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Visualizing coexisting surface states in the weak and crystalline topological insulator Bi2TeI


Dual topological materials are unique topological phases that host coexisting surface states of different topological nature on the same or on different material facets. Here, we show that Bi2TeI is a dual topological insulator. It exhibits band inversions at two time reversal symmetry points of the bulk band, which classify it as a weak topological insulator with metallic states on its ‘side’ surfaces. The mirror symmetry of the crystal structure concurrently classifies it as a topological crystalline insulator. We investigated Bi2TeI spectroscopically to show the existence of both two-dimensional Dirac surface states, which are susceptible to mirror symmetry breaking, and one-dimensional channels that reside along the step edges. Their mutual coexistence on the step edge, where both facets join, is facilitated by momentum and energy segregation. Our observation of a dual topological insulator should stimulate investigations of other dual topology classes with distinct surface manifestations coexisting at their boundaries.

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Fig. 1: Dual topological classification in Bi2TeI.
Fig. 2: TCI surface states under mirror symmetry-breaking perturbation.
Fig. 3: 1D edge channels of a WTI.
Fig. 4: Interaction between the TCI and WTI surface states coexisting on hinges.

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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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N.A., H.B., B.Y. and C.F. acknowledge the German–Israeli Foundation for Scientific Research and Development (GIF grant no. I-1364-303.7/2016). H.B. and N.A. acknowledge the European Research Council (ERC, project no. TOPO NW), B.Y. acknowledges support by the Ruth and Herman Albert Scholars Program for New Scientists in Weizmann Institute of Science, Israel. C.F.’s work was financially supported by the ERC Advanced (project no. 742068, ‘TOPMAT’). A.Z. and A.I. acknowledge the German Research Foundation (DFG) in the framework of the Special Priority Program 1666 ‘Topological Insulators’ (IS 250/1-2) and Würzburg–Dresden Cluster of Excellence ct.qmat (EXC 2147, Project id 39085490). We are grateful to A. Stern for fruitful discussions and to H. Eizenshtat for his contribution to the measurements.

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A.K.N., A.S. and A.N. acquired the data and performed the analysis. Y.Q., A.I., A.Z. and L.P. grew and characterized the samples. H.F., Y.S. and B.Y. calculated the ab initio model. C.F., H.B. and N.A. conceived the experiment and wrote the manuscript.

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Correspondence to Nurit Avraham.

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Avraham, N., Kumar Nayak, A., Steinbok, A. et al. Visualizing coexisting surface states in the weak and crystalline topological insulator Bi2TeI. Nat. Mater. 19, 610–616 (2020).

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