Skip to main content
SpringerLink
Log in

Type-II topological metals

  • Topical Review
  • Published:
Frontiers of Physics Aims and scope Submit manuscript

Abstract

Topological metals (TMs) are a kind of special metallic materials, which feature nontrivial band crossings near the Fermi energy, giving rise to peculiar quasiparticle excitations. TMs can be classified based on the characteristics of these band crossings. For example, according to the dimensionality of the crossing, TMs can be classified into nodal-point, nodal-line, and nodal-surface metals. Another important property is the type of dispersion. According to degree of the tilt of the local dispersion around the crossing, we have type-I and type-II dispersions. This leads to significant distinctions in the physical properties of the materials, owing to their contrasting Fermi surface topologies. In this article, we briefly review the recent advances in this research direction, focusing on the concepts, the physical properties, and the material realizations of the type-II nodal-point and nodal-line TMs.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. N. Armitage, E. Mele, and A. Vishwanath, Weyl and Dirac semimetals in three-dimensional solids, Rev. Mod. Phys. 90(1), 015001 (2018)

    ADS  MathSciNet  Google Scholar 

  2. A. Burkov, Topological semimetals, Nat. Mater. 15(11), 1145 (2016)

    ADS  Google Scholar 

  3. C. K. Chiu, J. C. Teo, A. P. Schnyder, and S. Ryu, Classification of topological quantum matter with symmetries, Rev. Mod. Phys. 88(3), 035005 (2016)

    ADS  Google Scholar 

  4. S. A. Yang, in: Spin, Vol. 6, World Scientific, 2016, p. 1640003

    ADS  Google Scholar 

  5. A. Bansil, H. Lin, and T. Das, Topological band theory, Rev. Mod. Phys. 88(2), 021004 (2016)

    ADS  Google Scholar 

  6. S. Murakami, Phase transition between the quantum spin Hall and insulator phases in 3D: Emergence of a topological gapless phase, New J. Phys. 9(9), 356 (2007)

    ADS  Google Scholar 

  7. X. Wan, A. M. Turner, A. Vishwanath, and S. Y. Savrasov, Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochloreiridates, Phys. Rev. B 83(20), 205101 (2011)

    ADS  Google Scholar 

  8. S. M. Young, S. Zaheer, J. C. Teo, C. L. Kane, E. J. Mele, and A. M. Rappe, Dirac semimetal in three dimensions, Phys. Rev. Lett. 108(14), 140405 (2012)

    ADS  Google Scholar 

  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)

    ADS  Google Scholar 

  10. Z. Wang, H. Weng, Q. Wu, X. Dai, and Z. Fang, Threedimensional Dirac semimetal and quantum transport in Cd3As2, Phys. Rev. B 88(12), 125427 (2013)

    ADS  Google Scholar 

  11. B. Bradlyn, J. Cano, Z. Wang, M. Vergniory, C. Felser, R. J. Cava, and B. A. Bernevig, Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals, Science 353(6299), aaf5037 (2016)

    MathSciNet  MATH  Google Scholar 

  12. H. Weng, C. Fang, Z. Fang, and X. Dai, Topological semimetals with triply degenerate nodal points in θ-phase tantalum nitride, Phys. Rev. B 93(24), 241202 (2016)

    ADS  Google Scholar 

  13. Z. Zhu, G. W. Winkler, Q. Wu, J. Li, and A. A. Soluyanov, Triple point topological metals, Phys. Rev. X 6(3), 031003 (2016)

    Google Scholar 

  14. G. Chang, S. Y. Xu, S. M. Huang, D. S. Sanchez, C. H. Hsu, G. Bian, Z. M. Yu, I. Belopolski, N. Alidoust, H. Zheng, T.-R. Chang, H.-T. Jeng, S. A. Yang, T. Neupert, H. Lin, and M. Z. Hasan, Nexus fermions in topological symmorphic crystalline metals, Sci. Rep. 7, 1688 (2017)

    ADS  Google Scholar 

  15. S. Singh, Q. Wu, C. Yue, A. H. Romero, and A. A. Soluyanov, Topological phonons and thermoelectricity in triple-point metals, Phys. Rev. Mater. 2(11), 114204 (2018)

