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.

Observation of the two-channel Kondo effect

Abstract

Some of the most intriguing problems in solid-state physics arise when the motion of one electron dramatically affects the motion of surrounding electrons. Traditionally, such highly correlated electron systems have been studied mainly in materials with complex transition metal chemistry1,2. Over the past decade, researchers have learned to confine one or a few electrons within a nanometre-scale semiconductor ‘artificial atom’, and to understand and control this simple system in detail3. Here we combine artificial atoms to create a highly correlated electron system within a nano-engineered semiconductor structure3. We tune the system in situ through a quantum phase transition between two distinct states, each a version of the Kondo state4, in which a bound electron interacts with surrounding mobile electrons. The boundary between these competing Kondo states is a quantum critical point—namely, the exotic and previously elusive two-channel Kondo state5,6, in which electrons in two reservoirs are entangled through their interaction with a single localized spin.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Figure 1: One and two-channel Kondo effects.
Figure 2: Artificial magnetic impurity.
Figure 3: The formation of two competing 1CK states with two different reservoirs.
Figure 4: Evidence for 2CK physics.

References

  1. 1

    Pruschke, T., Jarrel, M. & Freericks, J. Anomalous normal-state properties of high T c superconductors: Intrinsic properties of strongly correlated electron systems? Adv. Phys. 44, 187–210 (1995)

    ADS  CAS  Article  Google Scholar 

  2. 2

    Cox, D. L. & Zawadowski, A. Exotic Kondo effects in metals: magnetic ions in a crystalline electric field and tunnelling centres. Adv. Phys. 47, 599–942 (1998)

    CAS  Article  Google Scholar 

  3. 3

    Hanson, R., Kouwenhoven, L. P., Petta, J. R., Tarucha, S. & Vandersypen, L. M. K. Spins in few-electron quantum dots. Preprint at 〈http://arxiv.org/cond-mat/0610433〉 (2006)

  4. 4

    Oreg, Y. & Goldhaber-Gordon, D. Two-channel Kondo effect in a modified single electron transistor. Phys. Rev. Lett. 90, 136602 (2003)

    ADS  Article  Google Scholar 

  5. 5

    Wilson, K. G. The renormalization group: critical phenomena and the Kondo problem. Rev. Mod. Phys. 47, 773–840 (1974)

    ADS  MathSciNet  Article  Google Scholar 

  6. 6

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

    Article  Google Scholar 

  7. 7

    Zawadowski, A. Kondo-like state in a simple model for metallic glasses. Phys. Rev. Lett. 45, 211–214 (1980)

    ADS  CAS  Article  Google Scholar 

  8. 8

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

    ADS  CAS  Article  Google Scholar 

  9. 9

    Grobis, M., Rau, I. G., Potok, R. M. & Goldhaber-Gordon, D. Kondo effect in mesoscopic quantum dots. Preprint at 〈http://arxiv.org/cond-mat/0611480〉 (2006)

  10. 10

    Kondo, J. Resistance minimum in dilute magnetic alloys. Prog, Theor. Phys. 32, 37–49 (1964)

    ADS  CAS  Article  Google Scholar 

  11. 11

    Affleck, I. & Ludwig, A. W. W. Exact conformal-field-theory results on the multichannel Kondo effect: single-fermion Green’s function, self-energy, and resistivity. Phys. Rev. B 48, 7297–7321 (1993)

    ADS  CAS  Article  Google Scholar 

  12. 12

    Cox, D. L. Quadrupolar Kondo effect in uranium heavy-electron materials. Phys. Rev. Lett. 59, 1240–1243 (1987)

    ADS  CAS  Article  Google Scholar 

  13. 13

    Seaman, C. L. et al. Evidence for non-Fermi-liquid behavior in the Kondo alloy Y1-xUxPd3 . Phys. Rev. Lett. 67, 2882–2885 (1991)

    ADS  CAS  Article  Google Scholar 

  14. 14

    Besnus, M. J. et al. Specific-heat and NMR of the Kondo system YbPd2Si2 . J. Magn. Magn. Mater. 76–7, 471–472 (1988)

    ADS  Article  Google Scholar 

  15. 15

    Ralph, D. C. & Buhrman, R. A. Observations of Kondo scattering without magnetic-impurities — a point contact study of 2-level tunneling systems in metals. Phys. Rev. Lett. 69, 2118–2121 (1992)

    ADS  CAS  Article  Google Scholar 

  16. 16

    Ralph, D. C., Ludwig, A. W. W., von Delft, J. & Buhrman, R. A. 2-channel Kondo scaling in conductance signals from 2-level tunneling systems. Phys. Rev. Lett. 72, 1064–1067 (1994)

