Advertisement

Frontiers of Physics

, 12:127202 | Cite as

Topological nodal line semimetals predicted from first-principles calculations

Review Article
Part of the following topical collections:
  1. Recent Progress on Weyl Semimetals

Abstract

Topological semimetals are newly discovered states of quantum matter, which have extended the concept of topological states from insulators to metals and attracted great research interest in recent years. In general, there are three kinds of topological semimetals, namely Dirac semimetals, Weyl semimetals, and nodal line semimetals. Nodal line semimetals can be considered as precursor states for other topological states. For example, starting from such nodal line states, the nodal line structure might evolve into Weyl points, convert into Dirac points, or become a topological insulator by introducing the spin–orbit coupling (SOC) or mass term. In this review paper, we introduce theoretical materials that show the nodal line semimetal state, including the all-carbon Mackay–Terrones crystal (MTC), anti-perovskite Cu3PdN, pressed black phosphorus, and the CaP3 family of materials, and we present the design principles for obtaining such novel states of matter.

Keywords

topological states topological semimetals nodal line semimetal 

References

  1. 1.
    G. E. Volovik, The Universe in a Helium Droplet, Oxford, 2009CrossRefGoogle Scholar
  2. 2.
    Z. Fang, N. Nagaosa, K. S. Takahashi, A. Asamitsu, R. Mathieu, T. Ogasawara, H. Yamada, M. Kawasaki, Y. Tokura, and K. Terakura, The anomalous Hall effect and magnetic monopoles in momentum space, Science 302(5642), 92 (2003)ADSCrossRefGoogle Scholar
  3. 3.
    H. Weng, R. Yu, X. Hu, X. Dai, and Z. Fang, Quantum anomalous Hall effect and related topological electronic states, Adv. Phys. 64(3), 227 (2015)ADSCrossRefGoogle Scholar
  4. 4.
    C. Fang, Y. Chen, H. Y. Kee, and L. Fu, Topological nodal line semimetals with and without spin-orbital coupling, Phys. Rev. B 92(8), 081201 (2015)ADSCrossRefGoogle Scholar
  5. 5.
    Y. X. Zhao, A. P. Schnyder, and Z. D. Wang, Unified theory of PT and CP invariant topological metals and nodal superconductors, Phys. Rev. Lett. 116(15), 156402 (2016)ADSCrossRefGoogle Scholar
  6. 6.
    H. B. Nielsen and M. Ninomiya, The Adler–Bell–Jackiw anomaly and Weyl fermions in a crystal, Phys. Lett. B 130(6), 389 (1983)ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    X. Wan, A. M. Turner, A. Vishwanath, and S. Y. Savrasov, Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates, Phys. Rev. B 83(20), 205101 (2011)ADSCrossRefGoogle Scholar
  8. 8.
    G. Xu, H. Weng, Z. Wang, X. Dai, and Z. Fang, Chern semimetal and the quantized anomalous Hall effect in HgCr2Se4, Phys. Rev. Lett. 107(18), 186806 (2011)ADSCrossRefGoogle Scholar
  9. 9.
    L. Balents, Weyl electrons kiss, Physics 4, 36 (2011)CrossRefGoogle Scholar
  10. 10.
    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)ADSCrossRefGoogle Scholar
