Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

Quantum phase transition in a single-molecule quantum dot

Nature volume 453, pages 633–637 (2008)Cite this article

Abstract

Quantum criticality is the intriguing possibility offered by the laws of quantum mechanics when the wave function of a many-particle physical system is forced to evolve continuously between two distinct, competing ground states1. This phenomenon, often related to a zero-temperature magnetic phase transition, is believed to govern many of the fascinating properties of strongly correlated systems such as heavy-fermion compounds or high-temperature superconductors1. In contrast to bulk materials with very complex electronic structures, artificial nanoscale devices could offer a new and simpler means of understanding quantum phase transitions2,3. Here we demonstrate this possibility in a single-molecule quantum dot, where a gate voltage induces a crossing of two different types of electron spin state (singlet and triplet) at zero magnetic field. The quantum dot is operated in the Kondo regime, where the electron spin on the quantum dot is partially screened by metallic electrodes. This strong electronic coupling between the quantum dot and the metallic contacts provides the strong electron correlations necessary to observe quantum critical behaviour. The quantum magnetic phase transition between two different Kondo regimes is achieved by tuning gate voltages and is fundamentally different from previously observed Kondo transitions in semiconductor and nanotube quantum dots4,5. Our work may offer new directions in terms of control and tunability for molecular spintronics6.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Quantum phase transition, device and conductance characteristics.
Figure 2: Magnetic field and gate-induced singlet–triplet transition.
Figure 3: Singlet–triplet quantum phase transition and universal scaling.
Figure 4: Kondo effects in the singlet and triplet states.

Similar content being viewed by others

References

  1. Sachdev, S. Quantum magnetism and criticality. Nature Phys. 4, 173–185 (2008)

    Article  CAS  ADS  Google Scholar 

  2. Vojta, M., Bulla, R. & Hofstetter, W. Quantum phase transitions in models of coupled magnetic impurities. Phys. Rev. B 65, 140405 (2002)

    Article  ADS  Google Scholar 

  3. Hofstetter, W. & Schoeller, H. Quantum phase transition in a multilevel dot. Phys. Rev. Lett. 88, 016803 (2002)

    Article  ADS  Google Scholar 

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

    Article  CAS  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  6. Bogani, L. & Wernsdorfer, W. Molecular spintronics using single-molecule magnets. Nature Mater. 7, 179–186 (2008)

    Article  CAS  ADS  Google Scholar 

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

    Book  Google Scholar 

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

    ADS  Google Scholar 

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

    Article  CAS  ADS  Google Scholar 

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

    Article  CAS  ADS  Google Scholar 

  11. Georges, A. & Meir, Y. Electronic correlations in transport through coupled quantum dots. Phys. Rev. Lett. 82, 3508–3511 (1999)

    Article  CAS  ADS  Google Scholar 

  12. Jones, B. A., Varma, C. M. & Wilkins, J. W. Low-temperature properties of the two-impurity Kondo hamiltonian. Phys. Rev. Lett. 61, 125–128 (1988)

    Article  CAS  ADS  Google Scholar 

  13. Affleck, I., Ludwig, A. W. W. & Jones, B. A. Conformal-field-theory approach to the two-impurity Kondo problem: Comparison with numerical renormalization-group results. Phys. Rev. B 52, 9528–9546 (1995)

    Article  CAS  ADS  Google Scholar 

  14. Zarand, G., Chung, C.-H., Simon, P. & Vojta, M. Quantum criticality in a double-quantum-dot system. Phys. Rev. Lett. 97, 166802 (2006)

    Article  ADS  Google Scholar 

  15. 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  CAS  ADS  Google Scholar 

  16. Park, H., Lim, A. K. L., Alivisatos, A. P., Park, J. & McEuen, P. L. Fabrication of metallic electrodes with nanometer separation by electromigration. Appl. Phys. Lett. 75, 301–303 (1999)

    Article  CAS  ADS  Google Scholar 

  17. Park, H. et al. Nanomechanical oscillations in a single-C60 transistor. Nature 407, 57–60 (2000)

    Article  CAS  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  19. Quay, C. H. L. et al. Magnetic field dependence of the spin-1/2 and spin-1 Kondo effects in a quantum dot. Phys. Rev. B 76, 245311 (2007)

    Article  ADS  Google Scholar 

  20. Holm, J. V. et al. Gate-dependent tunneling-induced level shifts in carbon nanotube quantum dots. Preprint at 〈http://aps.arxiv.org/abs/0711.4913〉 (2007)

  21. Paaske, J. et al. Non-equilibrium singlet-triplet Kondo effect in carbon nanotubes. Nature Phys. 2, 460–464 (2006)

    Article  CAS  ADS  Google Scholar 

  22. Nozières, P. & Blandin, A. Kondo effect in real metals. J. Phys. (Paris) 41, 193–211 (1980)

    Article  Google Scholar 

  23. Pustilnik, M. & Glazman, L. I. Kondo effect induced by a magnetic field. Phys. Rev. B 64, 045328 (2001)

    Article  ADS  Google Scholar 

  24. Pustilnik, M., Avishai, Y. & Kikoin, K. Quantum dot with even number of electrons: Kondo effect in a finite magnetic field. Phys. Rev. Lett. 84, 1756–1759 (2000)

