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Topological Lifshitz transition and one-dimensional Weyl mode in HfTe5

Nature Materials volume 22, pages 84–91 (2023)Cite this article

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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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Fig. 1: Schematic plot of proposed magnetic-field-driven phase transitions.
Fig. 2: Band structure and magneto-infrared spectroscopy in HfTe5.
Fig. 3: Optical activity of Landau level transitions and field-driven phase transitions.
Fig. 4: Signature of 1D Pauli blocking and chiral anomaly.

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

References

  1. Shoenberg, D. Magnetic Oscillations in Metals (Cambridge Univ. Press, 2009).

  2. Klitzing, K. V., Dorda, G. & Pepper, M. New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance. Phys. Rev. Lett. 45, 494–497 (1980).

    Article  Google Scholar 

  3. Tsui, D. C., Stormer, H. L. & Gossard, A. C. Two-dimensional magnetotransport in the extreme quantum limit. Phys. Rev. Lett. 48, 1559–1562 (1982).

    Article  CAS  Google Scholar 

  4. Lupatini, M. et al. Spin reversal of a quantum Hall ferromagnet at a Landau level crossing. Phys. Rev. Lett. 125, 067404 (2020).

    Article  CAS  Google Scholar 

  5. Jungwirth, T. & MacDonald, A. H. Pseudospin anisotropy classification of quantum Hall ferromagnets. Phys. Rev. B 63, 035305 (2000).

    Article  Google Scholar 

  6. Ferreira, G. J., Freire, H. J. P. & Egues, J. C. Many-body effects on the ρxx ringlike structures in two-subband wells. Phys. Rev. Lett. 104, 066803 (2010).

    Article  Google Scholar 

  7. Taychatanapat, T., Watanabe, K., Taniguchi, T. & Jarillo-Herrero, P. Quantum Hall effect and Landau-level crossing of Dirac fermions in trilayer graphene. Nat. Phys. 7, 621–625 (2011).

    Article  CAS  Google Scholar 

  8. Das, I. et al. Symmetry-broken Chern insulators and Rashba-like Landau-level crossings in magic-angle bilayer graphene. Nat. Phys. 17, 710–714 (2021).

    Article  CAS  Google Scholar 

  9. Weyl, H. Gravitation and the electron. Proc. Natl Acad. Sci. USA 15, 323–334 (1929).

    Article  CAS  Google Scholar 

  10. Wan, X., Turner, A. M., Vishwanath, A. & Savrasov, S. Y. Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates. Phys. Rev. B 83, 205101 (2011).

    Article  Google Scholar 

  11. Weng, H., Fang, C., Fang, Z., Bernevig, B. A. & Dai, X. Weyl semimetal phase in noncentrosymmetric transition-metal monophosphides. Phys. Rev. X 5, 011029 (2015).

    Google Scholar 

  12. Lv, B. Q. et al. Experimental discovery of Weyl semimetal TaAs. Phys. Rev. X 5, 031013 (2015).

    Google Scholar 

  13. Xu, S. Y. et al. Discovery of a Weyl fermion semimetal and topological Fermi arcs. Science 349, 613–617 (2015).

    Article  CAS  Google Scholar 

  14. Morali, N. et al. Fermi-arc diversity on surface terminations of the magnetic Weyl semimetal Co3Sn2S2. Science 365, 1286–1291 (2019).

    Article  CAS  Google Scholar 

  15. Huang, X. et al. Observation of the chiral-anomaly-induced negative magnetoresistance in 3D Weyl semimetal TaAs. Phys. Rev. X 5, 031023 (2015).

    Google Scholar 

  16. Zhang, C. et al. Room-temperature chiral charge pumping in Dirac semimetals. Nat. Commun. 8, 13741 (2017).

    Article  CAS  Google Scholar 

  17. Suzuki, T. et al. Large anomalous Hall effect in a half-Heusler antiferromagnet. Nat. Phys. 12, 1119–1123 (2016).

    Article  CAS  Google Scholar 

  18. Zhang, C. et al. Quantum Hall effect based on Weyl orbits in Cd3As2. Nature 565, 331–336 (2019).

    Article  CAS  Google Scholar 

  19. Yuan, X. et al. The discovery of dynamic chiral anomaly in a Weyl semimetal NbAs. Nat. Commun. 11, 1259 (2020).

    Article  CAS  Google Scholar 

  20. Chen, R. Y. et al. Magnetoinfrared spectroscopy of Landau levels and Zeeman splitting of three-dimensional massless Dirac fermions in ZrTe5. Phys. Rev. Lett. 115, 176404 (2015).