  11. 11.
    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)ADSCrossRefGoogle Scholar
  12. 12.
    A. A. Burkov, M. D. Hook, and L. Balents, Topological nodal semimetals, Phys. Rev. B 84(23), 235126 (2011)ADSCrossRefGoogle Scholar
  13. 13.
    H. Weng, Y. Liang, Q. Xu, R. Yu, Z. Fang, X. Dai, and Y. Kawazoe, Topological node-line semimetal in three dimensional graphene networks, arxiv: 1411.2175Google Scholar
  14. 14.
    B. J. Yang and N. Nagaosa, Classification of stable three-dimensional Dirac semimetals with nontrivial topology, Nat. Commun. 5, 4898 (2014)CrossRefGoogle Scholar
  15. 15.
    A. Pariari, P. Dutta, and P. Mandal, Probing the Fermi surface of three-dimensional Dirac semimetal Cd3As2 through the de Haas–van Alphen technique, Phys. Rev. B 91(15), 155139 (2015)ADSCrossRefGoogle Scholar
  16. 16.
    L. P. He, X. C. Hong, J. K. Dong, J. Pan, Z. Zhang, J. Zhang, and S. Y. Li, Quantum transport evidence for the three-dimensional Dirac semimetal phase in Cd3As2, Phys. Rev. Lett. 113(24), 246402 (2014)ADSCrossRefGoogle Scholar
  17. 17.
    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, 3786 (2014)Google Scholar
  18. 18.
    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)Google Scholar
  19. 19.
    Z. K. Liu, J. Jiang, B. Zhou, Z. J. Wang, Y. Zhang, H. M. Weng, D. Prabhakaran, S. K. Mo, H. Peng, P. Dudin, 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(7), 677 (2014)ADSCrossRefGoogle Scholar
  20. 20.
    Q. D. Gibson, L. M. Schoop, L. Muechler, L. S. Xie, N. P. Ong, M. Hirschberger, R. Car, and R. J. Cava, Three-dimensional Dirac semimetals: Design principles and predictions of new materials, Phys. Rev. B 91(20), 205128 (2015)ADSCrossRefGoogle Scholar
  21. 21.
    H. Weng, C. Fang, Z. Fang, B. A. Bernevig, and X. Dai, Weyl semimetal phase in noncentrosymmetric transition-metal monophosphides, Phys. Rev. X 5(1), 011029 (2015)Google Scholar
  22. 22.
    S. M. Huang, S. Y. Xu, I. Belopolski, C. C. Lee, G. Chang, B. Wang, N. Alidoust, G. Bian, M. Neupane, C. Zhang, S. Jia, A. Bansil, H. Lin, and M. Z. Hasan, A Weyl fermion semimetal with surface Fermi arcs in the transition metal monopnictide TaAs class, Nat. Commun. 6, 7373 (2015)CrossRefGoogle Scholar
  23. 23.
    A. A. Soluyanov, D. Gresch, Z. Wang, Q. S. Wu, M. Troyer, X. Dai, and B. A. Bernevig, Type-II Weyl semimetals, Nature 527(7579), 495 (2015)ADSCrossRefGoogle Scholar
  24. 24.
    B. Q. Lv, H. M. Weng, B. B. Fu, X. P. Wang, H. Miao, J. Ma, P. Richard, X. C. Huang, L. X. Zhao, G. F. Chen, Z. Fang, X. Dai, T. Qian, and H. Ding, Experimental discovery of Weyl semimetal TaAs, Phys. Rev. X 5(3), 031013 (2015)Google Scholar
  25. 25.
    X. Huang, L. Zhao, Y. Long, P. Wang, D. Chen, Z. Yang, H. Liang, M. Xue, H. Weng, Z. Fang, X. Dai, and G. Chen, Observation of the chiral-anomaly-induced negative magnetoresistance in 3d Weyl semimetal TaAs, Phys. Rev. X 5(3), 031023 (2015)Google Scholar
  26. 26.