    Google Scholar 

  16. G. W. Winkler, S. Singh, and A. A. Soluyanov, Topology of triple-point metals, Chin. Phys. B 28(7), 077303 (2019)

    ADS  Google Scholar 

  17. R. Chapai, Y. Jia, W. Shelton, R. Nepal, M. Saghayezhian, J. DiTusa, E. Plummer, C. Jin, and R. Jin, Fermions and bosons in nonsymmorphic PdSb2 with six-fold degeneracy, Phys. Rev. B 99(16), 161110 (2019)

    ADS  Google Scholar 

  18. G. Shan and H. B. Gao, New topological semimetal candidate of nonsymmorphic PdSb2 with unique six-fold degenerate point, Front. Phys. 14(4), 43201 (2019)

    ADS  Google Scholar 

  19. B. J. Wieder, Y. Kim, A. Rappe, and C. Kane, Double Dirac semimetals in three dimensions, Phys. Rev. Lett. 116(18), 186402 (2016)

    ADS  Google Scholar 

  20. B. J. Yang and N. Nagaosa, Classification of stable three-dimensional Dirac semimetals with nontrivial topology, Nat. Commun. 5, 4898 (2014)

    ADS  Google Scholar 

  21. C. Fang, M. J. Gilbert, X. Dai, and B. A. Bernevig, Multi-Weyl topological semimetals stabilized by point group symmetry, Phys. Rev. Lett. 108(26), 266802 (2012)

    ADS  Google Scholar 

  22. Z. Zhu, Y. Liu, Z. M. Yu, S. S. Wang, Y. Zhao, Y. Feng, X. L. Sheng, and S. A. Yang, Quadratic contact point semimetal: Theory and material realization, Phys. Rev. B 98(12), 125104 (2018)

    ADS  Google Scholar 

  23. Z. M. Yu, W. Wu, X. L. Sheng, Y. Zhao, and S. A. Yang, Quadratic and cubic nodal lines stabilized by crystalline symmetry, Phys. Rev. B 99(12), 121106 (2019)

    ADS  Google Scholar 

  24. W. Wu, Z. M. Yu, X. Zhou, Y. Zhao, and S. A. Yang, Higher-order Dirac fermions in three dimensions, arXiv: 1912.09036 (2019)

    Google Scholar 

  25. X. P. Li, K. Deng, B. Fu, Y. Li, D. Ma, J. Han, J. Zhou, S. Zhou, and Y. Yao, Type-III Weyl semimetals and its materialization, arXiv: 1909.12178 (2019)

    Google Scholar 

  26. A. A. Soluyanov, D. Gresch, Z. Wang, Q. Wu, M. Troyer, X. Dai, and B. A. Bernevig, Type-II Weyl semimetals, Nature 527(7579), 495 (2015)

    ADS  Google Scholar 

  27. Y. Xu, F. Zhang, and C. Zhang, Structured Weyl points in spin–orbit coupled fermionic superfluids, Phys. Rev. Lett. 115(26), 265304 (2015)

    ADS  Google Scholar 

  28. S. Li, Z. M. Yu, Y. Liu, S. Guan, S. S. Wang, X. Zhang, Y. Yao, and S. A. Yang, Type-II nodal loops: Theory and material realization, Phys. Rev. B 96(8), 081106 (2017)

    ADS  Google Scholar 

  29. H. Huang, S. Zhou, and W. Duan, Type-II Dirac fermions in the PtSe2 class of transition metal dichalcogenides, Phys. Rev. B 94(12), 121117 (2016)

    ADS  Google Scholar 

  30. T. R. Chang, S. Y. Xu, D. S. Sanchez, W. F. Tsai, S. M. Huang, G. Chang, C. H. Hsu, G. Bian, I. Belopolski, Z. M. Yu, S. A. Yang, T. Neupert, H. T. Jeng, H. Lin, and M. Z. Hasan, Type-II symmetry-protected topological Dirac semimetals, Phys. Rev. Lett. 119(2), 026404 (2017)

    ADS  Google Scholar 

  31. C. Chen, S. S. Wang, L. Liu, Z. M. Yu, X. L. Sheng, Z. Chen, and S. A. Yang, Ternary Wurtzite CaAgBi materials family: A playground for essential and accidental, type-I and type-II Dirac fermions, Phys. Rev. Mater. 1(4), 044201 (2017)

