Advertisement

Frontiers of Physics

, 14:43603 | Cite as

Effective models for nearly ideal Dirac semimetals

  • Feng Tang
  • Xiangang WanEmail author
Research Article
Part of the following topical collections:
  1. Special Topic: Recent Advances in Topological Materials

Abstract

Topological materials (TMs) have gained intensive attention due to their novel behaviors compared with topologically trivial materials. Among various TMs, Dirac semimetal (DSM) has been studied extensively. Although several DSMs have been proposed and verified experimentally, the suitable DSM for realistic applications is still lacking. Thus finding ideal DSMs and providing detailed analyses to them are of both fundamental and technological importance. Here, we sort out 8 (nearly) ideal DSMs from thousands of topological semimetals in Nature 566(7745), 486 (2019). We show the concrete positions of the Dirac points in the Brillouin zone for these materials and clarify the symmetry-protection mechanism for these Dirac points as well as their low-energy effective models. Our results provide a useful starting point for future study such as topological phase transition under strain and transport study based on these effective models. These DSMs with high mobilities are expected to be applied in fabrication of functional electronic devices.

Keywords

Dirac semimetal symmetry effective model 

Notes

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Nos. 11525417, 11834006, 51721001, and 11790311) and the National Key R&D Program of China (Nos. 2018YFA0305704 and 2017YFA0303203).