    B. Q. Lv, N. Xu, H. M. Weng, J. Z. Ma, P. Richard, X. C. Huang, L. X. Zhao, G. F. Chen, C. E. Matt, F. Bisti, V. N. Strocov, J. Mesot, Z. Fang, X. Dai, T. Qian, M. Shi, and H. Ding, Observation of Weyl nodes in TaAs, Nat. Phys. 11(9), 724 (2015)CrossRefGoogle Scholar
  27. 27.
    S. Y. Xu, I. Belopolski, N. Alidoust, M. Neupane, G. Bian, C. Zhang, R. Sankar, G. Chang, Z. Yuan, C. C. Lee, S. M. Huang, H. Zheng, J. Ma, D. S. Sanchez, B. Wang, A. Bansil, F. Chou, P. P. Shibayev, H. Lin, S. Jia, and M. Z. Hasan, Discovery of a Weyl fermion semimetal and topological Fermi arcs, Science 349(6248), 613 (2015)ADSCrossRefGoogle Scholar
  28. 28.
    N. Xu, H. M. Weng, B. Q. Lv, C. E. Matt, J. Park, F. Bisti, V. N. Strocov, D. Gawryluk, E. Pomjakushina, K. Conder, N. C. Plumb, M. Radovic, G. Autès, O. V. Yazyev, Z. Fang, X. Dai, T. Qian, J. Mesot, H. Ding, and M. Shi, Observation of Weyl nodes and Fermi arcs in tantalum phosphide, Nat. Commun. 7, 11006 (2016)ADSCrossRefGoogle Scholar
  29. 29.
    B. Q. Lv, S. Muff, T. Qian, Z. D. Song, S. M. Nie, N. Xu, P. Richard, C. E. Matt, N. C. Plumb, L. X. Zhao, G. F. Chen, Z. Fang, X. Dai, J. H. Dil, J. Mesot, M. Shi, H. M. Weng, and H. Ding, Observation of Fermi-arc spin texture in TaAs, Phys. Rev. Lett. 115(21), 217601 (2015)ADSCrossRefGoogle Scholar
  30. 30.
    G. Chang, S. Y. Xu, D. S. Sanchez, S. M. Huang, C. C. Lee, T. R. Chang, H. Zheng, G. Bian, I. Belopolski, N. Alidoust, H. T. Jeng, A. Bansil, H. Lin, and M. Z. Hasan, A strongly robust Weyl fermion semimetal state in Ta3S2, arXiv: 1512.08781Google Scholar
  31. 31.
    J. Ruan, S. K. Jian, D. Zhang, H. Yao, H. Zhang, S. C. Zhang, and D. Xing, Ideal Weyl Semimetals in the Chalcopyrites CuTlSe2, AgTlTe2, AuTlTe2, and ZnPbAs2, Phys. Rev. Lett. 116(22), 226801 (2016)CrossRefGoogle Scholar
  32. 32.
    J. Ruan, S. K. Jian, H. Yao, H. Zhang, S. C. Zhang, and D. Xing, Symmetry-protected ideal Weyl semimetal in HgTe-class materials, Nat. Commun. 7, 11136 (2016)ADSCrossRefGoogle Scholar
  33. 33.
    M. Hirschberger, S. Kushwaha, Z. Wang, Q. Gibson, S. Liang, C. A. Belvin, B. A. Bernevig, R. J. Cava, and N. P. Ong, The chiral anomaly and thermopower of Weyl fermions in the half-Heusler GdPtBi, Nat. Mater. (2016), arXiv: 1602.07219Google Scholar
  34. 34.
    Z. Wang, M. G. Vergniory, S. Kushwaha, M. Hirschberger, E. V. Chulkov, A. Ernst, N. P. Ong, R. J. Cava, and B. A. Bernevig, Time-reversal breaking Weyl fermions in magnetic Heuslers, arXiv: 1603.00479Google Scholar
  35. 35.
    G. Autès, D. Gresch, M. Troyer, A. A. Soluyanov, and O. V. Yazyev, Robust type-II Weyl semimetal phase in transition metal diphosphides XP2 (X = Mo, W), Phys. Rev. Lett. 117(6), 066402 (2016)ADSCrossRefGoogle Scholar
  36. 36.
    C. K. Chiu and A. P. Schnyder, Classification of reflection-symmetry-protected topological semimetals and nodal superconductors, Phys. Rev. B 90(20), 205136 (2014)ADSCrossRefGoogle Scholar
  37. 37.
    T. T. Heikkilä, N. B. Kopnin, and G. E. Volovik, Flat bands in topological media, JETP Lett. 94(3), 233 (2011)ADSCrossRefGoogle Scholar