    Article  CAS  Google Scholar 

  21. Ma, Q. et al. Direct optical detection of Weyl fermion chirality in a topological semimetal. Nat. Phys. 13, 842–847 (2017).

    Article  CAS  Google Scholar 

  22. Yuan, X. et al. Chiral Landau levels in Weyl semimetal NbAs with multiple topological carriers. Nat. Commun. 9, 1854 (2018).

    Article  Google Scholar 

  23. Wu, L. et al. Giant anisotropic nonlinear optical response in transition metal monopnictide Weyl semimetals. Nat. Phys. 13, 350–355 (2017).

  24. Polatkan, S. et al. Magneto-optics of a Weyl semimetal beyond the conical band approximation: case study of TaP. Phys. Rev. Lett. 124, 176402 (2020).

    Article  CAS  Google Scholar 

  25. Volovik, G. E. Topological Lifshitz transitions. Low. Temp. Phys. 43, 47–55 (2017).

    Article  Google Scholar 

  26. Bernevig, B. A., Hughes, T. L. & Zhang, S.-C. Quantum spin Hall effect and topological phase transition in HgTe quantum wells. Science 314, 1757–1761 (2006).

    Article  CAS  Google Scholar 

  27. Jiang, Y. et al. Unraveling the topological phase of ZrTe5 via magneto-infrared spectroscopy. Phys. Rev. Lett. 125, 046403 (2020).

    Article  CAS  Google Scholar 

  28. Jiang, Y. et al. Landau-level spectroscopy of massive Dirac fermions in single-crystalline ZrTe5 thin flakes. Phys. Rev. B 96, 041101 (2017).

    Article  Google Scholar 

  29. You, L., Zhang, Z.-Y. & Wang, Y.-X. Magneto-optic signatures in the gapped Dirac semimetal with mixed linear and parabolic dispersions of ZrTe5. New J. Phys. 23, 123033 (2021).

    Article  CAS  Google Scholar 

  30. Wang, Y. et al. Gigantic magnetochiral anisotropy in the topological semimetal ZrTe5. Phys. Rev. Lett. 128, 176602 (2022).

    Article  CAS  Google Scholar 

  31. Weng, H., Dai, X. & Fang, Z. Transition-metal pentatelluride ZrTe5 and HfTe5: a paradigm for large-gap quantum spin Hall insulators. Phys. Rev. X 4, 011002 (2014).

  32. Monserrat, B. & Narayan, A. Unraveling the topology of ZrTe5 by changing temperature. Phys. Rev. Res. 1, 033181 (2019).

    Article  CAS  Google Scholar 

  33. Morice, C., Lettl, E., Kopp, T. & Kampf, A. P. Optical conductivity and resistivity in a four-band model for ZrTe5 from ab initio calculations. Phys. Rev. B 102, 155138 (2020).

    Article  CAS  Google Scholar 

  34. Wang, H. et al. Discovery of log-periodic oscillations in ultraquantum topological materials. Sci. Adv. 4, eaau5096 (2018).

    Article  CAS  Google Scholar 

  35. Chen, Z.-G. et al. Spectroscopic evidence for bulk-band inversion and three-dimensional massive Dirac fermions in ZrTe5. Proc. Natl Acad. Sci. USA 114, 816–821 (2017).

    Article  CAS  Google Scholar 

  36. Tang, F. et al. Three-dimensional quantum Hall effect and metal–insulator transition in ZrTe5. Nature 569, 537–541 (2019).

    Article  CAS  Google Scholar 

  37. Martino, E. et al. Two-dimensional conical dispersion in ZrTe5 evidenced by optical spectroscopy. Phys. Rev. Lett. 122, 217402 (2019).