References

  1. 1.
    K. Klitzing, G. Dorda, and M. Pepper, New method for high-accuracy determination of the fine-structure constant based on quantized Hall resistance, Phys. Rev. Lett. 45(6), 494 (1980)ADSGoogle Scholar
  2. 2.
    D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Quantized Hall conductance in a two-dimensional periodic potential, Phys. Rev. Lett. 49(6), 405 (1982)ADSGoogle Scholar
  3. 3.
    M. Z. Hasan and C. L. Kane, Colloquium: Topological insulators, Rev. Mod. Phys. 82(4), 3045 (2010)ADSGoogle Scholar
  4. 4.
    X. L. Qi and S. C. Zhang, Topological insulators and superconductors, Rev. Mod. Phys. 83(4), 1057 (2011)ADSGoogle Scholar
  5. 5.
    Y. Ando and L. Fu, Topological crystalline insulators and topological superconductors: From concepts to materials, Annu. Rev. Condens. Matter Phys. 6(1), 361 (2015)ADSGoogle Scholar
  6. 6.
    N. P. Armitage, E. J. Mele, and A. Vishwanath, Weyl and Dirac semimetals in three-dimensional solids, Rev. Mod. Phys. 90(1), 015001 (2018)ADSMathSciNetGoogle Scholar
  7. 7.
    T. O. Wehling, A. M. Black-Schaffer, and A. V. Balatsky, Dirac materials, Adv. Phys. 63(1), 1 (2014)ADSGoogle Scholar
  8. 8.
    S. M. Young, S. Zaheer, J. C. Y. Teo, C. L. Kane, E. J. Mele, and A. M. Rappe, Dirac semimetal in three dimensions, Phys. Rev. Lett. 108(14), 140405 (2012)ADSGoogle Scholar
  9. 9.
    Z. Wang, Y. Sun, X. Q. Chen, C. Franchini, G. Xu, H. Weng, X. Dai, and Z. Fang, Dirac semimetal and topological phase transitions in A3Bi (A = Na, K, Rb), Phys. Rev. B 85(19), 195320 (2012)ADSGoogle Scholar
  10. 10.
    Z. Wang, H. Weng, Q. Wu, X. Dai, and Z. Fang, Three-dimensional Dirac semimetal and quantum transport in Cd3As2, Phys. Rev. B 88(12), 125427 (2013)ADSGoogle Scholar
  11. 11.
    Z. K. Liu, B. Zhou, Y. Zhang, Z. J. Wang, H. M. Weng, D. Prabhakaran, S. K. Mo, Z. X. Shen, Z. Fang, X. Dai, Z. Hussain, and Y. L. Chen, Discovery of a three-dimensional topological Dirac semimetal, Na3Bi, Science 343(6173), 864 (2014)ADSGoogle Scholar
  12. 12.
    Z. K. Liu, J. Jiang, B. Zhou, Z. J. Wang, Y. Zhang, H. M. Weng, D. Prabhakaran, S.-K. Mo, H. Peng, P. Dudin6, T. Kim, M. Hoesch, Z. Fang, X. Dai, Z. X. Shen, D. L. Feng, Z. Hussain, and Y. L. Chen, A stable three-dimensional topological Dirac semimetal Cd3As2, Nat. Mater. 13, 677C681 (2014)Google Scholar
  13. 13.
    B. J. Yang and N. Nagaosa, Classification of stable three-dimensional Dirac semimetals with nontrivial topology, Nat. Commun. 5(1), 4898 (2014)Google Scholar
  14. 14.
    M. I. Katsnelson, K. S. Novoselov, and A. K. Geim, Chiral tunnelling and the Klein paradox in graphene, Nat. Phys. 2(9), 620 (2006)Google Scholar
  15. 15.
    M. Yan, H. Huang, K. Zhang, E. Wang, W. Yao, K. Deng, G. Wan, H. Zhang, M. Arita, H. Yang, Z. Sun, H. Yao, Y. Wu, S. Fan, W. Duan, and S. Zhou, Lorentz-violating type-II Dirac fermions in transition metal dichalcogenide PtTe2, Nat. Commun. 8(1), 257 (2017)ADSGoogle Scholar
  16. 16.
    H. J. Noh, J. Jeong, E. J. Cho, K. Kim, B. I. Min, and B. G. Park, Experimental realization of type-II Dirac fermions in a PdTe2 superconductor, Phys. Rev. Lett. 119(1), 016401 (2017)ADSGoogle Scholar
  17. 17.
    F. Fei, X. Bo, R. Wang, B. Wu, J. Jiang, D. Fu, M. Gao, H. Zheng, Y. Chen, X. Wang, H. Bu, F. Song, X. Wan, B. Wang, and G. Wang, Nontrivial Berry phase and type-II Dirac transport in the layered material PdTe2, Phys. Rev. B 96(4), 041201 (2017)ADSGoogle Scholar
  18. 18.
    Q. D. Gibson, L. M. Schoop, L. Muechler, L. S. Xie, M. Hirschberger, N. P. Ong, R. Car, and R. J. Cava, Three-dimensional Dirac semimetals: Design principles and predictions of new materials, Phys. Rev. B 91(20), 205128 (2015)ADSGoogle Scholar
  19. 19.
    Q. S. Wu, C. Piveteau, Z. Song, and O. V. Yazyev, MgTa2N3: A reference Dirac semimetal, Phys. Rev. 98, 081115(R) (2018)Google Scholar
  20. 20.
    W. D. Cao, P. Z. Tang, S.-C. Zhang, W. H. Duan, and A. Rubio, Stable Dirac semimetal in the allotropes of group-IV elements, Phys. Rev. B 93, 241117(R) (2016)ADSGoogle Scholar
  21. 21.
    X. Zhang, Q. Liu, Q. Xu, X. Dai, and A. Zunger, Topological insulators versus topological Dirac semimetals in honeycomb compounds, J. Am. Chem. Soc. 140(42), 13687 (2018)Google Scholar
  22. 22.
    X. L. Sheng, Z. Wang, R. Yu, H. Weng, Z. Fang, and X. Dai, Topological insulator to Dirac semimetal transition driven by sign change of spin-orbit coupling in thallium nitride, Phys. Rev. B 90(24), 245308 (2014)ADSGoogle Scholar
  23. 23.
    Y. Du, B. Wan, D. Wang, L. Sheng, C. G. Duan, and X. Wan, Dirac and Weyl semimetal in XYBi (X = Ba, Eu; Y = Cu, Ag and Au), Sci. Rep. 5(1), 14423 (2015)ADSGoogle Scholar
