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Observation of the Kondo screening cloud

Abstract

When a magnetic impurity exists in a metal, conduction electrons form a spin cloud that screens the impurity spin. This basic phenomenon is called the Kondo effect1,2. Unlike electric-charge screening, the spin-screening cloud3,4,5,6 occurs quantum coherently, forming spin-singlet entanglement with the impurity. Although the spins interact locally around the impurity, the Kondo cloud can theoretically spread out over several micrometres. The cloud has not so far been detected, and so its physical existence—a fundamental aspect of the Kondo effect—remains controversial7,8. Here we present experimental evidence of a Kondo cloud extending over a length of micrometres, comparable to the theoretical length ξK. In our device, a Kondo impurity is formed in a quantum dot2,9,10,11, coupling on one side to a quasi-one-dimensional channel12 that houses a Fabry–Pérot interferometer of various gate-defined lengths L exceeding one micrometre. When we sweep a voltage on the interferometer end gate—separated by L from the quantum dot—to induce Fabry–Pérot oscillations in conductance we observe oscillations in the measured Kondo temperature TK, which is a signature of the Kondo cloud at distance L. When L is less than ξK the TK oscillation amplitude becomes larger as L becomes smaller, obeying a scaling function of a single parameter L/ξK, whereas when L is greater than ξK the oscillation is much weaker. Our results reveal that ξK is the only length parameter associated with the Kondo effect, and that the cloud lies mostly within a length of ξK. Our experimental method offers a way of detecting the spatial distribution of exotic non-Fermi liquids formed by multiple magnetic impurities or multiple screening channels13,14,15,16 and of studying spin-correlated systems.

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Fig. 1: Measurement setup and characterization.
Fig. 2: Influence of FP interference on the Kondo effect.
Fig. 3: Shape of the Kondo cloud revealed from modulation of the Kondo temperature.

Data availability

The data that support the findings of this study are available from the corresponding authors upon reasonable request.

References

  1. 1.

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

  2. 2.

    Glazman, L. I. & Pustilnik, M. Low-temperature transport through a quantum dot. In Nanophysics: Coherence and Transport (ed. Bouchiat, H. et al.) 427–478 (Elsevier, 2005).

  3. 3.

    Affleck, I. The Kondo screening cloud: what it is and how to observe it. In Perspectives of Mesoscopic Physics (eds Aharony, A. & Entin-Wohlman, O.) Ch. 1, 1–44 (World Scientific Publishing, 2010).

  4. 4.

    Grüner, G. & Zawadowski, A. Magnetic impurities in non-magnetic metals. Rep. Prog. Phys. 37, 1497–1583 (1974).

    ADS  Google Scholar 

  5. 5.

    Gubernatis, J. E., Hirsch, J. E. & Scalapino, D. J. Spin and charge correlations around an Anderson magnetic impurity. Phys. Rev. B 35, 8478 (1987).

    ADS  CAS  Google Scholar 

  6. 6.

    Barzykin, V. & Affleck, I. The Kondo screening cloud: what can we learn from perturbation theory? Phys. Rev. Lett. 76, 4959 (1996).

    ADS  CAS  PubMed  Google Scholar 

  7. 7.

    Boyce, J. P. & Slichter, C. P. Conduction-electron spin density around Fe impurities in Cu above and below T K. Phys. Rev. Lett. 32, 61 (1974).

    ADS  CAS  Google Scholar 

  8. 8.

    Sørensen, E. S. & Affleck, I. Scaling theory of the Kondo screening cloud. Phys. Rev. B 53, 9153 (1996).

    ADS  Google Scholar 

  9. 9.

    Goldhaber-Gordon, D., Shtrikman, H., Mahalu, D., Abusch-Magder, D. & Meirav, U. Kondo effect in a single-electron transistor. Nature 391, 156–159 (1998).

    ADS  CAS  Google Scholar 

  10. 10.

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

    ADS  CAS  PubMed  Google Scholar 

  11. 11.

    Kouwenhoven, L. P. & Glazman, L. I. Revival of the Kondo effect. Phys. World 14, 33–38 (2001).