    Google Scholar 

  32. J. Hu, W. Wu, C. Zhong, N. Liu, C. Ouyang, H. Y. Yang, and S. A. Yang, Three-dimensional honeycomb carbon: Junction line distortion and novel emergent fermions, Carbon 141, 417 (2019)

    Google Scholar 

  33. Z. M. Yu, Y. Yao, and S. A. Yang, Predicted unusual magnetoresponsein type-II Weyl semimetals, Phys. Rev. Lett. 117(7), 077202 (2016)

    ADS  Google Scholar 

  34. V. Lukose, R. Shankar, and G. Baskaran, Novel electric field effects on Landau levels in graphene, Phys. Rev. Lett. 98(11), 116802 (2007)

    ADS  Google Scholar 

  35. P. Li, Y. Wen, X. He, Q. Zhang, C. Xia, Z. M. Yu, S. A. Yang, Z. Zhu, H. N. Alshareef, and X. X. Zhang, Evidence for topological type-II Weyl semimetal WTe2, Nat. Commun. 8, 2150 (2017)

    ADS  Google Scholar 

  36. S. Tchoumakov, M. Civelli, and M. O. Goerbig, Magneticfield-induced relativistic properties in type-I and type-II Weyl semimetals, Phys. Rev. Lett. 117(8), 086402 (2016)

    ADS  Google Scholar 

  37. M. Udagawa and E. J. Bergholtz, Field-selective anomaly and chiral mode reversal in type-II Weyl materials, Phys. Rev. Lett. 117(8), 086401 (2016)

    ADS  Google Scholar 

  38. H. B. Nielsen and M. Ninomiya, The Adler–Bell–Jackiw anomaly and Weyl fermions in a crystal, Phys. Lett. B130(6), 389 (1983)

    ADS  MathSciNet  Google Scholar 

  39. D. Son and B. Spivak, Chiral anomaly and classical negative magnetoresistance of Weyl metals, Phys. Rev. B88(10), 104412 (2013)

    ADS  Google Scholar 

  40. H. B. Nielsen and M. Ninomiya, Absence of neutrinos on a lattice, Nucl. Phys. B 185(1), 20 (1981)

    ADS  Google Scholar 

  41. H. B. Nielsen and M. Ninomiya, Absence of neutrinos on a lattice, Nucl. Phys. B 193(1), 173 (1981)

    ADS  Google Scholar 

  42. Z. M. Yu, W. Wu, Y. Zhao, and S. A. Yang, Circumventing the no-go theorem: A single Weyl point without surface Fermi arcs, Phys. Rev. B 100(4), 041118 (2019)

    ADS  Google Scholar 

  43. Y. Gao, S. A. Yang, and Q. Niu, Intrinsic relative magnetoconductivity of nonmagnetic metals, Phys. Rev. B95(16), 165135 (2017)

    ADS  Google Scholar 

  44. P. Goswami, J. H. Pixley, and S. Das Sarma, Axial anomaly and longitudinal magnetoresistance of a generic three-dimensional metal, Phys. Rev. B 92(7), 075205 (2015)

    ADS  Google Scholar 

  45. T. O’Brien, M. Diez, and C. Beenakker, Magnetic breakdown and Klein tunneling in a type-II Weyl semimetal, Phys. Rev. Lett. 116(23), 236401 (2016)

    ADS  Google Scholar 

  46. G. Sundaram and Q. Niu, Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects, Phys. Rev. B

  47. D. Xiao, M. C. Chang, and Q. Niu, Berry phase effects on electronic properties, Rev. Mod. Phys. 82(3), 1959 (2010)

    ADS  MathSciNet  MATH  Google Scholar 

  48. T. Cai, S. A. Yang, X. Li, F. Zhang, J. Shi, W. Yao, and Q. Niu, Magnetic control of the valley degree of freedom of massive Dirac fermions with application to transition metal dichalcogenides, Phys. Rev. B 88(11), 115140 (2013)

    ADS  Google Scholar 

  49. M. Koshino, Cyclotron resonance of figure-of-eight orbits in a type-II Weyl semimetal, Phys. Rev. B 94(3), 035202 (2016)

