Quantum transport in topological semimetals under magnetic fields (II)

doi:10.1007/s11467-019-0890-7

Front. Phys.

2019, Vol. 14

Issue (3) : 33405 https://doi.org/10.1007/s11467-019-0890-7

Review article

Quantum transport in topological semimetals under magnetic fields (II)

Hai-Peng Sun^1,^2,³, Hai-Zhou Lu^2,³(

)

¹. Department of Physics, Harbin Institute of Technology, Harbin 150001, China
². Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen 518055, China
³. Shenzhen Key Laboratory of Quantum Science and Engineering, Shenzhen 518055, China

Download: PDF(4045 KB)
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

Abstract

We review our recent works on the quantum transport, mainly in topological semimetals and also in topological insulators, organized according to the strength of the magnetic field. At weak magnetic fields, we explain the negative magnetoresistance in topological semimetals and topological insulators by using the semiclassical equations of motion with the nontrivial Berry curvature. We show that the negative magnetoresistance can exist without the chiral anomaly. At strong magnetic fields, we establish theories for the quantum oscillations in topological Weyl, Dirac, and nodal-line semimetals. We propose a new mechanism of 3D quantum Hall effect, via the “wormhole” tunneling through the Weyl orbit formed by the Fermi arcs and Weyl nodes in topological semimetals. In the quantum limit at extremely strong magnetic fields, we find that an unexpected Hall resistance reversal can be understood in terms of the Weyl fermion annihilation. Additionally, in parallel magnetic fields, longitudinal resistance dips in the quantum limit can serve as signatures for topological insulators.

Keywords topological semimetal topological insulator quantum oscillation negative magnetoresistance quantum Hall effect

Corresponding Author(s): Hai-Zhou Lu

Issue Date: 25 April 2019

Cite this article:

Hai-Peng Sun,Hai-Zhou Lu. Quantum transport in topological semimetals under magnetic fields (II)[J]. Front. Phys. , 2019, 14(3): 33405.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-019-0890-7
https://academic.hep.com.cn/fop/EN/Y2019/V14/I3/33405