    Article  CAS  Google Scholar 

  38. Qin, F. et al. Theory for the charge-density-wave mechanism of 3D quantum Hall effect. Phys. Rev. Lett. 125, 206601 (2020).

    Article  CAS  Google Scholar 

  39. Zhang, C. et al. Magnetic-field-induced nonlinear transport in HfTe5. Natl Sci. Rev. https://doi.org/10.1093/nsr/nwab208 (2021).

  40. Zhang, Y. et al. Electronic evidence of temperature-induced Lifshitz transition and topological nature in ZrTe5. Nat. Commun. 8, 15512 (2017).

    Article  CAS  Google Scholar 

  41. Xu, B. et al. Temperature-driven topological phase transition and intermediate Dirac semimetal phase in ZrTe5. Phys. Rev. Lett. 121, 187401 (2018).

    Article  CAS  Google Scholar 

  42. Kamm, G., Gillespie, D., Ehrlich, A., Peebles, D. & Levy, F. Fermi surface, effective masses, and energy bands of HfTe5 as derived from the Shubnikov–de Haas effect. Phys. Rev. B 35, 1223–1229 (1987).

    Article  CAS  Google Scholar 

  43. Zhang, J. L. et al. Anomalous thermoelectric effects of ZrTe5 in and beyond the quantum limit. Phys. Rev. Lett. 123, 196602 (2019).

    Article  CAS  Google Scholar 

  44. Cai, W. & Ting, C. S. Screening effect on the Landau-level broadening for electrons in GaAs-Ga1−xAlxAs heterojunctions. Phys. Rev. B 33, 3967–3972 (1986).

    Article  CAS  Google Scholar 

  45. Jiang, Z. et al. Infrared spectroscopy of Landau levels of graphene. Phys. Rev. Lett. 98, 197403 (2007).

    Article  CAS  Google Scholar 

  46. Han, X., Salehi, M., Oh, S. & Wu, L. A new type of cyclotron resonance from charge-impurity scattering in the bulk-insulating Bi2Se3 thin films. J. Phys. Appl. Phys. 55, 364004 (2022).

    Article  Google Scholar 

  47. Akrap, A. et al. Magneto-optical signature of massless Kane electrons in Cd3As2. Phys. Rev. Lett. 117, 136401 (2016).

    Article  CAS  Google Scholar 

  48. Mak, K. F. et al. Measurement of the optical conductivity of graphene. Phys. Rev. Lett. 101, 196405 (2008).

    Article  Google Scholar 

  49. Abrikosov, A. A. Quantum magnetoresistance. Phys. Rev. B 58, 2788–2794 (1998).

    Article  CAS  Google Scholar 

  50. Rodionov, Y. I., Kugel, K. I., Aronzon, B. A. & Nori, F. Effect of disorder on the transverse magnetoresistance of Weyl semimetals. Phys. Rev. B 102, 205105 (2020).

    Article  CAS  Google Scholar 

  51. Chen, R. et al. Optical spectroscopy study of the three-dimensional Dirac semimetal ZrTe5. Phys. Rev. B 92, 075107 (2015).

    Article  Google Scholar 

  52. Liu, Y. et al. Zeeman splitting and dynamical mass generation in Dirac semimetal ZrTe5. Nat. Commun. 7, 12516 (2016).

    Article  CAS  Google Scholar 

  53. Galeski, S. et al. Unconventional Hall response in the quantum limit of HfTe5. Nat. Commun. 11, 5926 (2020).

    Article  CAS  Google Scholar 

  54. Zhao, P.-L., Lu, H.-Z. & Xie, X. C. Theory for magnetic-field-driven 3D metal-insulator transitions in the quantum limit. Phys. Rev. Lett. 127, 046602 (2021).

    Article  CAS  Google Scholar 

  55. Fu, B., Wang, H.-W. & Shen, S.-Q. Dirac polarons and resistivity anomaly in ZrTe5 and HfTe5. Phys. Rev. Lett. 125, 256601 (2020).

