Skip to main content
Log in

Magnetic-field-induced electronic instability of Weyl-like fermions in compressed black phosphorus

  • Article
  • Published:
Science China Physics, Mechanics & Astronomy Aims and scope Submit manuscript

Abstract

Revealing the role of Coulomb interaction in topological semimetals with Dirac/Weyl-like band dispersion shapes a new frontier in condensed matter physics. Topological node-line semimetals (TNLSMs), anticipated as a fertile ground for exploring electronic correlation effects due to the anisotropy associated with their node-line structure, have recently attracted considerable attention. In this study, we report an experimental observation for correlation effects in TNLSMs realized by black phosphorus (BP) under hydrostatic pressure. By performing a combination of nuclear magnetic resonance measurements and band calculations on compressed BP, a magnetic-field-induced electronic instability of Weyl-like fermions is identified under an external magnetic field parallel to the so-called nodal ring in the reciprocal space. Anomalous spin fluctuations serving as the fingerprint of electronic instability are observed at low temperatures, and they are observed to maximize at approximately 1.0 GPa. This study presents compressed BP as a realistic material platform for exploring the rich physics in strongly coupled Weyl-like fermions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. M. Hirata, K. Ishikawa, K. Miyagawa, M. Tamura, C. Berthier, D. Basko, A. Kobayashi, G. Matsuno, and K. Kanoda, Nat. Commun. 7, 12666 (2016), arXiv: 1607.07142.

    Article  ADS  Google Scholar 

  2. H. Isobe, and N. Nagaosa, Phys. Rev. Lett. 116, 116803 (2016).

    Article  ADS  Google Scholar 

  3. H. K. Tang, J. N. Leaw, J. N. B. Rodrigues, I. F. Herbut, P. Sengupta, F. F. Assaad, and S. Adam, Science 361, 570 (2018), arXiv:1808.03648.

    Article  ADS  Google Scholar 

  4. H. Wei, S. P. Chao, and V. Aji, Phys. Rev. Lett. 109, 196403 (2012), arXiv: 1207.5065.

    Article  ADS  Google Scholar 

  5. Z. Wang, and S. C. Zhang, Phys. Rev. B 87, 161107 (2013), arXiv: 1207.5234.

    Article  ADS  Google Scholar 

  6. H. Wei, S. P. Chao, and V. Aji, Phys. Rev. B 89, 235109 (2014), arXiv: 1403.2456.

    Article  ADS  Google Scholar 

  7. J. Maciejko, and R. Nandkishore, Phys. Rev. B 90, 035126 (2014), arXiv: 1311.7133.

    Article  ADS  Google Scholar 

  8. B. Roy, and J. D. Sau, Phys. Rev. B 92, 125141 (2015), arXiv: 1406.4501.

    Article  ADS  Google Scholar 

  9. R. X. Zhang, J. A. Hutasoit, Y. Sun, B. Yan, C. Xu, and C. X. Liu, Phys. Rev. B 93, 041108 (2016), arXiv: 1503.00358.

    Article  ADS  Google Scholar 

  10. M. Laubach, C. Platt, R. Thomale, T. Neupert, and S. Rachel, Phys. Rev. B 94, 241102 (2016), arXiv: 1609.02925.

    Article  ADS  Google Scholar 

  11. B. Roy, P. Goswami, and V. Juričić, Phys. Rev. B 95, 201102 (2017), arXiv: 1610.05762.

    Article  ADS  Google Scholar 

  12. Z. Song, Z. Fang, and X. Dai, Phys. Rev. B 96, 235104 (2017), arXiv: 1705.05119.

    Article  ADS  Google Scholar 

  13. A. N. Rudenko, E. A. Stepanov, A. I. Lichtenstein, and M. I. Katsnelson, Phys. Rev. Lett. 120, 216401 (2018), arXiv: 1712.07916.

    Article  ADS  Google Scholar 

  14. M. Hirata, K. Ishikawa, G. Matsuno, A. Kobayashi, K. Miyagawa, M. Tamura, C. Berthier, and K. Kanoda, Science 358, 1403 (2017), arXiv: 1702.00097.

    Article  ADS  Google Scholar 

  15. Y. Shao, A. N. Rudenko, J. Hu, Z. Sun, Y. Zhu, S. Moon, A. J. Millis, S. Yuan, A. I. Lichtenstein, D. Smirnov, Z. Q. Mao, M. I. Katsnelson, and D. N. Basov, Nat. Phys. 16, 636 (2020).

    Article  Google Scholar 

  16. S. Pezzini, M. R. van Delft, L. M. Schoop, B. V. Lotsch, A. Carrington, M. I. Katsnelson, N. E. Hussey, and S. Wiedmann, Nat. Phys. 14, 178 (2018), arXiv: 1701.09119.

