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Tomonaga–Luttinger liquid in the edge channels of a quantum spin Hall insulator


Quantum spin Hall insulators are two-dimensional materials that host conducting helical electron states strictly confined to the one-dimensional boundaries. These edge channels are protected by time-reversal symmetry against single-particle backscattering, opening new avenues for spin-based electronics and computation. However, the effect of the interelectronic Coulomb repulsion also has to be taken into account, as two-particle scattering is not impeded by topological protection and may strongly affect the edge state conductance. Here, we explore the impact of electronic correlations on highly localized edge states of the unique quantum spin Hall material bismuthene on SiC(0001) (ref. 1). Exploiting the advantage of having an accessible monolayer substrate system, we use STM/STS to visualize the close-to-perfect one-dimensional confinement of the edge channels and scrutinize their suppressed density of states at the Fermi level. On the basis of the observed spectral behaviour and its universal scaling with energy and temperature, we demonstrate the correspondence with a (helical) Tomonaga–Luttinger liquid. In particular, the extracted interaction parameter K is directly relevant to the fundamental question of the temperatures at which the quantized conductance (a hallmark of quantum spin Hall materials) will become obscured by correlations2.

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Fig. 1: Strongly confined 1D metallic channels at bismuthene armchair edges.
Fig. 2: Power-law suppression of the ZBA.
Fig. 3: Temperature dependence of the ZBA.
Fig. 4: Universal scaling of the ZBA as a hallmark of a TLL.

Data availability

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


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We thank B. Trauzettel, M. Bode, A. Kowalewski and J. Maciejko for useful discussions. This work was supported by the DFG through the Würzburg-Dresden Cluster of Excellence on Complexity and Topology in Quantum Matter (EXC 2147, project 39085490), the Collaborative Research Center SFB 1170 ‘ToCoTronics’ in Würzburg and the SPP 1666 Priority Programme ‘Topological Insulators’. We are also grateful for support from the ERC through starting grant ERC-StG-Thomale-336012 ‘Topolectrics’.

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Authors and Affiliations



R.S. and F.R. carried out the measurements. R.S. analysed the data and made the figures. T.M., T.H., T.S and R.T. developed the theory for the helical edge with dielectric screening. J.S. conceived the experiment. R.S., F.R., J.S. and R.C. wrote the text, and all authors contributed to critical discussion of the data.

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Correspondence to J. Schäfer.

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Peer review information Nature Physics thanks Ward Plummer and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary Figs. 1–9, text and reference.

Supplementary Video

Continuous evolution of the DOS with energy and constant dI/dV scale.

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Stühler, R., Reis, F., Müller, T. et al. Tomonaga–Luttinger liquid in the edge channels of a quantum spin Hall insulator. Nat. Phys. 16, 47–51 (2020).

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