Interacting topological edge channels

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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.

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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.

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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

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.

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

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Supplementary Information

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

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Strunz, J., Wiedenmann, J., Fleckenstein, C. et al. Interacting topological edge channels. Nat. Phys. (2019) doi:10.1038/s41567-019-0692-4

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