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# Topological Lifshitz transition and one-dimensional Weyl mode in HfTe5

## Abstract

Landau band crossings typically stem from the intra-band evolution of electronic states in magnetic fields and enhance the interaction effect in their vicinity. Here in the extreme quantum limit of topological insulator HfTe5, we report the observation of a topological Lifshitz transition from inter-band Landau level crossings using magneto-infrared spectroscopy. By tracking the Landau level transitions, we demonstrate that band inversion drives the zeroth Landau bands to cross with each other after 4.5 T and forms a one-dimensional Weyl mode with the fundamental gap persistently closed. The unusual reduction of the zeroth Landau level transition activity suggests a topological Lifshitz transition at 21 T, which shifts the Weyl mode close to the Fermi level. As a result, a broad and asymmetric absorption feature emerges due to the Pauli blocking effect in one dimension, along with a distinctive negative magneto-resistivity. Our results provide a strategy for realizing one-dimensional Weyl quasiparticles in bulk crystals.

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## Data availability

Source data are provided with this paper. All other supporting data are available from the corresponding authors upon reasonable request.

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## Acknowledgements

X.Y. was supported by the National Natural Science Foundation of China (grant no. 12174104, no. 62005079 and no. 62111530237), the Shanghai Sailing Program (grant no. 20YF1411700), the International Scientific and Technological Cooperation Project of Shanghai (grant no. 20520710900) and a start-up grant from East China Normal University. C.Z. was supported by the National Natural Science Foundation of China (grant no. 12174069), Shanghai Sailing Program (grant no. 20YF1402300), Natural Science Foundation of Shanghai (grant no. 20ZR1407500), the Young Scientist project of the Ministry of Education innovation platform and a start-up grant from Fudan University. H.-Z.L. was supported by the National Natural Science Foundation of China (grant no. 11925402). A portion of this work was performed at the National High Magnetic Field Laboratory, which is supported by National Science Foundation cooperative agreement no. DMR-1644779 and the State of Florida. Part of the sample fabrication was performed at Fudan Nano-fabrication Laboratory. We thank M. Orlita, M. Potemski, H. Yan, Y. Jiang, Z.-G. Chen, Z. Sun, C.-G. Duan, F. Yue, B. Tian and Y. Liu for helpful discussions.

## Author information

Authors

### Contributions

X.Y. conceived the idea and supervised the overall research. X.M., B.L. and Y.M. carried out the growth of the HfTe5 single crystals. M.O., W.W., Z.S. and Y.D. performed the magneto-infrared experiments. C.Z. and Y.W. conducted the magneto-transport experiments. W.W., X.Y., Z.Y., F.Q. and H.-Z.L. performed the theoretical analyses based on the kp model. X.Y., W.W., C.Z., Z.S. and J.C. wrote the paper with the help of all the coauthors.

### Corresponding authors

Correspondence to Cheng Zhang or Xiang Yuan.

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### Competing interests

The authors declare no competing interests.

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### Peer review information

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## Supplementary information

### Supplementary Information

Supplementary Figs. 1–13, Discussion Sections I–XII and Tables 1–3.

## Source data

### Source Data Fig. 2

Magneto-resistivity (Fig. 2a), temperature-dependent oscillation amplitude (Fig. 2c) and relative magneto-transmittance spectrum (Fig. 2e).

### Source Data Fig. 3

Energy of Tα and Tβ (Fig. 3a(iv)), normalized Pauli-blocking-induced spectral weight with corresponding first-order derivative (Fig. 3a(v)) and theoretical real part of magneto-optical conductivity (Fig. 3d).

### Source Data Fig. 4

Magneto-resistivity (Fig. 4e).

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Wu, W., Shi, Z., Du, Y. et al. Topological Lifshitz transition and one-dimensional Weyl mode in HfTe5. Nat. Mater. (2022). https://doi.org/10.1038/s41563-022-01364-5

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• DOI: https://doi.org/10.1038/s41563-022-01364-5