1	H.-Z. Lu and S.-Q. Shen, Quantum transport in topological semimetals under magnetic fields, Front. Phys.12, 127201 (2017) https://doi.org/10.1007/s11467-016-0609-y
2	H. Z. Lu and S. Q. Shen, Weak antilocalization and localization in disordered and interacting Weyl semimetals, Phys. Rev. B92, 035203 (2015) https://doi.org/10.1103/PhysRevB.92.035203
3	X. Dai, H.-Z. Lu, S.-Q. Shen, and H. Yao, Detecting monopole charge in Weyl semimetals via quantum interference transport, Phys. Rev. B93, 161110(R) (2016) https://doi.org/10.1103/PhysRevB.93.161110
4	H. Li, H. T. He, H. Z. Lu, H. C. Zhang, H. C. Liu, R. Ma, Z. Y. Fan, S. Q. Shen, and J. N. Wang, Negative magnetoresistance in Dirac semimetal Cd3As2, Nat. Commun.7, 10301 (2016) https://doi.org/10.1038/ncomms10301
5	H. Z. Lu, S. B. Zhang, and S. Q. Shen, High-field magnetoconductivity of topological semimetals with short-range potential, Phys. Rev. B92, 045203 (2015) https://doi.org/10.1103/PhysRevB.92.045203
6	S.-B. Zhang, H.-Z. Lu, and S.-Q. Shen, Linear magnetoconductivity in an intrinsic topological Weyl semimetal, New J. Phys.18, 053039 (2016) https://doi.org/10.1088/1367-2630/18/5/053039
7	C. M. Wang, H.-P. Sun, H.-Z. Lu, and X. C. Xie, 3D quantum Hall effect of Fermi arcs in topological semimetals, Phys. Rev. Lett.119, 136806 (2017) https://doi.org/10.1103/PhysRevLett.119.136806
8	C. M. Wang, H.-Z. Lu, and S.-Q. Shen, Anomalous phase shift of quantum oscillations in 3D topological semimetals, Phys. Rev. Lett.117, 077201 (2016) https://doi.org/10.1103/PhysRevLett.117.077201
9	C. Li, C. M. Wang, B. Wan, X. Wan, H.-Z. Lu, and X. C. Xie, Rules for phase shifts of quantum oscillations in topological nodal-line semimetals, Phys. Rev. Lett.120, 146602 (2018) https://doi.org/10.1103/PhysRevLett.120.146602
10	X. Dai, Z. Z. Du, and H.-Z. Lu, Negative magnetoresistance without chiral anomaly in topological insulators, Phys. Rev. Lett.119, 166601 (2017) https://doi.org/10.1103/PhysRevLett.119.166601
11	C.-L. Zhang, et al., Magnetic-tunnelling-induced Weyl node annihilation in TaP, Nat. Phys.13, 979 (2017) https://doi.org/10.1038/nphys4183
12	Y. Chen, H.-Z. Lu, and X. C. Xie, Forbidden backscattering and resistance dip in the quantum limit as a signature for topological insulators, Phys. Rev. Lett.121, 036602 (2018) https://doi.org/10.1103/PhysRevLett.121.036602
13	H. Weng, X. Dai, and Z. Fang, Topological semimetals predicted from first-principles calculations, J. Phys.: Condens. Matter28, 303001 (2016) https://doi.org/10.1088/0953-8984/28/30/303001
14	B. Yan and C. Felser, Topological materials: Weyl semimetals, Ann. Rev. Condens. Matter Phys.8, 337 (2017) https://doi.org/10.1146/annurev-conmatphys-031016-025458
15	N. P. Armitage, E. J. Mele, and A. Vishwanath, Weyl and Dirac semimetals in three-dimensional solids, Rev. Mod. Phys.90, 015001 (2018) https://doi.org/10.1103/RevModPhys.90.015001
16	H. Wang and J. Wang, Electron transport in Dirac and Weyl semimetals, Chin. Phys. B27, 107402 (2018) https://doi.org/10.1088/1674-1056/27/10/107402
17	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. B83, 205101 (2011) https://doi.org/10.1103/PhysRevB.83.205101
18	K. Y. Yang, Y. M. Lu, and Y. Ran, Quantum Hall effects in a Weyl semimetal: Possible application in pyrochlore iridates, Phys. Rev. B84, 075129 (2011) https://doi.org/10.1103/PhysRevB.84.075129
19	A. A. Burkov and L. Balents, Weyl semimetal in a topological insulator multilayer, Phys. Rev. Lett.107, 127205 (2011) https://doi.org/10.1103/PhysRevLett.107.127205
20	G. Xu, H. M. Weng, Z. J. Wang, X. Dai, and Z. Fang, Chern semimetal and the quantized anomalous Hall effect in HgCr2Se4, Phys. Rev. Lett.107, 186806 (2011) https://doi.org/10.1103/PhysRevLett.107.186806
21	P. Delplace, J. Li, and D. Carpentier, Topological Weyl semi-metal from a lattice model, EPL97, 67004 (2012) https://doi.org/10.1209/0295-5075/97/67004
22	J.-H. Jiang, Tunable topological Weyl semimetal from simple-cubic lattices with staggered fluxes, Phys. Rev. A85, 033640 (2012) https://doi.org/10.1103/PhysRevA.85.033640
23	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, 140405 (2012) https://doi.org/10.1103/PhysRevLett.108.140405
24	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. B85, 195320 (2012) https://doi.org/10.1103/PhysRevB.85.195320
25	B. Singh, A. Sharma, H. Lin, M. Z. Hasan, R. Prasad, and A. Bansil, Topological electronic structure and Weyl semimetal in the TlBiSe2 class of semiconductors, Phys. Rev. B86, 115208 (2012) https://doi.org/10.1103/PhysRevB.86.115208
26	Z. Wang, H. Weng, Q. Wu, X. Dai, and Z. Fang, Threedimensional Dirac semimetal and quantum transport in Cd3As2, Phys. Rev. B88, 125427 (2013) https://doi.org/10.1103/PhysRevB.88.125427
27	J. Liu and D. Vanderbilt, Weyl semimetals from noncentrosymmetric topological insulators, Phys. Rev. B90, 155316 (2014) https://doi.org/10.1103/PhysRevB.90.155316
