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Non-equilibrium singlet–triplet Kondo effect in carbon nanotubes

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.

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Figure 1: Experimental setup and shell-filling scheme for a single-wall carbon nanotube.
Figure 2: Temperature and magnetic-field dependence of the finite-bias resonance.
Figure 3: Schematic diagram of the inelastic spin-exchange underlying the Kondo effect.
Figure 4: Fitting the nonlinear conductance by perturbative RG calculation.

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References

  1. Hewson, A. C. The Kondo Problem to Heavy Fermions (Cambridge Univ. Press, Cambridge, 1993).

    Book  Google Scholar 

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

    ADS  Google Scholar 

  3. Ng, T. & Lee, P. A. On-site Coulomb repulsion and resonant tunnelling. Phys. Rev. Lett. 61, 1768–1771 (1988).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  5. Cronenwett, S. M., Oosterkamp, T. H. & Kouwenhoven, L. P. A tunable Kondo effect in quantum dots. Science 281, 540–544 (1998).

    Article  ADS  Google Scholar 

  6. van der Wiel, W. G. et al. The Kondo effect in the unitary limit. Science 289, 2105–2108 (2000).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  8. Kogan, A., Granger, G., Kastner, M. A. & Goldhaber-Gordon, D. Singlet-triplet transition in a single-electron transistor at zero magnetic field. Phys. Rev. B 67, 113309 (2003).

    Article  ADS  Google Scholar 

  9. Zumbühl, D. M., Marcus, C. M., Hanson, M. P. & Gossard, A. C. Cotunnelling spectroscopy in few-electron quantum dots. Phys. Rev. Lett. 93, 256801 (2004).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  11. Nygård, J., Cobden, D. H. & Lindelof, P. E. Kondo physics in carbon nanotubes. Nature 408, 342–346 (2000).

    Article  ADS  Google Scholar 

  12. Liang, W., Shores, M. P., Bockrath, M., Long, J. R. & Park, H. Kondo resonance in a single-molecule transistor. Nature 417, 725–729 (2002).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  14. Babić, B., Kontos, T. & Schönenberger, C. Kondo effect in carbon nanotubes at half filling. Phys. Rev. B 70, 235419 (2004).

    Article  ADS  Google Scholar 

  15. Jarillo-Herrero, P. et al. Orbital Kondo effect in carbon nanotubes. Nature 434, 484–488 (2005).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  17. Paaske, J., Rosch, A. & Wölfle, P. Nonequilibrium transport through a Kondo dot in a magnetic field: perturbation theory. Phys. Rev. B 69, 155330 (2004).

    Article  ADS  Google Scholar 

  18. Kiselev, M. N., Kikoin, K. & Molenkamp, L. W. Resonance kondo tunnelling through a double quantum dot at finite bias. Phys. Rev. B 68, 155323 (2003).

    Article  ADS  Google Scholar 

  19. Liang, W., Bockrath, M. & Park, H. Shell filling and exchange coupling in metallic single-walled carbon nanotubes. Phys. Rev. Lett. 88, 126801 (2002).

    Article  ADS  Google Scholar 

  20. Jeong, H., Chang, A. M. & Melloch, M. R. The Kondo effect in an artificial quantum dot molecule. Science 293, 2221–2223 (2001).

    Article  ADS  Google Scholar 

  21. Wegewijs, M. R. & Nazarov, Yu. V. Inelastic co-tunnelling through an excited state of a quantum dot. Preprint at <http://arxiv.org/abs/cond-mat/0103579> (2001).

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

    Article  ADS  Google Scholar 

  23. Oreg, Y., Byczuk, K. & Halperin, B. I. Spin configurations of a carbon nanotube in a nonuniform external potential. Phys. Rev. Lett. 85, 365–368 (2000).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  26. Rosch, A., Paaske, J., Kroha, J. & Wölfle, P. Nonequilibrium transport through a Kondo dot in a magnetic field: perturbation theory and poor man’s scaling. Phys. Rev. Lett. 90, 076804 (2003).

    Article  ADS  Google Scholar 

  27. Rosch, A., Paaske, J., Kroha, J. & Wölfle, P. The Kondo effect in non-equilibrium quantum dots: perturbative renormalization group. J. Phys. Soc. Japan 74, 118–126 (2005).

    Article  ADS  Google Scholar 

  28. Paaske, J., Rosch, A., Kroha, J. & Wölfle, P. Nonequilibrium transport through a Kondo dot: decoherence effects. Phys. Rev. B 70, 155301 (2004).

    Article  ADS  Google Scholar 

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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.).

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Paaske, J., Rosch, A., Wölfle, P. et al. Non-equilibrium singlet–triplet Kondo effect in carbon nanotubes. Nature Phys 2, 460–464 (2006). https://doi.org/10.1038/nphys340

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