  38. 38.
    T. T. Heikkilä and G. E. Volovik, Dimensional crossover in topological matter: Evolution of the multiple Dirac point in the layered system to the flat band on the surface, JETP Lett. 93(2), 59 (2011)ADSCrossRefGoogle Scholar
  39. 39.
    T. T. Heikkila and G. E. Volovik, Flat bands as a route to high-temperature superconductivity in graphite, arXiv: 1504.05824Google Scholar
  40. 40.
    H. Weng, Y. Liang, Q. Xu, R. Yu, Z. Fang, X. Dai, and Y. Kawazoe, Topological node-line semimetal in three dimensional graphene networks, Phys. Rev. B 92(4), 045108 (2015)ADSCrossRefGoogle Scholar
  41. 41.
    K. Mullen, B. Uchoa, and D. T. Glatzhofer, Line of Dirac nodes in hyperhoney comb lattices, Phys. Rev. Lett. 115(2), 026403 (2015)ADSCrossRefGoogle Scholar
  42. 42.
    M. Ezawa, Loop-nodal and point-nodal semimetals in three-dimensional honeycomb lattices, Phys. Rev. Lett. 116(12), 127202 (2016)ADSCrossRefGoogle Scholar
  43. 43.
    L. S. Xie, L. M. Schoop, E. M. Seibel, Q. D. Gibson, W. Xie, and R. J. Cava, A new form of Ca3P2 with a ring of Dirac nodes, APL Mater. 3(8), 083602 (2015)ADSCrossRefGoogle Scholar
  44. 44.
    Y. H. Chan, C. K. Chiu, M. Y. Chou, and A. P. Schnyder, Ca3P2 and other topological semimetals with line nodes and drumhead surface states, Phys. Rev. B 93(20), 205132 (2016)ADSCrossRefGoogle Scholar
  45. 45.
    M. Zeng, C. Fang, G. Chang, Y.- A. Chen, T. Hsieh, A. Bansil, H. Lin, and L. Fu, Topological semimetals and topological insulators in rare earth monopnictides, arXiv: 1504.03492Google Scholar
  46. 46.
    R. Yu, H. Weng, Z. Fang, X. Dai, and X. Hu, Topological node-line semimetal and Dirac semimetal state in antiperovskite Cu3PdN, Phys. Rev. Lett. 115(3), 036807 (2015)ADSCrossRefGoogle Scholar
  47. 47.
    Y. Kim, B. J. Wieder, C. L. Kane, and A. M. Rappe, Dirac line nodes in inversion-symmetric crystals, Phys. Rev. Lett. 115(3), 036806 (2015)ADSCrossRefGoogle Scholar
  48. 48.
    Y. Chen, Y. Xie, S. A. Yang, H. Pan, F. Zhang, M. L. Cohen, and S. Zhang, Nanostructured carbon allotropes with Weyl-like loops and points, Nano Lett. 15(10), 6974 (2015)ADSCrossRefGoogle Scholar
  49. 49.
    G. Bian, T. R. Chang, H. Zheng, S. Velury, S. Y. Xu, T. Neupert, C. K. Chiu, S. M. Huang, D. S. Sanchez, I. Belopolski, N. Alidoust, P. J. Chen, G. Chang, A. Bansil, H. T. Jeng, H. Lin, and M. Z. Hasan, Drumhead surface states and topological nodal-line fermions in TlTaSe2, Phys. Rev. B 93(12), 121113 (2016)ADSCrossRefGoogle Scholar
  50. 50.
    G. Bian, T.- R. Chang, R. Sankar, S.- Y. Xu, H. Zheng, T. Neupert, C.- K. Chiu, S.- M. Huang, G. Chang, I. Belopolski, D. S. Sanchez, M. Neupane, N. Alidoust, C. Liu, B. Wang, C.- C. Lee, H.- T. Jeng, A. Bansil, F. Chou, H. Lin, and M. Zahid Hasan, Topological nodalline fermions in the non-centrosymmetric superconductor compound PbTaSe2, arXiv: 1505.03069Google Scholar
  51. 51.
