Please wait a minute...

Frontiers of Physics

Front. Phys.    2020, Vol. 15 Issue (4) : 43201     https://doi.org/10.1007/s11467-020-0963-7
TOPICAL REVIEW
Type-II topological metals
Si Li1,2(), Zhi-Ming Yu3, Yugui Yao3, Shengyuan A. Yang2
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
2. Research Laboratory for Quantum Materials, Singapore University of Technology and Design, Singapore 487372, Singapore
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
Download: PDF(2737 KB)  
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks
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.

Keywords type-II      nodal point      nodal line      topological metals     
This article is part of themed collection: Recent Advances in Topological Materials (Eds. Yugui Yao, Xiangang Wan, Shengyuan A. Yang, Hua Chen)
Corresponding Author(s): Si Li   
Issue Date: 12 May 2020
 Cite this article:   
Si Li,Zhi-Ming Yu,Yugui Yao, et al. Type-II topological metals[J]. Front. Phys. , 2020, 15(4): 43201.
 URL:  
http://journal.hep.com.cn/fop/EN/10.1007/s11467-020-0963-7
http://journal.hep.com.cn/fop/EN/Y2020/V15/I4/43201
Service
E-mail this article
E-mail Alert
RSS
Articles by authors
Si Li
Zhi-Ming Yu
Yugui Yao
Shengyuan A. Yang
1 N. Armitage, E. Mele, and A. Vishwanath, Weyl and Dirac semimetals in three-dimensional solids, Rev. Mod. Phys. 90(1), 015001 (2018)
2 A. Burkov, Topological semimetals, Nat. Mater. 15(11), 1145 (2016)
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)
4 S. A. Yang, in: Spin, Vol. 6, World Scientific, 2016, p. 1640003
5 A. Bansil, H. Lin, and T. Das, Topological band theory, Rev. Mod. Phys. 88(2), 021004 (2016)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
16 G. W. Winkler, S. Singh, and A. A. Soluyanov, Topology of triple-point metals, Chin. Phys. B 28(7), 077303 (2019)
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)
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)
19 B. J. Wieder, Y. Kim, A. Rappe, and C. Kane, Double Dirac semimetals in three dimensions, Phys. Rev. Lett. 116(18), 186402 (2016)
20 B. J. Yang and N. Nagaosa, Classification of stable threedimensional Dirac semimetals with nontrivial topology, Nat. Commun. 5, 4898 (2014)
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)
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)
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)
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)
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)
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)
27 Y. Xu, F. Zhang, and C. Zhang, Structured Weyl points in spin–orbit coupled fermionic superfluids, Phys. Rev. Lett. 115(26), 265304 (2015)
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)
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)
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)
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)
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)
33 Z. M. Yu, Y. Yao, and S. A. Yang, Predicted unusual magnetoresponsein type-II Weyl semimetals, Phys. Rev. Lett. 117(7), 077202 (2016)
34 V. Lukose, R. Shankar, and G. Baskaran, Novel electric field effects on Landau levels in graphene, Phys. Rev. Lett. 98(11), 116802 (2007)
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)
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)
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)
38 H. B. Nielsen and M. Ninomiya, The Adler–Bell–Jackiw anomaly and Weyl fermions in a crystal, Phys. Lett. B 130(6), 389 (1983)
39 D. Son and B. Spivak, Chiral anomaly and classical negative magnetoresistance of Weyl metals, Phys. Rev. B 88(10), 104412 (2013)
40 H. B. Nielsen and M. Ninomiya, Absence of neutrinos on a lattice, Nucl. Phys. B 185(1), 20 (1981)
41 H. B. Nielsen and M. Ninomiya, Absence of neutrinos on a lattice, Nucl. Phys. B 193(1), 173 (1981)
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)
43 Y. Gao, S. A. Yang, and Q. Niu, Intrinsic relative magnetoconductivity of nonmagnetic metals, Phys. Rev. B 95(16), 165135 (2017)
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)
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)
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)
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)
49 M. Koshino, Cyclotron resonance of figure-of-eight orbits in a type-II Weyl semimetal, Phys. Rev. B 94(3), 035202 (2016)
50 W. G. Unruh, Experimental black-hole evaporation? Phys. Rev. Lett. 46(21), 1351 (1981)
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)
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)
54 A. A. Zyuzin and R. P. Tiwari, Intrinsic anomalous Hall effect in type-II Weyl semimetals, JETP Lett. 103(11), 717 (2016)
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)
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)
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)
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)
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)
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)
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)
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)
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 noncentrosymmetric TaIrTe4, Phys. Rev. B 95(24), 241108 (2017)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
74 P. J. Guo, H. C. Yang, K. Liu, and Z. Y. Lu, Type-II Dirac semimetals in the YPd2 Sn class, Phys. Rev. B 95(15), 155112 (2017)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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)
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. B 97(12), 125143 (2018)
87 T. T. Heikkilä and G. E. Volovik, Nexus and Dirac lines in topological materials, New J. Phys. 17(9), 093019 (2015)
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)
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)
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)
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)
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)
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)
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)
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)
96 O. Türker and S. Moroz, Weyl nodal surfaces, Phys. Rev. B 97(7), 075120 (2018)
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)
98 F. Tang and X. Wan, Effective models for nearly ideal Dirac semimetals, Front. Phys. 14(4), 43603 (2019)
Related articles from Frontiers Journals
[1] Hao Yuan, Zhenyu Li. Interfacial properties of black phosphorus/transition metal carbide van der Waals heterostructures[J]. Front. Phys. , 2018, 13(3): 138103-.
[2] Rui Yu,Zhong Fang,Xi Dai,Hongming Weng. Topological nodal line semimetals predicted from first-principles calculations[J]. Front. Phys. , 2017, 12(3): 127202-.
[3] Xing-Chen Pan,Yiming Pan,Juan Jiang,Huakun Zuo,Huimei Liu,Xuliang Chen,Zhongxia Wei,Shuai Zhang,Zhihe Wang,Xiangang Wan,Zhaorong Yang,Donglai Feng,Zhengcai Xia,Liang Li,Fengqi Song,Baigeng Wang,Yuheng Zhang,Guanghou Wang. Carrier balance and linear magnetoresistance in type-II Weyl semimetal WTe2[J]. Front. Phys. , 2017, 12(3): 127203-.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed