Interacting topological edge channels

A Publisher Correction to this article was published on 04 November 2020

This article has been updated

Abstract

Electrical currents in a quantum spin Hall insulator are confined to the boundary of the system. The charge carriers behave as massless relativistic particles whose spin and momentum are coupled to each other. Although the helical character of those states is already established by experiments, there is an open question regarding how those edge states interact with each other when they are brought into close spatial proximity. We employ an inverted HgTe quantum well to guide edge channels from opposite sides of a device into a quasi-one-dimensional constriction. Our transport measurements show that, apart from the expected quantization in integer steps of 2e2/h, we find an additional plateau at e2/h. We combine band structure calculations and repulsive electron–electron interaction effects captured within the Tomonaga–Luttinger liquid model and Rashba spin–orbit coupling to explain our observation in terms of the opening of a spin gap. These results may have direct implications for the study of one-dimensional helical electron quantum optics, and for understanding Majorana and para fermions.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

Fig. 1: Realization of a topological QPC.
Fig. 2: Width dependencies of the 0.5 anomaly.
Fig. 3: k  p band structure calculations and illustrations of the scattering process.
Fig. 4: Temperature and d.c. bias dependence of the 0.5 anomaly.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

Change history

  • 04 November 2020

    An amendment to this paper has been published and can be accessed via a link at the top of the paper.

References

  1. 1.

    Kane, C. L. & Mele, E. J. Quantum spin Hall effect in graphene. Phys. Rev. Lett. 95, 226801 (2005).

    ADS  Article  Google Scholar 

  2. 2.

    Kane, C. L. & Mele, E. J. Z 2 topological order and the quantum spin Hall effect. Phys. Rev. Lett. 95, 146802 (2005).

    ADS  Article  Google Scholar 

  3. 3.

    Bernevig, B. A., Hughes, T. L. & Zhang, S.-C. Quantum spin Hall effect and topological phase transition in HgTe quantum wells. Science 314, 1757–1761 (2006).

    ADS  Article  Google Scholar 

  4. 4.

    König, M. et al. Quantum spin Hall insulator state in HgTe quantum wells. Science 318, 766–770 (2007).

    ADS  Article  Google Scholar 

  5. 5.

    Knez, I., Du, R.-R. & Sullivan, G. Evidence for helical edge modes in inverted InAs/GaSb quantum wells. Phys. Rev. Lett. 107, 136603 (2011).

    ADS  Article  Google Scholar 

  6. 6.

    Wu, S. et al. Observation of the quantum spin Hall effect up to 100 kelvin in a monolayer crystal. Science 359, 76–79 (2018).

    ADS  MathSciNet  Article  Google Scholar 

  7. 7.

    Reis, F. et al. Bismuthene on a SiC substrate: a candidate for a high-temperature quantum spin Hall material. Science 357, 287–290 (2017).

    ADS  MathSciNet  Article  Google Scholar 

  8. 8.

    Roth, A. et al. Nonlocal transport in the quantum spin Hall state. Science 325, 294–297 (2009).

    ADS  Article  Google Scholar 

  9. 9.

    Brüne, C. et al. Spin polarization of the quantum spin Hall edge states. Nat. Phys. 8, 486–491 (2012).

    Article  Google Scholar 

  10. 10.

    Hou, C.-Y., Kim, E.-A. & Chamon, C. Corner junction as a probe of helical edge states. Phys. Rev. Lett. 102, 076602 (2009).

    ADS  Article  Google Scholar 

  11. 11.

    Ström, A. & Johannesson, H. Tunneling between edge states in a quantum spin Hall system. Phys. Rev. Lett. 102, 096806 (2009).

    ADS  Article  Google Scholar 

  12. 12.

    Teo, J. C. Y. & Kane, C. L. Critical behavior of a point contact in a quantum spin Hall insulator. Phys. Rev. B 79, 235321 (2009).

    ADS  Article  Google Scholar 

  13. 13.

    Tanaka, Y. & Nagaosa, N. Two interacting helical edge modes in quantum spin Hall systems. Phys. Rev. Lett. 103, 166403 (2009).

    ADS  Article  Google Scholar 

  14. 14.

    Dolcini, F. Full electrical control of charge and spin conductance through interferometry of edge states in topological insulators. Phys. Rev. B 83, 165304 (2011).

    ADS  Article  Google Scholar 

  15. 15.

    Krueckl, V. & Richter, K. Switching spin and charge between edge states in topological insulator constrictions. Phys. Rev. Lett. 107, 086803 (2011).

    ADS  Article  Google Scholar 

  16. 16.

    Zhang, L. B., Cheng, F., Zhai, F. & Chang, K. Electrical switching of the edge channel transport in HgTe quantum wells with an inverted band structure. Phys. Rev. B 83, 081402 (2011).

    ADS  Article  Google Scholar 

  17. 17.

    Orth, C. P., Strübi, G. & Schmidt, T. L. Point contacts and localization in generic helical liquids. Phys. Rev. B 88, 165315 (2013).

    ADS  Article  Google Scholar 

  18. 18.

    Sternativo, P. & Dolcini, F. Tunnel junction of helical edge states: determining and controlling spin-preserving and spin-flipping processes through transconductance. Phys. Rev. B 89, 035415 (2014).

    ADS  Article  Google Scholar 

  19. 19.

    Dolcini, F. Noise and current correlations in tunnel junctions of quantum spin Hall edge states. Phys. Rev. B 92, 155421 (2015).

    ADS  Article  Google Scholar 

  20. 20.

    Papaj, M., Cywiński, L., Wróbel, J. & Dietl, T. Conductance oscillations in quantum point contacts of InAs/GaSb heterostructures. Phys. Rev. B 93, 195305 (2016).

    ADS  Article  Google Scholar 

  21. 21.

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

    ADS  Article  Google Scholar 

  22. 22.

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

    ADS  Article  Google Scholar 

  23. 23.

    Bendias, K. et al. High mobility HgTe microstructures for quantum spin Hall studies. Nano Lett. 18, 4831–4836 (2018).

    ADS  Article  Google Scholar 

  24. 24.

    Novik, E. G. et al. Band structure of semimagnetic Hg1 − yMnyTe quantum wells. Phys. Rev. B 72, 035321 (2005).

    ADS  Article  Google Scholar 

  25. 25.

    Skolasinski, R., Pikulin, D. I., Alicea, J. & Wimmer, M. Robust helical edge transport in quantum spin Hall quantum wells. Phys. Rev. B 98, 201404 (2018).

    ADS  Article  Google Scholar 

  26. 26.

    Schmidt, T. L., Rachel, S., von Oppen, F. & Glazman, L. I. Inelastic electron backscattering in a generic helical edge channel. Phys. Rev. Lett. 108, 156402 (2012).

    ADS  Article  Google Scholar 

  27. 27.

    Ortiz, L., Molina, R. A., Platero, G. & Lunde, A. M. Generic helical edge states due to Rashba spin–orbit coupling in a topological insulator. Phys. Rev. B 93, 205431 (2016).

    ADS  Article  Google Scholar 

  28. 28.

    Xie, H.-Y., Li, H., Chou, Y.-Z. & Foster, M. S. Topological protection from random Rashba spin–orbit backscattering: ballistic transport in a helical Luttinger liquid. Phys. Rev. Lett. 116, 086603 (2016).

    ADS  Article  Google Scholar 

  29. 29.

    Kharitonov, M., Geissler, F. & Trauzettel, B. Backscattering in a helical liquid induced by Rashba spin–orbit coupling and electron interactions: locality, symmetry and cutoff aspects. Phys. Rev. B 96, 155134 (2017).

    ADS  Article  Google Scholar 

  30. 30.

    Liu, C.-X., Budich, J. C., Recher, P. & Trauzettel, B. Charge-spin duality in nonequilibrium transport of helical liquids. Phys. Rev. B 83, 035407 (2011).

    ADS  Article  Google Scholar 

  31. 31.

    Giamarchi, T. Quantum Physics in One Dimension (International Series of Monographs on Physics, Oxford Univ. Press, 2003).

  32. 32.

    Lunde, A. M., De Martino, A., Schulz, A., Egger, R. & Flensberg, K. Electron–electron interaction effects in quantum point contacts. New J. Phys. 11, 023031 (2009).

    ADS  Article  Google Scholar 

  33. 33.

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

    ADS  Article  Google Scholar 

  34. 34.

    Wang, J., Meir, Y. & Gefen, Y. Spontaneous breakdown of topological protection in two dimensions. Phys. Rev. Lett. 118, 046801 (2017).

    ADS  Article  Google Scholar 

  35. 35.

    Matveev, K. A. Conductance of a quantum wire in the Wigner-crystal regime. Phys. Rev. Lett. 92, 106801 (2004).

    ADS  Article  Google Scholar 

  36. 36.

    Hsu, C.-H., Stano, P., Klinovaja, J. & Loss, D. Effects of nuclear spins on the transport properties of the edge of two-dimensional topological insulators. Phys. Rev. B 97, 125432 (2018).

    ADS  Article  Google Scholar 

Download references

Acknowledgements

We thank E. Bocquillon, T. Borzenko, Y. Gefen, C. Gould, A. Currie, V. Hock, P. Leubner and Y. Meir for fruitful discussions. We acknowledge financial support by the DFG (SPP1666 and SFB1170 ‘ToCoTronics’), the ENB Graduate school on ‘Topological Insulators’, the EU ERC-AG Program (project 4-TOPS) and the Würzburg–Dresden Cluster of Excellence on Complexity and Topology in Quantum Matter (EXC 2147, project ID 39085490). C.F. acknowledges support from the Studienstiftung des Deutschen Volkes.

Author information

Affiliations

Authors

Contributions

J.S. prepared the samples and performed the experiments. V.L.M. and P.S. contributed to implementation of the fabrication process, and S.S. and J.W. helped to carry out measurements. J.K. supervised the sample fabrication. J.W. guided the experiments. L.L. grew the material. W.B. provided the code for the band structure calculations. C.F., N.T.Z. and B.T. developed the theoretic model. H.B. and L.W.M. planned the project and design of the experiment. All authors participated in the analysis of the data, led by J.S. and J.W. All authors jointly wrote the manuscript.

Corresponding authors

Correspondence to Jonas Strunz or Björn Trauzettel or Laurens W. Molenkamp.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Additional theoretical details and Supplementary Figs. 1–6, Tables 1 and 2, and refs. 1–17.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Strunz, J., Wiedenmann, J., Fleckenstein, C. et al. Interacting topological edge channels. Nat. Phys. 16, 83–88 (2020). https://doi.org/10.1038/s41567-019-0692-4

Download citation

Further reading

Search

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