    Article  Google Scholar 

  17. F. C. Chen, Y. Fei, S. J. Li, Q. Wang, X. Luo, J. Yan, W. J. Lu, P. Tong, W. H. Song, X. B. Zhu, L. Zhang, H. B. Zhou, F. W. Zheng, P. Zhang, A. L. Lichtenstein, M. I. Katsnelson, Y. Yin, N. Hao, and Y. P. Sun, Phys. Rev. Lett. 124, 236601 (2020), arXiv: 2006.08428.

    Article  ADS  Google Scholar 

  18. H. Liu, A. T. Neal, Z. Zhu, Z. Luo, X. Xu, D. Tománek, and P. D. Ye, ACS Nano 8, 4033 (2014).

    Article  Google Scholar 

  19. L. Li, G. J. Ye, V. Tran, R. Fei, G. Chen, H. Wang, J. Wang, K. Watanabe, T. Taniguchi, L. Yang, X. H. Chen, and Y. Zhang, Nat. Nanotech. 10, 608 (2015).

    Article  ADS  Google Scholar 

  20. Z. J. Xiang, G. J. Ye, C. Shang, B. Lei, N. Z. Wang, K. S. Yang, D. Y. Liu, F. B. Meng, X. G. Luo, L. J. Zou, Z. Sun, Y. Zhang, and X. H. Chen, Phys. Rev. Lett. 115, 186403 (2015), arXiv: 1504.00125.

    Article  ADS  Google Scholar 

  21. C. H. Li, Y. J. Long, L. X. Zhao, L. Shan, Z. A. Ren, J. Z. Zhao, H. M. Weng, X. Dai, Z. Fang, C. Ren, and G. F. Chen, Phys. Rev. B 95, 125417 (2017).

    Article  ADS  Google Scholar 

  22. J. Zhao, R. Yu, H. Weng, and Z. Fang, Phys. Rev. B 94, 195104 (2016), arXiv: 1511.05704.

    Article  ADS  Google Scholar 

  23. Z. Sun, Z. Xiang, Z. Wang, J. Zhang, L. Ma, N. Wang, C. Shang, F. Meng, L. Zou, Y. Zhang, and X. Chen, Sci. Bull. 63, 1539 (2018).

    Article  Google Scholar 

  24. K. Kitagawa, H. Gotou, T. Yagi, A. Yamada, T. Matsumoto, Y. Uwatoko, and M. Takigawa, J. Phys. Soc. Jpn. 79, 024001 (2010), arXiv: 0910.1767.

    Article  ADS  Google Scholar 

  25. K. Murata, H. Yoshino, H. O. Yadav, Y. Honda, and N. Shirakawa, Rev. Sci. Instrum. 68, 2490 (1997).

    Article  ADS  Google Scholar 

  26. K. Yokogawa, K. Murata, H. Yoshino, and S. Aoyama, Jpn. J. Appl. Phys. 46, 3636 (2007).

    Article  ADS  Google Scholar 

  27. M. S. Torikachvili, S. K. Kim, E. Colombier, S. L. Bud’ko, and P. C. Canfield, Rev. Sci. Instrum. 86, 123904 (2015), arXiv: 1512.00087.

    Article  ADS  Google Scholar 

  28. P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo, A. Dal Corso, S. de Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerst-mann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia, S. Scandolo, G. Sclauzero, A. P. Seitsonen, A. Smogunov, P. Umari, and R. M. Wentzcovitch, J. Phys.-Condens. Matter 21, 395502 (2009), arXiv: 0906.2569.

    Article  Google Scholar 

  29. P. Giannozzi, O. Andreussi, T. Brumme, O. Bunau, M. Buongiorno Nardelli, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, M. Cococcioni, N. Colonna, I. Carnimeo, A. Dal Corso, S. de Gironcoli, P. Delugas, R. A. DiStasio Jr, A. Ferretti, A. Floris, G. Fratesi, G. Fugallo, R. Gebauer, U. Gerstmann, F. Giustino, T. Gorni, J. Jia, M. Kawamura, H. Y. Ko, A. Kokalj, E. Küçükbenli, M. Lazzeri, M. Marsili, N. Marzari, F. Mauri, N. L. Nguyen, H. V. Nguyen, A. Oterode-la-Roza, L. Paulatto, S. Poncé, D. Rocca, R. Sabatini, B. Santra, M. Schlipf, A. P. Seitsonen, A. Smogunov, I. Timrov, T. Thonhauser, P. Umari, N. Vast, X. Wu, and S. Baroni, J. Phys.-Condens. Matter 29, 465901 (2017), arXiv: 1709.10010.

    Article  Google Scholar 

  30. J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996).

    Article  ADS  Google Scholar 

  31. D. R. Hamann, Phys. Rev. B 88, 085117 (2013), arXiv: 1306.4707.

    Article  ADS  Google Scholar 

  32. M. J. van Setten, M. Giantomassi, E. Bousquet, M. J. Verstraete, D. R. Hamann, X. Gonze, and G. M. Rignanese, Comput. Phys. Commun. 226, 39 (2018), arXiv: 1710.10138.