    ADS  MathSciNet  Google Scholar 

  50. W. G. Unruh, Experimental black-hole evaporation? Phys. Rev. Lett. 46(21), 1351 (1981)

    ADS  Google Scholar 

  51. G. E. Volovik, The Universe in a Helium Droplet, Vol. 117, Oxford University Press on Demand, 2003

  52. S. Guan, Z.-M. Yu, Y. Liu, G.-B. Liu, L. Dong, Y. Lu, Y. Yao, and S. A. Yang, Artificial gravity field, astrophysical analogues, and topological phase transitions in strained topological semimetals, npj Quant. Mater. 2, 23 (2017)

    ADS  Google Scholar 

  53. K. Y. Yang, Y. M. Lu, and Y. Ran, Quantum Hall effects in a Weyl semimetal: Possible application in pyrochloreiridates, Phys. Rev. B 84(7), 075129 (2011)

    ADS  Google Scholar 

  54. A. A. Zyuzin and R. P. Tiwari, Intrinsic anomalous Hall effect in type-II Weyl semimetals, JETP Lett. 103(11), 717 (2016)

    ADS  Google Scholar 

  55. J. Jiang, Z. Liu, Y. Sun, H. Yang, C. Rajamathi, Y. Qi, L. Yang, C. Chen, H. Peng, C. Hwang, S. Z. Sun, S. K. Mo, I. Vobornik, J. Fujii, S. S. P. Parkin, C. Felser, B. H. Yan, and Y. L. Chen, Signature of type-II Weyl semimetal phase in MoTe2, Nat. Commun. 8(1), 13973 (2017)

    ADS  Google Scholar 

  56. K. Deng, G. Wan, P. Deng, K. Zhang, S. Ding, E. Wang, M. Yan, H. Huang, H. Zhang, Z. Xu, J. Denlinger, A. Fedorov, H. Yang, W. Duan, H. Yao, Y. Wu, S. Fan, H. Zhang, X. Chen, and S. Zhou, Experimental observation of topological Fermi arcs in type-II Weyl semimetal MoTe2, Nat. Phys. 12(12), 1105 (2016)

    Google Scholar 

  57. L. Huang, T. M. McCormick, M. Ochi, Z. Zhao, M. T. Suzuki, R. Arita, Y. Wu, D. Mou, H. Cao, J. Yan, N. Trivedi, and A. Kaminski, Spectroscopic evidence for a type II Weyl semimetallic state in MoTe2, Nat. Mater. 15(11), 1155 (2016)

    ADS  Google Scholar 

  58. A. Tamai, Q. Wu, I. Cucchi, F. Y. Bruno, S. Riccò, T. K. Kim, M. Hoesch, C. Barreteau, E. Giannini, C. Besnard, A. A. Soluyanov, and F. Baumberger, Fermi arcs and their topological character in the candidate type-II Weyl Semimetal MoTe2, Phys. Rev. X 6(3), 031021 (2016)

    Google Scholar 

  59. I. Belopolski, D. S. Sanchez, Y. Ishida, X. Pan, P. Yu, S. Y. Xu, G. Chang, T. R. Chang, H. Zheng, N. Alidoust, G. Bian, M. Neupane, S. M. Huang, C. C. Lee, Y. Song, H. Bu, G. Wang, S. Li, G. Eda, H. T. Jeng, T. Kondo, H. Lin, Z. Liu, F. Song, S. Shin, and M. Z. Hasan, Discovery of a new type of topological Weyl fermion semimetal state in MoxW1−xTe2, Nat. Commun. 7(1), 13643 (2016)

    ADS  Google Scholar 

  60. I. Belopolski, S. Y. Xu, Y. Ishida, X. Pan, P. Yu, D. S. Sanchez, H. Zheng, M. Neupane, N. Alidoust, G. Chang, T. R. Chang, Y. Wu, G. Bian, S. M. Huang, C. C. Lee, D. Mou, L. Huang, Y. Song, B. Wang, G. Wang, Y. W. Yeh, N. Yao, J. E. Rault, P. Le Fèvre, F. Bertran, H. T. Jeng, T. Kondo, A. Kaminski, H. Lin, Z. Liu, F. Song, S. Shin, and M. Z. Hasan, Fermi arc electronic structure and Chern numbers in the type-II Weyl semimetal candidate MoxW1−xTe2, Phys. Rev. B 94(8), 085127 (2016)