    CAS  Google Scholar 

  12. 12.

    Park, J., Lee, S.-S. B., Oreg, Y. & Sim, H.-S. How to directly measure a Kondo cloud’s length. Phys. Rev. Lett. 110, 246603 (2013).

    ADS  PubMed  Google Scholar 

  13. 13.

    Cox, D. L. & Jarrell, M. The two-channel Kondo route to non-Fermi-liquid metals. J. Phys. Condens. Matter 8, 9825–9853 (1996).

    ADS  CAS  Google Scholar 

  14. 14.

    Affleck, I. Non-Fermi liquid behavior in Kondo models. J. Phys. Soc. Jpn 74, 59–66 (2005).

    ADS  CAS  Google Scholar 

  15. 15.

    Potok, R. M., Rau, I. G., Shtrikman, H., Oreg, Y. & Goldhaber-Gordon, D. Observation of the two-channel Kondo effect. Nature 446, 167–171 (2007).

    ADS  CAS  PubMed  Google Scholar 

  16. 16.

    Iftikhar, Z. et al. Two-channel Kondo effect and renormalization flow with macroscopic quantum charge states. Nature 526, 233–236 (2015).

    ADS  CAS  PubMed  Google Scholar 

  17. 17.

    Prüser, H. et al. Long-range Kondo signature of a single magnetic impurity. Nat. Phys. 7, 203–206 (2011).

    Google Scholar 

  18. 18.

    Borda, L. Kondo screening cloud in a one-dimensional wire: numerical renormalization group study. Phys. Rev. B 75, 041307 (2007).

    ADS  Google Scholar 

  19. 19.

    Thimm, W. B., Kroha, J. & von Delft, J. Kondo box: a magnetic impurity in an ultrasmall metallic grain. Phys. Rev. Lett. 82, 2143 (1999).

    ADS  CAS  Google Scholar 

  20. 20.

    Simon, P. & Affleck, I. Finite-size effects in conductance measurements on quantum dots. Phys. Rev. Lett. 89, 206602 (2002).

    ADS  PubMed  Google Scholar 

  21. 21.

    Bomze, Yu. et al. Two-stage Kondo effect and Kondo-box level spectroscopy in a carbon nanotube. Phys. Rev. B 82, 161411 (2010).

    ADS  Google Scholar 

  22. 22.

    Holzner, A., McCulloch, I. P., Schollwöck, U., von Delft, J. & Heidrich-Meisner, F. Kondo screening cloud in the single-impurity Anderson model: a density matrix renormalization group study. Phys. Rev. B 80, 205114 (2009).

    ADS  Google Scholar 

  23. 23.

    Büsser, C. A. et al. Numerical analysis of the spatial range of the Kondo effect. Phys. Rev. B 81, 045111 (2010).

    ADS  Google Scholar 

  24. 24.

    Mitchell, A. K., Becker, M. & Bulla, R. Real-space renormalization group flow in quantum impurity systems: local moment formation and the Kondo screening cloud. Phys. Rev. B 84, 115120 (2011).

    ADS  Google Scholar 

  25. 25.

    Lee, S.-S. B., Park, J. & Sim, H.-S. Macroscopic quantum entanglement of a Kondo cloud at finite temperature. Phys. Rev. Lett. 114, 057203 (2015).

    ADS  PubMed  Google Scholar 

  26. 26.

    Takada, S. et al. Transmission phase in the Kondo regime revealed in a two-path interferometer. Phys. Rev. Lett. 113, 126601 (2014).

    ADS  CAS  PubMed  Google Scholar 

  27. 27.

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

    ADS  PubMed  Google Scholar 

  28. 28.

    van Houten, H. et al. Coherent electron focusing with quantum point contacts in a two-dimensional electron gas. Phys. Rev. B 39, 8556 (1989).

    ADS  Google Scholar 

  29. 29.

