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


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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Figure 1: Experimental set-up and model.
Figure 2: Conductance: theory versus experiment.
Figure 3: Finite excitation energies.


  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)

    Article  CAS  ADS  Google Scholar 

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

    Article  Google Scholar 

  3. Büttiker, M. Quantized transmission of a saddle-point constriction. Phys. Rev. B 41, 7906(R) (1990)

    Article  ADS  Google Scholar 

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

    Article  CAS  ADS  Google Scholar 

  5. Appleyard, N. J. et al. Direction-resolved transport and possible many-body effects in one-dimensional thermopower. Phys. Rev. B 62, R16275–R16278 (2000)

    Article  CAS  ADS  Google Scholar 

  6. 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)

    Article  CAS  ADS  Google Scholar 

  7. DiCarlo, L. et al. Shot-noise signatures of 0.7 structure and spin in a quantum point contact. Phys. Rev. Lett. 97, 036810 (2006)

    Article  CAS  ADS  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)

    Article  CAS  ADS  Google Scholar 

  9. Sarkozy, S. et al. Zero-bias anomaly in quantum wires. Phys. Rev. B 79, 161307R (2009)

    Article  ADS  Google Scholar 

  10. Ren, Y. et al. Zero-bias anomaly of quantum point contacts in the low-conductance limit. Phys. Rev. B 82, 045313 (2010)

    Article  ADS  Google Scholar 

  11. 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)

    Article  CAS  ADS  Google Scholar 

  12. Burke, A. 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)

    Article  CAS  ADS  Google Scholar 

  13. 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)

    Article  ADS  Google Scholar 

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

    Article  CAS  ADS  Google Scholar 

  15. Ihnatsenka, S. & Zozoulenko, I. V. Conductance of a quantum point contact based on spin density-functional theory. Phys. Rev. B 76, 045338 (2007)

    Article  ADS  Google Scholar 

  16. Matveev, K. A. Conductance of a quantum wire at low electron density. Phys. Rev. B 70, 245319 (2004)

    Article  ADS  Google Scholar 

  17. Reilly, D. J. Phenomenological model for the 0.7 conductance feature in quantum wires. Phys. Rev. B 72, 033309 (2005)

    Article  ADS  Google Scholar 

  18. Sloggett, C. Milstein, A. I. & Sushkov, O. P. Correlated electron current and temperature dependence of the conductance of a quantum point contact. Eur. Phys. J. B 61, 427–432 (2008)

    Article  CAS  ADS  Google Scholar 

  19. Aryanpour, K. & Han, J. E. Ferromagnetic spin coupling as the origin of 0.7 anomaly in quantum point contacts. Phys. Rev. Lett. 102, 056805 (2009)

    Article  CAS  ADS  Google Scholar 

  20. Güçlü, A. D. et al. Localization in an inhomogeneous quantum wire. Phys. Rev. B 80, 201302(R) (2009)

    Article  ADS  Google Scholar 

  21. Lunde, A. M. et al. Electron-electron interaction effects in quantum point contacts. New J. Phys. 11, 023031 (2009)

    Article  ADS  Google Scholar 

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

    Article  CAS  ADS  Google Scholar 

  23. Oguri, A. Transmission probability for interacting electrons connected to reservoirs. J. Phys. Soc. Jpn 70, 2666–2681 (2001)

    Article  CAS  ADS  Google Scholar 

  24. Andergassen, S. et al. Renormalization-group analysis of the one-dimensional extended Hubbard model with a single impurity. Phys. Rev. B 73, 045125 (2006)

    Article  ADS  Google Scholar 

  25. Karrasch, C., Enss, T. & Meden, V. Functional renormalization group approach to transport through correlated quantum dots. Phys. Rev. B 73, 235337 (2006)

    Article  ADS  Google Scholar 

  26. Metzner, W. et al. Functional renormalization group approach to correlated fermion systems. Rev. Mod. Phys. 84, 299–352 (2012)

    Article  ADS  Google Scholar 

  27. Nozières, P. A “fermi-liquid” description of the Kondo problem at low temperatures. J. Low Temp. Phys. 17, 31–42 (1974)

    Article  ADS  Google Scholar 

  28. Glazman, L. &. Pustilnik, M. in Nanophysics: Coherence and Transport (eds Bouchiat, H. et al.) 427–478 (Elsevier, 2005)

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

    Article  CAS  ADS  Google Scholar 

  30. Meir, Y. & Wingreen, N. S. Landauer formula for the current through an interacting electron region. Phys. Rev. Lett. 68, 2512–2515 (1992)

    Article  CAS  ADS  Google Scholar 

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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.

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Authors and Affiliations



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.

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Correspondence to Jan von Delft or Stefan Ludwig.

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The authors declare no competing financial interests.

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Bauer, F., Heyder, J., Schubert, E. et al. Microscopic origin of the ‘0.7-anomaly’ in quantum point contacts. Nature 501, 73–78 (2013).

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