# Symmetry-enforced chiral hinge states and surface quantum anomalous Hall effect in the magnetic axion insulator Bi2–xSmxSe3

## Abstract

The existence of topological hinge states is a key signature for a newly proposed class of topological matter, the second-order topological insulators. In the present paper, a universal mechanism to generate chiral hinge states in the ferromagnetic axion insulator phase is introduced, which leads to an exotic transport phenomenon, the quantum anomalous Hall effect (QAHE) on some particular surfaces determined by both the crystalline symmetry and the magnetization direction. A realistic material system, Sm-doped Bi2Se3, is then proposed to realize such exotic hinge states by combining first-principles calculations and Green’s function techniques. A physically accessible way to manipulate the surface QAHE is also proposed, which makes it very different from the QAHE in ordinary 2D systems.

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## Data availability

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

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## Acknowledgements

We thank B.A. Bernevig and T. Neupert for helpful discussions. X.D., C.F. and H.M.W. are supported by the Ministry of Science and Technology of China (grant no. 2016YFA0300600) and the K.C. Wong Education Foundation (grant no. GJTD-2018-01). X.D. acknowledges financial support from the Hong Kong Research Grants Council (project no. GRF16300918). C.F. acknowledges financial support from the Ministry of Science and Technology of China (grant no. 2016YFA0302400), the Natural Science Foundation of China (grant no. 11674370), the Chinese Academy of Sciences (no. XXH13506-202, XDB28000000), the Beijing Municipal Science & Technology Commission (no. Z181100004218001) and the Beijing Natural Science Foundation (no. Z180008). H.M.W. is also supported by the Ministry of Science and Technology of China (grant no. 2018YFA0305700), the National Natural Science Foundation (grant no. 11674369) and the Science Challenge Project (no. TZ2016004). Y.-M.L. acknowledges the NSF under award number DMR-1653769.

## Author information

C.F., Y.M.L. and X.D. developed the theory and designed the research. C.M.Y. carried out the numerical calculations for the hinge states. Y.F.X. and H.M.W. did the calculations for the effective exchange field. Z.D.S. did the symmetry analyses for the numerical results. All authors contributed to the writing of the manuscript.

Correspondence to Xi Dai.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Journal peer review information: Nature Physics thanks Minoru Kawamura, Titus Neupert and other anonymous reviewer(s) for their contribution to the peer review of this work.

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## Supplementary information

### Supplementary Information

Supplementary Appendices and Supplementary Figures 1–4

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