule. Science 293, 2221–2223 (2001).

  21. 21.

    & Inelastic co-tunnelling through an excited state of a quantum dot. Preprint at <> (2001).

  22. 22.

    & Transport through a double quantum dot in the sequential tunnelling and cotunnelling regimes. Phys. Rev. B 69, 245327 (2004).

  23. 23.

    , & Spin configurations of a carbon nanotube in a nonuniform external potential. Phys. Rev. Lett. 85, 365–368 (2000).

  24. 24.

    et al. Electronic excitation spectrum of metallic carbon nanotubes. Phys. Rev. B 71, 153402 (2005).

  25. 25.

    A poor man’s derivation of scaling laws for the Kondo problem. J. Phys. C 3, 2436–2441 (1966).

  26. 26.

    , , & Nonequilibrium transport through a Kondo dot in a magnetic field: perturbation theory and poor man’s scaling. Phys. Rev. Lett. 90, 076804 (2003).

  27. 27.

    , , & The Kondo effect in non-equilibrium quantum dots: perturbative renormalization group. J. Phys. Soc. Japan 74, 118–126 (2005).

  28. 28.

    , , & Nonequilibrium transport through a Kondo dot: decoherence effects. Phys. Rev. B 70, 155301 (2004).

Download references

Acknowledgements

We thank L. DiCarlo and W. F. Koehl for experimental contributions and D. H. Cobden and V. Körting for useful discussions. This research was supported by the Center for Functional Nanostructures of the DFG (J.P., P.W.), the European Commission through project FP6-003673 CANEL of the IST Priority (J.P.), ARO/ARDA (DAAD19-02-1-0039), NSF-NIRT (EIA-0210736) (N.M., C.M.M.) and the Danish Technical Research Council (J.N.).

Author information

Affiliations

  1. The Niels Bohr Institute & The Nano-Science Center, University of Copenhagen, DK-2100 Copenhagen, Denmark

    • J. Paaske
    •  & J. Nygård
  2. Institut für Theoretische Physik, Universität zu Köln, 50937 Köln, Germany

    • A. Rosch
  3. Institut für Theorie der Kondensierten Materie, Universität Karlsruhe, 76128 Karlsruhe, Germany

    • P. Wölfle
  4. Department of Physics, University of Illinois at Urbana Champaign, Urbana, Illinois 61801-3080, USA

    • N. Mason
  5. Department of Physics, Harvard University, Cambridge, Massachusetts 0213, USA

    • N. Mason
    •  & C. M. Marcus

Authors

  1. Search for J. Paaske in:

  2. Search for A. Rosch in:

  3. Search for P. Wölfle in:

  4. Search for N. Mason in:

  5. Search for C. M. Marcus in:

  6. Search for J. Nygård in:

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to J. Paaske.

Supplementary information

About this article

Publication history

Received

Accepted

Published

DOI

https://doi.org/10.1038/nphys340

Further reading