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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The data that support the findings of this study are available from the corresponding authors upon reasonable request.
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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.
The authors declare no competing interests.
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
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.
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∞.
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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