    ADS  Google Scholar 

  61. H. Zheng, G. Bian, G. Chang, H. Lu, S. Y. Xu, G. Wang, T. R. Chang, S. Zhang, I. Belopolski, N. Alidoust, D. S. Sanchez, F. Song, H. T. Jeng, N. Yao, A. Bansil, S. Jia, H. Lin, and M. Z. Hasan, Atomic-scale visualization of quasiparticle interference on a type-II Weyl semimetal surface, Phys. Rev. Lett. 117(26), 266804 (2016)

    ADS  Google Scholar 

  62. K. Koepernik, D. Kasinathan, D. Efremov, S. Khim, S. Borisenko, B. Büchner, and J. van den Brink, TaIrTe4: A ternary type-II Weyl semimetal, Phys. Rev. B 93(20), 201101 (2016)

    ADS  Google Scholar 

  63. E. Haubold, K. Koepernik, D. Efremov, S. Khim, A. Fedorov, Y. Kushnirenko, J. van den Brink, S. Wurmehl, B. Büchner, T. Kim, M. Hoesch, K. Sumida, K. Taguchi, T. Yoshikawa, A. Kimura, T. Okuda, and S. V. Borisenko, Experimental realization of type-II Weyl state in non-centrosymmetric TaIrTe4, Phys. Rev. B 95(24), 241108 (2017)

    ADS  Google Scholar 

  64. S. Y. Xu, N. Alidoust, G. Chang, H. Lu, B. Singh, I. Belopolski, D. S. Sanchez, X. Zhang, G. Bian, H. Zheng, M. A. Husanu, Y. Bian, S. M. Huang, C. H. Hsu, T. R. Chang, H. T. Jeng, A. Bansil, T. Neupert, V. N. Strocov, H. Lin, S. Jia, and M. Z. Hasan, Discovery of Lorentzviolating type II Weyl fermions in LaAlGe, Sci. Adv. 3(6), e1603266 (2017)

    ADS  Google Scholar 

  65. 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)

    ADS  Google Scholar 

  66. N. Kumar, Y. Sun, N. Xu, K. Manna, M. Yao, V. Süss, I. Leermakers, O. Young, T. Förster, M. Schmidt, H. Borrmann, B. Yan, U. Zeitler, M. Shi, C. Felser, and C. Shekhar, Extremely high magnetoresistance and conductivity in the type-II Weyl semimetals WP2 and MoP2, Nat. Commun. 8, 1642 (2017)

    ADS  Google Scholar 

  67. G. Chang, S. Y. Xu, D. S. Sanchez, S. M. Huang, C. C. Lee, T. R. Chang, G. Bian, H. Zheng, I. Belopolski, N. Alidoust, H. T. Jeng, A. Bansil, H. Lin, and M. Z. Hasan, A strongly robust type II Weyl fermion semimetal state in Ta3S2, Sci. Adv. 2(6), e1600295 (2016)

    ADS  Google Scholar 

  68. S. Borisenko, D. Evtushinsky, Q. Gibson, A. Yaresko, K. Koepernik, T. Kim, M. Ali, J. van den Brink, M. Hoesch, A. Fedorov, E. Haubold, Y. Kushnirenko, I. Soldatov, R. Schäfer, and R. J. Cava, Time-reversal symmetry breaking type-II Weyl state in YbMnBi2, Nat. Commun. 10(1), 1 (2019)

    Google Scholar 

  69. Z. Zhu, D. Yan, X. A. Nie, H. K. Xu, X. Yang, D. D. Guan, S. Wang, Y. Y. Li, C. Liu, J. W. Liu, H. X. Luo, H. Zheng, and J. F. Jia, Scanning tunneling microscopic investigation on morphology of magnetic Weyl semimetal YbMnBi2, Chin. Phys. B 28(7), 077302 (2019)

    ADS  Google Scholar 

  70. 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. S. Fan, W. H. Duan, and S. Y. Zhou, Lorentz-violating type-II Dirac fermions in transition metal dichalcogenide PtTe2, Nat. Commun. 8, 257 (2017)

    ADS  Google Scholar 

  71. K. Zhang, M. Yan, H. Zhang, H. Huang, M. Arita, Z. Sun, W. Duan, Y. Wu, and S. Zhou, Experimental evidence for type-II Dirac semimetal in PtSe2, Phys. Rev. B 96(12), 125102 (2017)