    L. M. Schoop, M. N. Ali, C. Straßer, A. Topp, A. Varykhalov, D. Marchenko, V. Duppel, S. S. P. Parkin, B. V. Lotsch, and C. R. Ast, Dirac cone protected by non-symmorphic symmetry and three dimensional Dirac line node in ZrSiS, Nat. Commun. 7, 11696 (2016)ADSCrossRefGoogle Scholar
  52. 52.
    J. M. Carter, V. V. Shankar, M. A. Zeb, and H. Y. Kee, Semimetal and topological insulator in perovskite iridates, Phys. Rev. B 85(11), 115105 (2012)ADSCrossRefGoogle Scholar
  53. 53.
    H. S. Kim, Y. Chen, and H. Y. Kee, Surface states of perovskite iridates AIrO3: Signatures of a topological crystalline metal with nontrivial Z2 index, Phys. Rev. B 91(23), 235103 (2015)ADSCrossRefGoogle Scholar
  54. 54.
    J. Liu, D. Kriegner, L. Horak, D. Puggioni, C. Rayan Serrao, R. Chen, D. Yi, C. Frontera, V. Holy, A. Vishwanath, J. M. Rondinelli, X. Marti, and R. Ramesh, Strain-induced nonsymmorphic symmetry breaking and removal of Dirac semimetallic nodal line in an orthoperovskite iridate, Phys. Rev. B 93(8), 085118 (2016)ADSCrossRefGoogle Scholar
  55. 55.
    Y. Chen, Y. M. Lu, and H. Y. Kee, Topological crystalline metal in orthorhombic perovskite iridates, Nat. Commun. 6, 6593 (2015)CrossRefGoogle Scholar
  56. 56.
    A. Yamakage, Y. Yamakawa, Y. Tanaka, and Y. Okamoto, Line-node Dirac semimetal and topological insulating phase in noncentrosymmetric pnictides CaAgX (X = P, As), JPSJ 85(1), 013708 (2016)ADSCrossRefGoogle Scholar
  57. 57.
    Q. F. Liang, J. Zhou, R. Yu, Z. Wang, and H. Weng, Node-surface and node-line fermions from nonsymmorphic lattice symmetries, Phys. Rev. B 93(8), 085427 (2016)ADSCrossRefGoogle Scholar
  58. 58.
    J. Zhao, R. Yu, H. Weng, and Z. Fang, Topological node-line semimetal in compressed black phosphorus, arXiv: 1511.05704Google Scholar
  59. 59.
    Q. Xu, R. Yu, Z. Fang, X. Dai, and H. Weng, Topological nodal line semimetals in CaP3 family of materials, arXiv: 1608.03172Google Scholar
  60. 60.
    M. Hirayama, R. Okugawa, T. Miyake, and S. Murakami, Topological Dirac nodal lines in fcc calcium, strontium, and ytterbium, arXiv: 1602.06501Google Scholar
  61. 61.
    J. T. Wang, H. Weng, S. Nie, Z. Fang, Y. Kawazoe, and C. Chen, Body-centered orthorhombic C16: A novel topological node-line semimetal, Phys. Rev. Lett. 116(19), 195501 (2016)ADSCrossRefGoogle Scholar
  62. 62.
    R. Li, H. Ma, X. Cheng, S. Wang, D. Li, Z. Zhang, Y. Li, and X. Q. Chen, Dirac node lines in pure alkali earth metals, Phys. Rev. Lett. 117(9), 096401 (2016)ADSCrossRefGoogle Scholar
  63. 63.
    J. L. Lu, W. Luo, X. Y. Li, S. Q. Yang, J. X. Cao, X. G. Gong, and H. J. Xiang, Two-dimensional nodeline semimetals in a Honeycomb-Kagome lattice, arXiv: 1603.04596Google Scholar
  64. 64.
    Y. Jin, R. Wang, J. Zhao, C. Zheng, L. Y. Gan, J. Liu, H. Xu, and S. Y. Tong, A family group of two dimensional node-line semimetals, arXiv: 1608.05791Google Scholar
  65. 65.
    G. E. Volovik, The Topology of the Quantum Vacuum, Analogue Gravity Phenomenology, Lecture Notes in Physics, Vol. 870, p. 343 (2013)CrossRefMATHGoogle Scholar