    Kouwenhoven, L. P. et al. Electron transport in quantum dots. In Mesoscopic Electron Transport (eds Sohn, L. L., Kouwenhoven, L. P. & Schön, G.) NATO Advanced Study Institutes Series E, Vol. 345, 105–214 (Kluwer Academic, 1997).

  30. 30.

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

    ADS  CAS  Google Scholar 

  31. 31.

    Noziéres, P. A Fermi-liquid description of the Kondo problem at low temperatures. J. Low Temp. Phys. 17, 31–42 (1974).

    ADS  Google Scholar 

  32. 32.

    Yoo, G., Lee, S.-S. B. & Sim, H.-S. Detecting Kondo entanglement by electron conductance. Phys. Rev. Lett. 120, 146801 (2018).

    ADS  CAS  PubMed  Google Scholar 

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Acknowledgements

I.V.B. acknowledges CityU New Research Initiatives/Infrastructure Support from Central (APRC) (grant number 9610395), and the Hong Kong Research Grants Council (ECS) Project (grant number 21301818). S.T. and M.Y. acknowledge KAKENHI (grant number 38000131). M.Y. acknowledges KAKENHI (grant number 18H04284) and CREST-JST (grant number JPMJCR1876). S.T. acknowledges CREST-JST (grant number JPMJCR1675). M.Y. acknowledges discussions with R. Sakano. H.-S.S. acknowledges support by Korea NRF via the SRC Center for Quantum Coherence in Condensed Matter (grant number 2016R1A5A1008184). A.L. and A.D.W. acknowledge support from DFG-TRR160,BMBF—Q.Link.X16KIS0867 and DFH/UFA CDFA-05-06.

Author information

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Contributions

I.V.B. performed the experimental measurements and analysed experimental data. J.S. and H.-S. S. performed the theoretical calculations. J.C.H.C. fabricated and characterized the device. A.L. and A.D.W. designed and grew the 2DEG wafer. M.Y. designed the experiment. M.Y. and S.T. supervised the project. All authors were involved in discussing results and preparing the manuscript.

Corresponding authors

Correspondence to Ivan V. Borzenets or H.-S. Sim or Michihisa Yamamoto.

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The authors declare no competing interests.

Additional information

Peer review information Nature thanks GuoPing Guo, Robert Peters and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data figures and tables

Extended Data Fig. 1 Calibration of measured sample temperature.

a, Conductance versus QD gate voltage VG taken at a temperature of 300 mK. The grey lines show the fit of the data to the theoretical lineshape for a Coulomb blockade peak. b, The electron temperature in our device Tcalibrated versus the lattice temperature measured by a thermometer located at the mixing chamber Tmeasured. c, Conductance of the Coulomb blockade peaks versus gate voltage (around the peak centre) δVG shown for several values of the measured temperature. (a.u., arbitrary units).

Extended Data Fig. 2 Full width at half maximum of a Coulomb blockade peak versus QPC gate voltage VQPC.

Data are shown for a Coulomb blockade peak away from the Kondo valley. The inset shows conductance G through the QD as a function of (shifted) gate voltage δVG and QPC gate voltage VQPC. Oscillations of both peak conductance and peak width with respect to VQPC are clearly observed.

Extended Data Fig. 3 Plot of conductance versus temperature at the centre of the Kondo valley.

The lines are fits to the empirical formula. a, The data in red correspond to VQPC, at which the minimum Kondo temperature was observed. The data in blue correspond to VQPC, at which the maximum Kondo temperature was observed. Green data points correspond to data taken at a midpoint beween the red and blue datasets. b, Data at VQPC = 0 V, for several QD settings corresponding to different L/ξK∞.

Extended Data Table 1 Coulomb-blockade peak FP oscillation amplitude
Extended Data Table 2 Fitting parameters with upper and lower bounds

Supplementary information

Supplementary Information

This file contains Supplementary text, which includes Supplementary Table S1 and Supplementary Figures S1-S4.

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V. Borzenets, I., Shim, J., Chen, J.C.H. et al. Observation of the Kondo screening cloud. Nature 579, 210–213 (2020). https://doi.org/10.1038/s41586-020-2058-6

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