    ADS  Google Scholar 

  72. H. J. Noh, J. Jeong, E. J. Cho, K. Kim, B. Min, and B. G. Park, Experimental realization of type-II Dirac fermions in a PdTe2 superconductor, Phys. Rev. Lett. 119(1), 016401 (2017)

    ADS  Google Scholar 

  73. 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)

    ADS  Google Scholar 

  74. P. J. Guo, H. C. Yang, K. Liu, and Z. Y. Lu, Type-II Dirac semimetals in the YPd2 Sn class, Phys. Rev. B95(15), 155112 (2017)

    ADS  Google Scholar 

  75. L. Tao and E. Y. Tsymbal, Two-dimensional type-II Dirac fermions in a LaAlO3/LaNiO3/LaAlO3 quantum well, Phys. Rev. B 98(12), 121102 (2018)

    ADS  Google Scholar 

  76. M. Horio, C. Matt, K. Kramer, D. Sutter, A. Cook, Y. Sassa, K. Hauser, M. Månsson, N. C. Plumb, M. Shi, O. J. Lipscombe, S. M. Hayden, T. Neupert, and J. Chang, Two-dimensional type-II Dirac fermions in layered oxides, Nat. Commun. 9(1), 3252 (2018)

    ADS  Google Scholar 

  77. C. Mondal, C. K. Barman, B. Pathak, and A. Alam, Type-II Dirac states in full Heusler compounds XInPd2 (X = Ti, Zr, and Hf), Phys. Rev. B 100(24), 245151 (2019)

    ADS  Google Scholar 

  78. B. Ghosh, D. Mondal, C. N. Kuo, C. S. Lue, J. Nayak, J. Fujii, I. Vobornik, A. Politano, and A. Agarwal, Observation of bulk states and spin-polarized topological surface states in transition metal dichalcogenide Dirac semimetal candidate NiTe2, Phys. Rev. B 100(19), 195134 (2019)

    ADS  Google Scholar 

  79. S. Li, Y. Liu, Z. M. Yu, Y. Jiao, S. Guan, X. L. Sheng, Y. Yao, and S. A. Yang, Two-dimensional antiferromagnetic Dirac fermions in monolayer TaCoTe2, Phys. Rev. B 100(20), 205102 (2019)

    ADS  Google Scholar 

  80. F. Y. Li, X. Luo, X. Dai, Y. Yu, F. Zhang, and G. Chen, Hybrid Weyl semimetal, Phys. Rev. B 94(12), 121105 (2016)

    ADS  Google Scholar 

  81. S. Khim, K. Koepernik, D. V. Efremov, J. Klotz, T. Förster, J. Wosnitza, M. I. Sturza, S. Wurmehl, C. Hess, J. van den Brink, and B. Büchner, Magnetotransport and de Haas–van Alphen measurements in the type-II Weyl semimetal TaIrTe4, Phys. Rev. B 94(16), 165145 (2016)

    ADS  Google Scholar 

  82. R. Chen, B. Zhou, and D. H. Xu, FloquetWeyl semimetals in light-irradiated type-II and hybrid line-node semimetals, Phys. Rev. B 97(15), 155152 (2018)

    ADS  Google Scholar 

  83. X. Zhang, L. Jin, X. Dai, and G. Liu, Topological type-II nodal line semimetal and Dirac semimetal state in stable Kagome compound Mg3Bi2, J. Phys. Chem. Lett. 8(19), 4814 (2017)

    Google Scholar 

  84. T. R. Chang, I. Pletikosic, T. Kong, G. Bian, A. Huang, J. Denlinger, S. K. Kushwaha, B. Sinkovic, H. T. Jeng, T. Valla, W. Xie, and R. J. Cava, Realization of a type-II nodal-line semimetal in Mg3Bi2, Adv. Sci. 6(4), 1800897 (2019)

    Google Scholar 

  85. D. Kim, S. Ahn, J. H. Jung, H. Min, J. Ihm, J. H. Han, and Y. Kim, Type-II Dirac line node in strained Na3N, Phys. Rev. Mater. 2(10), 104203 (2018)

    Google Scholar 

  86. X. Zhang, Z. M. Yu, Y. Lu, X. L. Sheng, H. Y. Yang, and S. A. Yang, Hybrid nodal loop metal: Unconventional magnetoresponse and material realization, Phys. Rev. B97(12), 125143 (2018)