    ADS  CAS  Article  Google Scholar 

  17. 17

    Cichorek, T. et al. Two-channel Kondo effect in glasslike ThAsSe. Phys. Rev. Lett. 94, 236603 (2005)

    ADS  CAS  Article  Google Scholar 

  18. 18

    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 

  19. 19

    Costi, T. A. & Hewson, A. C. Transport coefficients of the Anderson model via the numerical renormalization group. J. Phys. Condens. Matter 6, 2519–2558 (1994)

    ADS  CAS  Article  Google Scholar 

  20. 20

    Goldhaber-Gordon, D. et al. From the Kondo regime to the mixed-valence regime in a single-electron transistor. Phys. Rev. Lett. 81, 5225–5228 (1998)

    ADS  CAS  Article  Google Scholar 

  21. 21

    Göres, J. et al. Fano resonances in electronic transport through a single-electron transistor. Phys. Rev. B 62, 2188–2194 (2000)

    ADS  Article  Google Scholar 

  22. 22

    Majumdar, K., Schiller, A. & Hershfield, S. Nonequilibrium Kondo impurity: Perturbation about an exactly solvable point. Phys. Rev. B 57, 2991–2999 (1998)

    ADS  CAS  Article  Google Scholar 

  23. 23

    Hettler, M. H., Kroha, J. & Hershfield, S. Nonlinear conductance for the two channel Anderson model. Phys. Rev. Lett. 73, 1967–1970 (1994)

    ADS  CAS  Article  Google Scholar 

  24. 24

    Oreg, Y. & Goldhaber-Gordon, D. Physics of Zero and One Dimensional Nanoscopic Systems (Springer Series in Solid State Sciences, Springer, in the press).

  25. 25

    Pustilnik, M., Borda, L., Glazman, L. & von Delft, J. Quantum phase transition in a two-channel-Kondo quantum dot device. Phys. Rev. B 69, 115316 (2004)

    ADS  Article  Google Scholar 

  26. 26

    von Delft, J., Ludwig, A. W. W. & Ambegaokar, V. The 2-channel Kondo model. II. CFT calculation of non-equilibrium conductance through a nanoconstriction containing 2-channel Kondo impurities. Ann. Phys. 273, 175–241 (1999)

    ADS  CAS  Article  Google Scholar 

  27. 27

    Florens, S. & Rosch, A. Climbing the entropy barrier: Driving the single- towards the multichannel Kondo effect by a weak Coulomb blockade of the leads. Phys. Rev. Lett. 92, 216601 (2004)

    ADS  CAS  Article  Google Scholar 

  28. 28

    Lebanon, E., Schiller, A. & Anders, F. B. Enhancement of the two-channel Kondo effect in single-electron boxes. Phys. Rev. B 68, 155301 (2003)

    ADS  Article  Google Scholar 

  29. 29

    Le Hur, K., Simon, P. & Borda, L. Maximized orbital and spin Kondo effects in a single-electron transistor. Phys. Rev. B 69, 045326 (2004)

    ADS  Article  Google Scholar 

  30. 30

    Haldane, F. D. M. Scaling theory of the asymmetric Anderson model. Phys. Rev. Lett. 40, 416–419 (1978)

    ADS  CAS  Article  Google Scholar 

Download references

Acknowledgements

We thank A. Schiller, E. Lebanon, F. Anders, I. Affleck, T. Costi, L. Glazman, K. Le Hur, C. Marcus, M. Pustilnik, E. Sela, J. von Delft and G. Zarand for discussions. E. Lebanon and F. Anders also performed NRG calculations that gave us crucial intuition regarding where our experimental system was in parameter space. S. Roy helped us understand how to perform nonlinear fits to determine the exponents α and α2 for the energy dependence in both 1CK and 2CK regimes. This work was supported by an NSF CAREER Award, a US-Israel BSF Award, DIP and ISF. D.G.-G. acknowledges Fellowships from the Sloan and Packard Foundations, and a Research Corporation Research Innovation Award. R.M.P. was supported by an ARO Graduate Fellowship during the early stages of this work.

Author information

Affiliations

Authors

Corresponding author

Correspondence to D. Goldhaber-Gordon.

Ethics declarations

Competing interests

Reprints and permissions information is available at www.nature.com/reprints. The authors declare no competing financial interests.

Supplementary information

Supplementary Discussion

This file contains Supplementary Discussion of data analysis and interpretation with brief mention of measurement techniques and relations to other proposed experimental two-channel Kondo systems. The file also contains Supplementary Figures S1-S7 with Legends and additional references. (PDF 382 kb)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Potok, R., Rau, I., Shtrikman, H. et al. Observation of the two-channel Kondo effect. Nature 446, 167–171 (2007). https://doi.org/10.1038/nature05556

Download citation

Further reading

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

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