    Article  ADS  Google Scholar 

  33. B. G. Márkus, F. Simon, K. Nagy, T. Fehér, S. Wild, G. Abellán, J. C. Chacón-Torres, A. Hirsch, and F. Hauke, Phys. Status Solidi (b) 254, 1700232 (2017), arXiv: 1805.01495.

    Article  ADS  Google Scholar 

  34. F. Martini, S. Borsacchi, G. Barcaro, M. Caporali, M. Vanni, M. Serrano-Ruiz, M. Geppi, M. Peruzzini, and L. Calucci, J. Phys. Chem. Lett. 10, 5122 (2019).

    Article  Google Scholar 

  35. S. M. Day, E. Otsuka, and B. Josephson, Phys. Rev. 137, A108 (1965).

    Article  ADS  Google Scholar 

  36. T. L. Guzzle, and P. P. Mahendroo, Phys. Rev. 150, 361 (1966).

    Article  ADS  Google Scholar 

  37. B. J. Suh, P. C. Hammel, M. Hücker, B. Büchner, U. Ammerahl, and A. Revcolevschi, Phys. Rev. B 61, R9265 (2000), arXiv: cond-mat/9911272.

    Article  ADS  Google Scholar 

  38. N. J. Curro, P. C. Hammel, B. J. Suh, M. Hücker, B. Büchner, U. Ammerahl, and A. Revcolevschi, Phys. Rev. Lett. 85, 642 (2000), arXiv: cond-mat/9911268.

    Article  ADS  Google Scholar 

  39. N. Bloembergen, E. M. Purcell, and R. V. Pound, Phys. Rev. 73, 679 (1948).

    Article  ADS  Google Scholar 

  40. H. Yasuoka, T. Kubo, Y. Kishimoto, D. Kasinathan, M. Schmidt, B. Yan, Y. Zhang, H. Tou, C. Felser, A. P. Mackenzie, and M. Baenitz, Phys. Rev. Lett. 118, 236403 (2017), arXiv: 1611.07311.

    Article  ADS  Google Scholar 

  41. C. G. Wang, Y. Honjo, L. X. Zhao, G. F. Chen, K. Matano, R. Zhou, and G. Zheng, Phys. Rev. B 101, 241110 (2020), arXiv: 2006.00213.

    Article  ADS  Google Scholar 

  42. Z. Okvátovity, F. Simon, and B. Dóra, Phys. Rev. B 94, 245141 (2016), arXiv: 1609.03370.

    Article  ADS  Google Scholar 

  43. H. Maebashi, T. Hirosawa, M. Ogata, and H. Fukuyama, J. Phys. Chem. Solids 128, 138 (2019).

    Article  ADS  Google Scholar 

  44. Z. Okvátovity, H. Yasuoka, M. Baenitz, F. Simon, and B. Dóra, Phys. Rev. B 99, 115107 (2019), arXiv: 1806.08163.

    Article  ADS  Google Scholar 

  45. P. Schlottmann, Phys. Rev. B 25, 4828 (1982).

    Article  ADS  Google Scholar 

  46. T. Hirosawa, H. Maebashi, and M. Ogata, Phys. Rev. B 101, 155103 (2020), arXiv: 1912.11996.

    Article  ADS  Google Scholar 

  47. C. Fang, Y. Chen, H. Y. Kee, and L. Fu, Phys. Rev. B 92, 081201 (2015), arXiv: 1506.03449.

    Article  ADS  Google Scholar 

  48. K. G. Klimenko, Z. Phys. C-Particles Fields 54, 323 (1992).

    Article  ADS  Google Scholar 

  49. V. P. Gusynin, V. A. Miransky, and I. A. Shovkovy, Phys. Lett. B 349, 477 (1995).

    Article  ADS  Google Scholar 

  50. Y. Huh, E. G. Moon, and Y. B. Kim, Phys. Rev. B 93, 035138 (2016), arXiv: 1506.05105.

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Rui Yu, Tao Wu or Xianhui Chen.

Ethics declarations

Conflict of interest The authors declare that they have no conflict of interest.

Additional information

This work was supported by the National Key R&D Program of the Ministry of Science and Technology of China (Grant Nos. 2017YFA0300201, and 2016YFA0303000), the Anhui Initiative in Quantum Information Technologies (Grant No. AHY160000), the National Natural Science Foundation of China (Grant No. 11534010), and the Key Research Program of Frontier Sciences, Chinese Academy of Sciences, China (Grant No. QYZDY-SSW-SLH021). Tao Wu thanks Yi Zhou, Zhong Wang, and Guozhu Liu for insightful discussion.

Supporting Information

The supporting information is available online at http://phys.scichina.com and https://link.springer.com. The supporting materials are published as submitted, without typesetting or editing. The responsibility for scientific accuracy and content remains entirely with the authors.

Supplementary Material for

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zheng, L., Luo, K., Sun, Z. et al. Magnetic-field-induced electronic instability of Weyl-like fermions in compressed black phosphorus. Sci. China Phys. Mech. Astron. 66, 117011 (2023). https://doi.org/10.1007/s11433-023-2189-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11433-023-2189-7

Navigation