  24. 24.
    Y. P. Du, F. Tang, D. Wang, L. Sheng, E. J. Kan, C.-G. Duan, S. Y. Savrasov, and X. G. Wan, CaTe: A new topological node-line and Dirac semimetal, npj Quant. Mater. 2, 3 (2017)ADSGoogle Scholar
  25. 25.
    R. Chen, H. C. Po, J. B. Neaton, and A. Vishwanath, Topological materials discovery using electron filling constraints, Nat. Phys. 14(1), 55 (2018)Google Scholar
  26. 26.
    T. Zhang, Y. Jiang, Z. Song, H. Huang, Y. He, Z. Fang, H. Weng, and C. Fang, Catalogue of topological electronic materials, Nature 566(7745), 475 (2019)Google Scholar
  27. 27.
    M. G. Vergniory, L. Elcoro, C. Felser, N. Regnault, B. A. Bernevig, and Z. Wang, A complete catalogue of high-quality topological materials, Nature 566(7745), 480 (2019)Google Scholar
  28. 28.
    F. Tang, H. C. Po, A. Vishwanath, and X. Wan, Comprehensive search for topological materials using symmetry indicators, Nature 566(7745), 486 (2019)Google Scholar
  29. 29.
    J. Xiong, S. K. Kushwaha, T. Liang, J. W. Krizan, M. Hirschberger, W. Wang, R. J. Cava, and N. P. Ong, Evidence for the chiral anomaly in the Dirac semimetal Na3Bi, Science 350(6259), 413 (2015)ADSMathSciNetzbMATHGoogle Scholar
  30. 30.
    M. Neupane, S. Y. Xu, R. Sankar, N. Alidoust, G. Bian, C. Liu, I. Belopolski, T. R. Chang, H. T. Jeng, H. Lin, A. Bansil, F. Chou, and M. Z. Hasan, Observation of a three-dimensional topological Dirac semimetal phase in high-mobility Cd3As2, Nat. Commun. 5(1), 3786 (2014)Google Scholar
  31. 31.
    H. C. Po, A. Vishwanath, and H. Watanabe, Symmetry-based indicators of band topology in the 230 space groups, Nat. Commun. 8(1), 50 (2017)ADSGoogle Scholar
  32. 32.
    F. Tang, H. C. Po, A. Vishwanath, and X. Wan, Efficient topological materials discovery using symmetry indicators, Nat. Phys. 15, 470 (2019)Google Scholar
  33. 33.
    O. Muller and R. Roy, Synthesis and crystal chemistry of some new complex palladium oxides, Adv. Chem. Ser. 98, 28 (1971)Google Scholar
  34. 34.
    P. Norby, R. E. Dinnebier, and A. N. Fitch, Decomposition of silver carbonate: the crystal structure of two high-temperature modifications of Ag2CO3, Inorg. Chem. 41(14), 3628 (2002)Google Scholar
  35. 35.
    C. J. Bradley and A. P. Cracknell, The Mathematical Theory of Symmetry in Solids, Oxford: Claredon Press, 1972zbMATHGoogle Scholar
  36. 36.
    O. Graudejus and B. G. Mueller, Ag2+ in trigonalbipyramidaler Umgebung: Neue Fluoride mit zweiwertigem Silber: Ag M(II)3 M(IV)3 F20 (M(II) = Cd, Ca, Hg; M(IV) = Zr, Hf), Zeitschrift fuer Anorganische und Allgemeine Chemie (1950) (DE) 622, 1549–1556 (1996)Google Scholar
  37. 37.
    T. Yamada, V. L. Deringer, R. Dronskowski, and H. Yamane, Synthesis, crystal structure, chemical bonding, and physical properties of the ternary Na/Mg stannide, Na2MgSn, Inorg. Chem. 51(8), 4810 (2012)Google Scholar
  38. 38.
    B. Peng, C. M. Yue, H. Zhang, Z. Fang, and H. M. Weng, Predicting Dirac semimetals based on sodium ternary compounds, npj Comput. Mater. 4, 68 (2018)ADSGoogle Scholar
  39. 39.
    H. Zentgraf, K. Claes, and R. Hoppe, Oxide eines neuen Formeltyps: Zur Kenntnis von K3Ni2O4 und K3Pt2O4, Zeitschrift fuer Anorganische und Allgemeine Chemie (1950) (DE) 462, 92–105 (1980)Google Scholar
  40. 40.
    Z. Nong, J. Zhu, X. Yang, Y. Cao, Z. Lai, and Y. Liu, The mechanical, thermodynamic and electronic properties of Al3Nb with DO22 structure: A first-principles study, Physica B 407(17), 3555 (2012)ADSGoogle Scholar
  41. 41.
    H. He, C. Tyson, and S. Bobev, Eight-coordinated arsenic in the Zintl phases RbCd4As3 and RbZn4As3: Synthesis and structural characterization, Inorg. Chem. 50(17), 8375 (2011)Google Scholar
  42. 42.
    R. W. Henning and J. D. Corbett, Cs8Ga11, a new isolated cluster in a binary gallium compound: A family of valence analogues A8Tr11X: A = Cs, Rb; Tr = Ga, In, Tl; X = Cl, Br, I, Inorg. Chem. 36(26), 6045 (1997)Google Scholar
  43. 43.
    P. Blaha, K. Schwarz, G. Madsen, D. Kvasicka, and J. Luitz, WIEN2k: An Augmented Plane Wave Plus Local Orbitals Program for Calculating Crystal Properties, 2001Google Scholar
  44. 44.
    J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77(18), 3865(1996)ADSGoogle Scholar

Copyright information

© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.National Laboratory of Solid State Microstructures and School of PhysicsNanjing UniversityNanjingChina
  2. 2.Collaborative Innovation Center of Advanced MicrostructuresNanjing UniversityNanjingChina

Personalised recommendations