Skip to main content

Thank you for visiting 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.

Odd and even Kondo effects from emergent localization in quantum point contacts


A quantum point contact (QPC) is a basic nanometre-scale electronic device: a short and narrow transport channel between two electron reservoirs. In clean channels, electron transport is ballistic and the conductance is then quantized as a function of channel width1,2 with plateaux at integer multiples of 2e2/h (where e is the electron charge and h is Planck’s constant). This can be understood in a picture where the electron states are propagating waves, without the need to account for electron–electron interactions. Quantized conductance could thus be the signature of ultimate control over nanoscale electron transport. However, even studies with the cleanest QPCs generically show significant anomalies in the quantized conductance traces, and there is consensus that these result from electron many-body effects3,4. Despite extensive experimental and theoretical studies4,5,6,7,8,9,10,11, understanding these anomalies is an open problem. Here we report that the many-body effects have their origin in one or more spontaneously localized states that emerge from Friedel oscillations in the electron charge density within the QPC channel. These localized states will have electron spins associated with them, and the Kondo effect—related to electron transport through such localized electron spins—contributes to the formation of the many-body state5,6,7. We present evidence for such localization, with Kondo effects of odd or even character, directly reflecting the parity of the number of localized states; the evidence is obtained from experiments with length-tunable QPCs that show a periodic modulation of the many-body properties with Kondo signatures that alternate between odd and even Kondo effects. Our results are of importance for assessing the role of QPCs in more complex hybrid devices12,13 and for proposals for spintronic and quantum information applications14,15. In addition, our results show that tunable QPCs offer a versatile platform for investigating many-body effects in nanoscale systems, with the ability to probe such physics at the level of a single site.

Your institute does not have access to this article

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Conductance of quantum point contacts.
Figure 2: Length-tunable QPCs.
Figure 3: ZBAs in the nonlinear conductance of a QPC6F.
Figure 4: Comparison between experiments and theory of the Anderson model for a two-impurity Kondo system.


  1. van Wees, B. J. et al. Quantized conductance of point contacts in a two-dimensional electron gas. Phys. Rev. Lett. 60, 848–850 (1988)

    ADS  CAS  Article  Google Scholar 

  2. Wharam, D. A. et al. One-dimensional transport and the quantisation of the ballistic resistance. J. Phys. Chem. 21, L209–L214 (1988)

    Google Scholar 

  3. Thomas, K. J. et al. Possible spin polarization in a one-dimensional electron gas. Phys. Rev. Lett. 77, 135–138 (1996)

    ADS  CAS  Article  Google Scholar 

  4. Micolich, A. P. What lurks below the last plateau: experimental studies of the 0.7×2e2/h conductance anomaly in one-dimensional systems. J. Phys. Condens. Matter 23, 443201 (2011)

    ADS  CAS  Article  Google Scholar 

  5. Cronenwett, S. M. et al. Low-temperature fate of the 0.7 structure in a point contact: a Kondo-like correlated state in an open system. Phys. Rev. Lett. 88, 226805 (2002)

    ADS  CAS  Article  Google Scholar 

  6. Meir, Y., Hirose, K. & Wingreen, N. S. Kondo model for the “0.7 anomaly” in transport through a quantum point contact. Phys. Rev. Lett. 89, 196802 (2002)

    ADS  Article  Google Scholar 

  7. Rejec, T. & Meir, Y. Magnetic impurity formation in quantum point contacts. Nature 442, 900–903 (2006)

    ADS  CAS  Article  Google Scholar 

  8. Koop, E. J. et al. The influence of device geometry on many-body effects in quantum point contacts: signatures of the 0.7 anomaly, exchange and Kondo. J. Supercond. Nov. Magn. 20, 433–441 (2007)

    ADS  CAS  Article  Google Scholar 

  9. Komijani, Y. et al. Evidence for localization and 0.7 anomaly in hole quantum point contacts. Europhys. Lett. 91, 67010 (2010)

    ADS  Article  Google Scholar 

  10. Burke, A. M. et al. Extreme sensitivity of the spin-splitting and 0.7 anomaly to confining potential in one-dimensional nanoelectronic devices. Nano Lett. 12, 4495–4502 (2012)

    ADS  CAS  Article  Google Scholar 

  11. Wu, P. M., Li, P., Zhang, H. & Chang, A. M. Evidence for the formation of quasibound states in an asymmetrical quantum point contact. Phys. Rev. B 85, 085305 (2012)

    ADS  Article  Google Scholar 

  12. Mourik, V. et al. Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices. Science 336, 1003–1007 (2012)

    ADS  CAS  Article  Google Scholar 

  13. Churchill, H. O. H. et al. Superconductor-nanowire devices from tunneling to the multichannel regime: zero-bias oscillations and magnetoconductance crossover. Phys. Rev. B 87, 241401(R) (2013)