    Article  CAS  ADS  Google Scholar 

  25. Craig, N. J. et al. Tunable nonlocal spin control in a coupled-quantum dot system. Science 304, 565–567 (2004)

    Article  CAS  ADS  Google Scholar 

  26. Grobis, M., Rau, I. G., Potok, R. M. & Goldhaber-Gordon, D. Kondo effect in mesoscopic quantum dots, in Handbook of Magnetism and Magnetic Materials Vol. 1 (eds Kronmüller, H. & Parkin, S.) Part II (Wiley, Chichester, 2007)

    Google Scholar 

  27. Costi, T. A. Kondo effect in a magnetic field and the magnetoresistivity of Kondo alloys. Phys. Rev. Lett. 85, 1504–1507 (2000)

    Article  CAS  ADS  Google Scholar 

  28. Potok, R. M., Rau, I. G., Shtrikman, H., Oreg, Y. & Goldhaber-Gordon, D. Observation of the two-channel Kondo effect. Nature 446, 167–171 (2006)

    Article  ADS  Google Scholar 

  29. Hofstetter, W. & Zarand, G. Singlet-triplet transition in lateral quantum dots: A numerical renormalization group study. Phys. Rev. B 69, 235301 (2004)

    Article  ADS  Google Scholar 

  30. Yu, L. H. & Natelson, D. The Kondo effect in C60 single-molecule transistors. Nano Lett. 4, 79–83 (2004)

    Article  CAS  ADS  Google Scholar 

  31. Pasupathy, A. N. et al. The Kondo effect in the presence of ferromagnetism. Science 306, 86–89 (2004)

    Article  CAS  ADS  Google Scholar 

  32. Parks, J. J. et al. Tuning the Kondo effect with a mechanically controllable break junction. Phys. Rev. Lett. 99, 026601 (2007)

    Article  CAS  ADS  Google Scholar 

  33. Strachan, D. R. et al. Controlled fabrication of nanogaps in ambient environment for molecular electronics. Appl. Phys. Lett. 86, 043109 (2005)

    Article  ADS  Google Scholar 

  34. Houck, A. A., Labaziewicz, J., Chan, E. K., Folk, J. A. & Chuang, I. L. Kondo effect in electromigrated gold break junctions. Nano Lett. 5, 1685–1688 (2005)

    Article  CAS  ADS  Google Scholar 

  35. Esen, G. & Fuhrer, M. S. Temperature control of electromigration to form gold nanogap junctions. Appl. Phys. Lett. 87, 263101 (2005)

    Article  ADS  Google Scholar 

  36. Trouwborst, M. L., van der Molen, S. J. & van Wees, B. J. The role of Joule heating in the formation of nanogaps by electromigration. J. Appl. Phys. 99, 114316 (2006)

    Article  ADS  Google Scholar 

  37. O'Neill, K., Osorio, E. A. & van der Zant, H. S. J. Self-breaking in planar few-atom Au constrictions for nanometer-spaced electrodes. Appl. Phys. Lett. 90, 133109 (2007)

    Article  ADS  Google Scholar 

  38. Wu, Z. M. et al. Feedback controlled electromigration in four-terminal nanojunctions. Appl. Phys. Lett. 91, 053118 (2007)

    Article  ADS  Google Scholar 

  39. van der Zant, H. S. J. et al. Molecular three-terminal devices: fabrication and measurements. Faraday Discuss. 131, 347–356 (2006)

    Article  CAS  ADS  Google Scholar 

Download references

Acknowledgements

We acknowledge E. Eyraud and D. Lepoittevin for discussions and technical contributions regarding electronics and dilutions. We thank E. Bonet, T. Crozes and T. Fournier for lithography development, and C. Winkelmann, T. Costi and L. Calvet for discussions. The sample used in the investigations was made in the NANOFAB facility of the Néel Institut. This work is partially financed by ANR-PNANO, Contract MolSpintronics.

Author information

Authors and Affiliations

  1. Institut Néel, CNRS and Université Joseph Fourier, BP 166, 38042 Grenoble cedex 9, France,

    Nicolas Roch, Serge Florens, Vincent Bouchiat, Wolfgang Wernsdorfer & Franck Balestro

Authors
  1. Nicolas Roch
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Serge Florens
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Vincent Bouchiat
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Wolfgang Wernsdorfer
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Franck Balestro
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Franck Balestro.

Supplementary information

Supplementray Information

The file contains Supplementray Notes, Supplementray Fugures S1-S6 with Legends and additional references. The Supplementray Information includes the following parts: 1. Experimental setup ; 2. Fully-screened spin S=1/2 Kondo effect in a C60 quantum dot ; 3. Non-equilibrium singlet-triplet Kondo effect on the singlet side ; 4. Singlet-triplet transition: low versus very low temperature ; 5. Temperature dependence of the zero-bias conductance ; 6. Statistics and reproducibility of the results. (PDF 6050 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Roch, N., Florens, S., Bouchiat, V. et al. Quantum phase transition in a single-molecule quantum dot. Nature 453, 633–637 (2008). https://doi.org/10.1038/nature06930

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature06930

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing