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# Evidence for a higher-order topological insulator in a three-dimensional material built from van der Waals stacking of bismuth-halide chains

## Abstract

Low-dimensional van der Waals materials have been extensively studied as a platform with which to generate quantum effects. Advancing this research, topological quantum materials with van der Waals structures are currently receiving a great deal of attention. Here, we use the concept of designing topological materials by the van der Waals stacking of quantum spin Hall insulators. Most interestingly, we find that a slight shift of inversion centre in the unit cell caused by a modification of stacking induces a transition from a trivial insulator to a higher-order topological insulator. Based on this, we present angle-resolved photoemission spectroscopy results showing that the real three-dimensional material Bi4Br4 is a higher-order topological insulator. Our demonstration that various topological states can be selected by stacking chains differently, combined with the advantages of van der Waals materials, offers a playground for engineering topologically non-trivial edge states towards future spintronics applications.

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## Data availability

The data that support the findings of this study are available from the corresponding authors upon request.

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## Acknowledgements

We thank D. Hamane for SEM characterization of the sample surface. We also thank X. Ma and D. Abeysinghe for their support in the exfoliation of Bi4Br4 samples. The work done at Tokyo Institute of Technology was supported by a CREST project [JPMJCR16F2] from Japan Science and Technology Agency (JST). The GISAXS experiments were performed under the approval of PF-PAC number 2018G661. We thank Diamond Light Source for access to beamline I05 under proposal SI20445, which contributed to the results presented here. Use of the Stanford Synchrotron Radiation Lightsource at the SLAC National Accelerator Laboratory is supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under contract no. DE-AC02-76SF00515. The MIM work was supported by the United States Army Research Office under grant number W911NF-17-1-0542. This work was supported by the JSPS KAKENHI (grant numbers JP18H01165, JP18K03484, JP19H02683, JP19F19030 and JP19H00651), and by MEXT Q-LEAP (grant number JPMXS0118068681). R.N. acknowledges support by JSPS under KAKENHI grant number JP18J21892 and support by JSPS through the Program for Leading Graduate Schools (ALPS). This work was also supported by MEXT under the “Program for Promoting Researches on the Supercomputer Fugaku” (Basic Science for Emergence and Functionality in Quantum Matter Innovative Strongly Correlated Electron Science by Integration of “Fugaku” and Frontier Experiments) (Project ID: hp200132).

## Author information

Authors

### Contributions

T.K. and T. Sasagawa planned the experimental project. R.N. conducted ARPES experiments and analysed the data. K. Kuroda, P.Z., C.L., C.B., S. Sakuragi, H.T., S.K., K. Kurokawa, K.Y., A.H., V.K., A.G., A.B., T.K.K., C.C., M. Hashimoto, D. Lu, S. Shin and T.K. supported the ARPES experiment. R.N., Z.J., Z.X., D. Lee and K.L. performed MIM experiments and analysed the data. M.K., T.T. and T. Sasagawa made and characterized Bi4Br4 single crystals and performed transport experiments. R.N. and M.K. collected laser microscope images. T. Shirasawa performed the GISAXS experiments. R.N. performed the SEM experiment. T. Sasagawa, M. Hirayama, M.O. and R.A. calculated the band structure and analysed the band topology. R.N., Z.J., K. Kuroda, M. Hirayama, M.O., T. Shirasawa, K.L., T. Sasagawa and T.K. wrote the paper. All authors discussed the results and commented on the manuscript.

### Corresponding authors

Correspondence to Takao Sasagawa or Takeshi Kondo.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature Materials thanks Xingjiang Zhou 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 Notes 1–14, Figs. 1–4 and references.

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Noguchi, R., Kobayashi, M., Jiang, Z. et al. Evidence for a higher-order topological insulator in a three-dimensional material built from van der Waals stacking of bismuth-halide chains. Nat. Mater. 20, 473–479 (2021). https://doi.org/10.1038/s41563-020-00871-7

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• DOI: https://doi.org/10.1038/s41563-020-00871-7

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