    Article  CAS  Google Scholar 

  56. Choi, Y., Villanova, J. W. & Park, K. Zeeman-splitting-induced topological nodal structure and anomalous Hall conductivity in ZrTe5. Phys. Rev. B 101, 035105 (2020).

    Article  CAS  Google Scholar 

  57. Wang, C. Thermodynamically induced transport anomaly in dilute metals ZrTe5 and HfTe5. Phys. Rev. Lett. 126, 126601 (2021).

    Article  CAS  Google Scholar 

  58. Zheng, G. et al. Field-induced topological phase transition from a three-dimensional Weyl semimetal to a two-dimensional massive Dirac metal in ZrTe5. Phys. Rev. B 96, 121401 (2017).

    Article  Google Scholar 

  59. Liang, T. et al. Anomalous Hall effect in ZrTe5. Nat. Phys. 14, 451–455 (2018).

    Article  CAS  Google Scholar 

  60. Xiong, H. et al. Three-dimensional nature of the band structure of ZrTe5 measured by high-momentum-resolution photoemission spectroscopy. Phys. Rev. B 95, 195119 (2017).

    Article  Google Scholar 

  61. Zhang, Y. et al. Temperature-induced Lifshitz transition in topological insulator candidate HfTe5. Sci. Bull. 62, 950–956 (2017).

    Article  CAS  Google Scholar 

  62. Li, Q. et al. Chiral magnetic effect in ZrTe5. Nat. Phys. 12, 550–554 (2016).

    Article  Google Scholar 

  63. Büttner, B. et al. Single valley Dirac fermions in zero-gap HgTe quantum wells. Nat. Phys. 7, 418–422 (2011).

    Article  Google Scholar 

  64. Klier, J., Gornyi, I. V. & Mirlin, A. D. Transversal magnetoresistance in Weyl semimetals. Phys. Rev. B 92, 205113 (2015).

    Article  Google Scholar 

  65. Pesin, D. A., Mishchenko, E. G. & Levchenko, A. Density of states and magnetotransport in Weyl semimetals with long-range disorder. Phys. Rev. B 92, 174202 (2015).

    Article  Google Scholar 

  66. Xiao, X., Law, K. T. & Lee, P. A. Magnetoconductivity in Weyl semimetals: effect of chemical potential and temperature. Phys. Rev. B 96, 165101 (2017).

    Article  Google Scholar 

  67. Könye, V. & Ogata, M. Magnetoresistance of a three-dimensional Dirac gas. Phys. Rev. B 98, 195420 (2018).

    Article  Google Scholar 

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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.

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Author notes

  1. These authors contributed equally: Wenbin Wu, Zeping Shi.

Authors and Affiliations

  1. State Key Laboratory of Precision Spectroscopy, East China Normal University, Shanghai, China

    Wenbin Wu, Zeping Shi, Yuhan Du, Xianghao Meng, Binglin Liu, Yuanji Ma & Xiang Yuan

  2. State Key Laboratory of Surface Physics and Institute for Nanoelectronic Devices and Quantum Computing, Fudan University, Shanghai, China

    Yuxiang Wang & Cheng Zhang

  3. Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology (SUSTech), Shenzhen, China

    Fang Qin & Hai-Zhou Lu

  4. School of Physics, Sun Yat-Sen University, Guangzhou, China

    Zhongbo Yan

  5. National High Magnetic Field Laboratory, Florida State University, Tallahassee, FL, USA

    Mykhaylo Ozerov

  6. Zhangjiang Fudan International Innovation Center, Fudan University, Shanghai, China

    Cheng Zhang

  7. Shenzhen Key Laboratory of Quantum Science and Engineering, Shenzhen, China

    Hai-Zhou Lu

  8. School of Physics and Electronic Science, East China Normal University, Shanghai, China

    Junhao Chu & Xiang Yuan

  9. Key Laboratory of Polar Materials and Devices, Ministry of Education, East China Normal University, Shanghai, China

    Junhao Chu

  10. Institute of Optoelectronics, Fudan University, Shanghai, China

    Junhao Chu

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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 k ⋅ p 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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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. 22, 84–91 (2023). https://doi.org/10.1038/s41563-022-01364-5

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