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Two-channel Kondo effect and renormalization flow with macroscopic quantum charge states

Nature volume 526, pages 233236 (08 October 2015) | Download Citation

Abstract

Many-body correlations and macroscopic quantum behaviours are fascinating condensed matter problems. A powerful test-bed for the many-body concepts and methods is the Kondo effect1,2, which entails the coupling of a quantum impurity to a continuum of states. It is central in highly correlated systems3,4,5 and can be explored with tunable nanostructures6,7,8,9. Although Kondo physics is usually associated with the hybridization of itinerant electrons with microscopic magnetic moments10, theory predicts that it can arise whenever degenerate quantum states are coupled to a continuum4,11,12,13,14. Here we demonstrate the previously elusive ‘charge’ Kondo effect in a hybrid metal–semiconductor implementation of a single-electron transistor, with a quantum pseudospin of 1/2 constituted by two degenerate macroscopic charge states of a metallic island11,15,16,17,18,19,20. In contrast to other Kondo nanostructures, each conduction channel connecting the island to an electrode constitutes a distinct and fully tunable Kondo channel11, thereby providing unprecedented access to the two-channel Kondo effect and a clear path to multi-channel Kondo physics1,4,21,22. Using a weakly coupled probe, we find the renormalization flow, as temperature is reduced, of two Kondo channels competing to screen the charge pseudospin. This provides a direct view of how the predicted quantum phase transition develops across the symmetric quantum critical point4,21. Detuning the pseudospin away from degeneracy, we demonstrate, on a fully characterized device, quantitative agreement with the predictions for the finite-temperature crossover from quantum criticality17.

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Acknowledgements

This work was supported by the ERC (ERC-2010-StG-20091028, no. 259033) and the French RENATECH network. We acknowledge E. Boulat, J. von Delft, S. De Franceschi, L. Glazman, D. Goldhaber-Gordon, K. Le Hur, A. Keller, K. Matveev, L. Peeters, P. Simon and G. Zaránd for critical reading of our manuscript and discussions.

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Affiliations

  1. CNRS, Laboratoire de Photonique et de Nanostructures (LPN), 91460 Marcoussis, France

    • Z. Iftikhar
    • , S. Jezouin
    • , A. Anthore
    • , U. Gennser
    • , F. D. Parmentier
    • , A. Cavanna
    •  & F. Pierre
  2. Univ Paris Diderot, Sorbonne Paris Cité, LPN, 91460 Marcoussis, France

    • A. Anthore

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Contributions

Z.I. and F.P. performed the experiment. Z.I., A.A. and F.P. analysed the data. F.D.P. fabricated the sample. U.G. and A.C. grew the 2DEG. S.J. contributed to a preliminary experiment. F.P. led the project and wrote the manuscript with input from Z.I., A.A. and U.G.

Competing interests

The authors declare no competing financial interests.

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Correspondence to F. Pierre.

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https://doi.org/10.1038/nature15384

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