    ADS  Article  Google Scholar 

  14. Bertoni, A., Bordone, P., Brunetti, R., Jacoboni, C. & Reggiani, S. Quantum logic gates based on coherent electron transport in quantum wires. Phys. Rev. Lett. 84, 5912–5915 (2000)

    ADS  CAS  Article  Google Scholar 

  15. Blaauboer, M. & DiVincenzo, D. P. Detecting entanglement using a double-quantum-dot turnstile. Phys. Rev. Lett. 95, 160402 (2005)

    ADS  CAS  Article  Google Scholar 

  16. Bagraev, N. T., Shelykh, I. A., Ivanov, V. K. & Klyachkin, L. E. Spin depolarization in quantum wires polarized spontaneously in zero magnetic field. Phys. Rev. B 70, 155315 (2004)

    ADS  Article  Google Scholar 

  17. Tombros, N. et al. Quantized conductance of a suspended graphene nanoconstriction. Nature Phys. 7, 697–700 (2011)

    ADS  CAS  Article  Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

  20. Jeong, H., Chang, A. M. & Melloch, M. R. The Kondo effect in an artificial quantum dot molecule. Science 293, 2221–2223 (2001)

    ADS  CAS  Article  Google Scholar 

  21. Jones, B. A., Kotliar, B. G. & Millis, A. J. Mean-field analysis of 2 antiferromagnetically coupled Anderson impurities. Phys. Rev. B 39, 3415–3418 (1989)

    ADS  CAS  Article  Google Scholar 

  22. Ivanov, T. The nonlinear conductance of a double quantum dot in the Kondo regime. Europhys. Lett. 40, 183–188 (1997)

    ADS  CAS  Article  Google Scholar 

  23. Pohjola, T. et al. Resonant tunneling through a two-level dot and double quantum dots. Europhys. Lett. 40, 189–194 (1997)

    ADS  CAS  Article  Google Scholar 

  24. Aono, T., Eto, M. & Kawamura, K. Conductance through quantum dot dimer below the Kondo temperature. J. Phys. Soc. Jpn 67, 1860–1863 (1998)

    ADS  CAS  Article  Google Scholar 

  25. Georges, A. & Meir, Y. Electronic correlations in transport through coupled quantum dots. Phys. Rev. Lett. 82, 3508–3511 (1999)

    ADS  CAS  Article  Google Scholar 

  26. Aguado, R. & Langreth, D. C. Out-of-equilibrium Kondo effect in double quantum dots. Phys. Rev. Lett. 85, 1946–1949 (2000)

    ADS  CAS  Article  Google Scholar 

  27. Aguado, R. & Langreth, D. C. Kondo effect in coupled quantum dots: a noncrossing approximation study. Phys. Rev. B 67, 245307 (2003)

    ADS  Article  Google Scholar 

  28. Kanisawa, K., Butcher, M. J., Yamaguchi, H. & Hirayama, Y. Imaging of Friedel oscillation patterns of two-dimensionally accumulated electrons at epitaxially grown InAs(111)A surfaces. Phys. Rev. Lett. 86, 3384–3387 (2001)

    ADS  CAS  Article  Google Scholar 

  29. Vernek, E. et al. Kondo regime in triangular arrangements of quantum dots: molecular orbitals, interference, and contact effects. Phys. Rev. B 80, 035119 (2009)

    ADS  Article  Google Scholar 

  30. Simion, G. E. & Giuliani, G. F. Friedel oscillations in a Fermi liquid. Phys. Rev. B 72, 045127 (2005)

    ADS  Article  Google Scholar 

Download references


We thank B. J. van Wees, A. Aqeel, S. Ludwig, J. von Delft and Y. Komijani for discussions and B. Wolfs, J. Holstein and M. de Roosz for technical assistance. We acknowledge financial support from the German programmes DFG-SPP 1285, Research School Ruhr-Universität Bochum and BMBF QuaHL-Rep 16BQ1035, and grants FIS2009-08744 and FIS2012-33521 from the Spanish Ministry of Economy and Innovation. M.J.I. acknowledges a scholarship from the Higher Education Commission of Pakistan. Y.M. and R.L. acknowledge support from the ISF.

Author information

Authors and Affiliations



M.J.I. was the lead researcher for experiments, with C.H.v.d.W. as supervisor, experimental contributions from E.J.K., J.B.D., J.P.d.J. and J.H.M.v.d.V., and design contributions from Y.M. The devices were fabricated from wafer material that was grown by D.R. and A.D.W. The calculations of electron transport in Kondo systems were carried out by R.A. The SDFT contribution was worked out by R.L. with Y.M. as supervisor. M.J.I., C.H.v.d.W. and Y.M. wrote the paper.

Corresponding authors

Correspondence to M. J. Iqbal or C. H. van der Wal.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

This file contains Supplementary Text and Data, Supplementary Figures 1-14 and Supplementary References. (PDF 3021 kb)

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Iqbal, M., Levy, R., Koop, E. et al. Odd and even Kondo effects from emergent localization in quantum point contacts. Nature 501, 79–83 (2013).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

Further reading


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.


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