Letter | Published:

Microscopic origin of the ‘0.7-anomaly’ in quantum point contacts

Nature volume 501, pages 7378 (05 September 2013) | Download Citation


Quantum point contacts are narrow, one-dimensional constrictions usually patterned in a two-dimensional electron system, for example by applying voltages to local gates. The linear conductance of a point contact, when measured as function of its channel width, is quantized1,2,3 in units of GQ = 2e2/h, where e is the electron charge and h is Planck’s constant. However, the conductance also has an unexpected shoulder at 0.7GQ, known as the ‘0.7-anomaly’4,5,6,7,8,9,10,11,12, whose origin is still subject to debate11,12,13,14,15,16,17,18,19,20,21. Proposed theoretical explanations have invoked spontaneous spin polarization4,17, ferromagnetic spin coupling19, the formation of a quasi-bound state leading to the Kondo effect13,14, Wigner crystallization16,20 and various treatments of inelastic scattering18,21. However, explicit calculations that fully reproduce the various experimental observations in the regime of the 0.7-anomaly, including the zero-bias peak that typically accompanies it6,9,10,11, are still lacking. Here we offer a detailed microscopic explanation for both the 0.7-anomaly and the zero-bias peak: their common origin is a smeared van Hove singularity in the local density of states at the bottom of the lowest one-dimensional subband of the point contact, which causes an anomalous enhancement in the Hartree potential barrier, the magnetic spin susceptibility and the inelastic scattering rate. We find good qualitative agreement between theoretical calculations and experimental results on the dependence of the conductance on gate voltage, magnetic field, temperature, source–drain voltage (including the zero-bias peak) and interaction strength. We also clarify how the low-energy scale governing the 0.7-anomaly depends on gate voltage and interactions. For low energies, we predict and observe Fermi-liquid behaviour similar to that associated with the Kondo effect in quantum dots22. At high energies, however, the similarities between the 0.7-anomaly and the Kondo effect end.

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We thank B. Altshuler, P. Brouwer, R. Egger, J. Folk, L. Glazman, V. Golovach, A. Hamilton, A. Högele, Y. Imry, M. Kiselev, J. Kotthaus, D. Logan, D. Loss, C. Marcus, Y. Meir, H. Monien, M. Pepper, M. Pustilnik, A. Rosch, K. Schönhammer, B. Spivak and A. Yacoby for discussions, and, in particular, S. Andergassen, C. Honerkamp, S. Jakobs, C. Karrasch, V. Meden, M. Pletyukhov and H. Schoeller for FRG-related help and advice. We acknowledge support from the DFG through SFB-631, SFB-TR12, De730/3-2, De730/4-1, De730/4-2, De730/4-3, HO 4687/1-3, LU819/4-1 and the Cluster of Excellence Nanosystems Initiative Munich; from the Center for NanoScience; and from the US National Science Foundation under grant no. NSF PHY05-51164. S.L. acknowledges support through a Heisenberg fellowship of the DFG.

Author information

Author notes

    • Florian Bauer
    •  & Jan Heyder

    These authors contributed equally to this work.


  1. Center for NanoScience and Fakultät für Physik, Ludwig-Maximilians-Universität München, Geschwister-Scholl-Platz 1, 80539 München, Germany

    • Florian Bauer
    • , Jan Heyder
    • , Enrico Schubert
    • , David Borowsky
    • , Daniela Taubert
    • , Benedikt Bruognolo
    • , Jan von Delft
    •  & Stefan Ludwig
  2. Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, D-80333 München, Germany

    • Florian Bauer
    • , Jan Heyder
    • , Benedikt Bruognolo
    •  & Jan von Delft
  3. Institut für Angewandte Physik, Universität Regensburg, D-93040 Regensburg, Germany

    • Dieter Schuh
  4. Laboratory for Solid State Physics, ETH Zürich, CH-8093 Zürich, Switzerland

    • Werner Wegscheider


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J.v.D. and S.L. coordinated the project: J.v.D. initiated and supervised the theoretical work, and S.L. planned and supervised the experiments and their analysis. F.B. and J.H. carried out the calculations using FRG, and J.H., F.B. and B.B. carried out the calculations using perturbation theory. D.S. and W.W. provided the wafer material, and D.B. fabricated the nanostructure. E.S., D.B., D.T. and S.L. carried out the measurements, and E.S., D.B., F.B. and J.H. carried out the experimental data analysis. J.H. and F.B. prepared the figures, and J.v.D., S.L., F.B., J.H. and E.S. wrote the paper.

Competing interests

The authors declare no competing financial interests.

Corresponding authors

Correspondence to Jan von Delft or Stefan Ludwig.

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    Supplementary Information

    This file contains Supplementary Text, Supplementary Figures 1-18, Supplementary Tables 1 and Supplementary References.

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