  66. 66.
    N. B. Kopnin, T. T. Heikkila, and G. E. Volovik, Hightemperature surface superconductivity in topological flat-band systems, Phys. Rev. B 83(22), 220503 (2011)ADSCrossRefGoogle Scholar
  67. 67.
    G. E. Volovik, From standard model of particle physics to room-temperature superconductivity, Phys. Scr. 2015(T164), 014014 (2015)CrossRefGoogle Scholar
  68. 68.
    T. T. Heikkila and G. E. Volovik, Flat bands as a route to high-temperature superconductivity in graphite, arXiv: 1504.05824Google Scholar
  69. 69.
    J. W. Rhim and Y. B. Kim, Landau level quantization and almost flat modes in three-dimensional semimetals with nodal ring spectra, Phys. Rev. B 92(4), 045126 (2015)ADSCrossRefGoogle Scholar
  70. 70.
    Z. Yan, P. W. Huang, and Z. Wang, Collective modes in nodal line semimetals, Phys. Rev. B 93(8), 085138 (2016)ADSCrossRefGoogle Scholar
  71. 71.
    A. L. Mackay, Periodic minimal surfaces, Nature 314(6012), 604 (1985)ADSCrossRefGoogle Scholar
  72. 72.
    R. S. K. Mong and V. Shivamoggi, Edge states and the bulk-boundary correspondence in Dirac hamiltonians, Phys. Rev. B 83(12), 125109 (2011)ADSCrossRefGoogle Scholar
  73. 73.
    A. A. Mostofi, J. R. Yates, Y. S. Lee, I. Souza, D. Vanderbilt, and N. Marzari, wannier90: A tool for obtaining maximally-localised Wannier functions, Comput. Phys. Commun. 178(9), 685 (2008)ADSCrossRefMATHGoogle Scholar
  74. 74.
    N. Marzari, A. A. Mostofi, J. R. Yates, I. Souza, and D. Vanderbilt, Maximally localized Wannier functions: Theory and applications, Rev. Mod. Phys. 84(4), 1419 (2012)ADSCrossRefGoogle Scholar
  75. 75.
    R. Fei, V. Tran, and L. Yang, Topologically protected Dirac cones in compressed bulk black phosphorus, Phys. Rev. B 91(19), 195319 (2015)ADSCrossRefGoogle Scholar
  76. 76.
    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, Pressure-induced electronic transition in black phosphorus, Phys. Rev. Lett. 115(18), 186403 (2015)ADSCrossRefGoogle Scholar
  77. 77.
    K. Akiba, A. Miyake, Y. Akahama, K. Matsubayashi, Y. Uwatoko, H. Arai, Y. Fuseya, and M. Tokunaga, Anomalous quantum transport properties in semimetallic black phosphorus, J. Phys. Soc. Jpn. 84(7), 073708 (2015)ADSCrossRefGoogle Scholar
  78. 78.
    W. Dahlmann and H. G. v. Schnering, CaP3, ein neues Calciumphosphid, Naturwissenschaften 60(11), 518 (1973)ADSCrossRefGoogle Scholar
  79. 79.
    Z. Yan and Z. Wang, Tunable Weyl points in periodically driven nodal line semimetals, Phys. Rev. Lett. 117(8), 087402 (2016)ADSCrossRefGoogle Scholar

Copyright information

© Higher Education Press and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.School of Physics and TechnologyWuhan UniversityWuhanChina
  2. 2.Beijing National Laboratory for Condensed Matter Physics, and Institute of PhysicsChinese Academy of SciencesBeijingChina
  3. 3.Collaborative Innovation Center of Quantum MatterBeijingChina

Personalised recommendations