    ADS  Google Scholar 

  87. T. T. Heikkilä and G. E. Volovik, Nexus and Dirac lines in topological materials, New J. Phys. 17(9), 093019 (2015)

    ADS  MATH  Google Scholar 

  88. T. Hyart and T. Heikkilä, Momentum-space structure of surface states in a topological semimetal with a nexus point of Dirac lines, Phys. Rev. B 93(23), 235147 (2016)

    ADS  Google Scholar 

  89. Y. Gao, Y. Chen, Y. Xie, P. Y. Chang, M. L. Cohen, and S. Zhang, A class of topological nodal rings and its realization in carbon networks, Phys. Rev. B 97(12), 121108 (2018)

    ADS  Google Scholar 

  90. Z. Zhao, Y. Hang, Z. Zhang, and W. Guo, Topological hybrid nodal-loop semimetal in a carbon allotrope constructed by interconnected Riemann surfaces, Phys. Rev. B 100(11), 115420 (2019)

    ADS  Google Scholar 

  91. Z. Li, W. Wang, P. Zhou, Z. Ma, and L. Sun, New type of hybrid nodal line semimetal in Be2Si, New J. Phys. 21(3), 033018 (2019)

    ADS  Google Scholar 

  92. M. P. Kennett, N. Komeilizadeh, K. Kaveh, and P. M. Smith, Birefringent breakup of Dirac fermions on a square optical lattice, Phys. Rev. A 83(5), 053636 (2011)

    ADS  Google Scholar 

  93. B. Roy, P. M. Smith, and M. P. Kennett, Asymmetric spatial structure of zero modes for birefringent Dirac fermions, Phys. Rev. B 85(23), 235119 (2012)

    ADS  Google Scholar 

  94. C. Zhong, Y. Chen, Y. Xie, S. A. Yang, M. L. Cohen, and S. Zhang, Towards three-dimensional Weyl-surface semimetals in graphene networks, Nanoscale 8(13), 7232 (2016)

    ADS  Google Scholar 

  95. 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)

    ADS  Google Scholar 

  96. O. Türker and S. Moroz, Weyl nodal surfaces, Phys. Rev. B 97(7), 075120 (2018)

    ADS  Google Scholar 

  97. W. Wu, Y. Liu, S. Li, C. Zhong, Z. M. Yu, X. L. Sheng, Y. Zhao, and S. A. Yang, Nodal surface semimetals: Theory and material realization, Phys. Rev. B 97(11), 115125 (2018)

    ADS  Google Scholar 

  98. F. Tang and X. Wan, Effective models for nearly ideal Dirac semimetals, Front. Phys. 14(4), 43603 (2019)

    ADS  MathSciNet  Google Scholar 

Download references

Acknowledgements

The authors thank D. L. Deng for valuable discussions. The work was supported by the National Natural Science Foundation of China (Grants No. 11734003), the National Key R&D Program of China (Grant No. 2016YFA0300600), the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB30000000), and the Singapore Ministry of Education AcRF Tier 2 (Grant Nos. MOE2017-T2-2-108 and MOE2019-T2-1-001).

Author information

Authors and Affiliations

  1. Key Laboratory of Low-Dimensional Quantum Structures and Quantum Control of Ministry of Education, Department of Physics and Synergetic Innovation Center for Quantum Effects and Applications, Hunan Normal University, Changsha, 410081, China

    Si Li

  2. Research Laboratory for Quantum Materials, Singapore University of Technology and Design, Singapore, 487372, Singapore

    Si Li & Shengyuan A. Yang

  3. Key Lab of Advanced Optoelectronic Quantum Architecture and Measurement (MOE), Beijing Key Lab of Nanophotonics & Ultrafine Optoelectronic Systems, and School of Physics, Beijing Institute of Technology, Beijing, 100081, China

    Zhi-Ming Yu & Yugui Yao

Authors
  1. Si Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhi-Ming Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yugui Yao
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Shengyuan A. Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Si Li.

Additional information

arXiv: 2003.03328.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Li, S., Yu, ZM., Yao, Y. et al. Type-II topological metals. Front. Phys. 15, 43201 (2020). https://doi.org/10.1007/s11467-020-0963-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11467-020-0963-7

Keywords

Search

Navigation