28	D. Bulmash, C.-X. Liu, and X.-L. Qi, Prediction of a Weyl semimetal in HgCdMnTe, Phys. Rev. B89, 081106 (2014) https://doi.org/10.1103/PhysRevB.89.081106
29	Z. K. Liu, et al., Discovery of a three-dimensional topological Dirac semimetal, Na3Bi, Science343, 864 (2014) https://doi.org/10.1126/science.1245085
30	S. Y. Xu, et al., Observation of Fermi arc surface states in a topological metal, Science347, 294 (2015) https://doi.org/10.1126/science.1256742
31	Z. K. Liu, et al., A stable three-dimensional topological Dirac semimetal Cd3As2, Nat. Mater.13, 677 (2014) https://doi.org/10.1038/nmat3990
32	M. Neupane, et al., Observation of a three-dimensional topological Dirac semimetal phase in high-mobility Cd3As2, Nat. Commun.5, 3786 (2014) https://doi.org/10.1038/ncomms4786
33	S. Borisenko, Q. Gibson, D. Evtushinsky, V. Zabolotnyy, B. Büchner, and R. J. Cava, Experimental realization of a three-dimensional Dirac semimetal, Phys. Rev. Lett.113, 027603 (2014) https://doi.org/10.1103/PhysRevLett.113.027603
34	H. Yi, et al., Evidence of topological surface state in three-dimensional Dirac semimetal Cd3As2, Sci. Rep.4, 6106 (2014) https://doi.org/10.1038/srep06106
35	C. Zhang, et al., Room-temperature chiral charge pumping in Dirac semimetals, Nat. Commun.8, 13741 (2017) https://doi.org/10.1038/ncomms13741
36	C. Z. Li, L. X. Wang, H. W. Liu, J. Wang, Z. M. Liao, and D. P. Yu, Giant negative magnetoresistance induced by the chiral anomaly in individual Cd3As2 nanowires, Nat. Commun.6, 10137 (2015) https://doi.org/10.1038/ncomms10137
37	S. M. Huang, et al., A Weyl fermion semimetal with surface Fermi arcs in the transition metal monopnictide TaAs class, Nat. Commun.6, 7373 (2015) https://doi.org/10.1038/ncomms8373
38	H. M. Weng, C. Fang, Z. Fang, B. A. Bernevig, and X. Dai, Weyl semimetal phase in noncentrosymmetric transition-metal monophosphides, Phys. Rev. X5, 011029 (2015) https://doi.org/10.1103/PhysRevX.5.011029
39	B. Q. Lv, et al., Experimental discovery of Weyl semimetal TaAs, Phys. Rev. X5, 031013 (2015) https://doi.org/10.1103/PhysRevX.5.031013
40	B. Q. Lv, et al., Observation of Weyl nodes in TaAs, Nat. Phys.11, 724 (2015) https://doi.org/10.1038/nphys3426
41	B. Q. Lv, et al., Observation of Fermi-arc spin texture in TaAs, Phys. Rev. Lett.115, 217601 (2015) https://doi.org/10.1103/PhysRevLett.115.217601
42	S. Y. Xu, et al., Discovery of a Weyl fermion semimetal and topological Fermi arcs, Science349, 613 (2015) https://doi.org/10.1126/science.aaa9297
43	L. X. Yang, et al., Weyl semimetal phase in the noncentrosymmetric compound TaAs, Nat. Phys.11, 728 (2015) https://doi.org/10.1038/nphys3425
44	Z. K. Liu, et al., Evolution of the Fermi surface of Weyl semimetals in the transition metal pnictide family, Nat. Mater.15, 27 (2015) https://doi.org/10.1038/nmat4457
45	C. L. Zhang, et al., Signatures of the Adler–Bell–Jackiw chiral anomaly in a Weyl Fermion semimetal, Nat. Commun.7, 10735 (2016) https://doi.org/10.1038/ncomms10735
46	X. C. Huang, et al., Observation of the chiralanomaly-induced negative magnetoresistance in 3D Weyl semimetal TaAs, Phys. Rev. X5, 031023 (2015) https://doi.org/10.1103/PhysRevX.5.031023
47	S.-Y. Xu, et al., Discovery of a Weyl fermion state with Fermi arcs in niobium arsenide, Nat. Phys.11, 748 (2015) https://doi.org/10.1038/nphys3437
48	N. Xu, et al., Observation of Weyl nodes and Fermi arcs in tantalum phosphide, Nat. Commun.7, 11006 (2016) https://doi.org/10.1038/ncomms11006
49	S.-Y. Xu, et al., Spin polarization and texture of the Fermi arcs in the Weyl fermion semimetal TaAs, Phys. Rev. Lett.116, 096801 (2016)
50	I. Belopolski, et al., Criteria for directly detecting topological Fermi arcs in Weyl semimetals, Phys. Rev. Lett.116, 066802 (2016) https://doi.org/10.1103/PhysRevLett.116.066802
51	I. Belopolski, et al., Fermi arc electronic structure and Chern numbers in the type-II Weyl semimetal candidate MoxW1-xTe2, Phys. Rev. B94, 085127 (2016) https://doi.org/10.1103/PhysRevB.94.085127
52	S.-Y. Xu, et al., Experimental discovery of a topological weyl semimetal state in tap, Sci. Adv.1, 10 (2015)
53	I. Belopolski, et al., Signatures of a time-reversal symmetric Weyl semimetal with only four Weyl points, Nat. Commun.8, 942 (2017) https://doi.org/10.1038/s41467-017-00938-1
54	S. Borisenko, D. Evtushinsky, Q. Gibson, A. Yaresko, T. Kim, M. N. Ali, B. Buechner, M. Hoesch, and R. J. Cava, Time-reversal symmetry breaking type-II Weyl state in YbMnBi2, arXiv: 1507.04847 (2015)
55	M. Hirschberger, S. Kushwaha, Z. Wang, Q. Gibson, S. Liang, C. 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.15, 1161 (2016) https://doi.org/10.1038/nmat4684
56	C. Felser and B. Yan, Weyl semimetals: Magnetically induced, Nat. Mater.15, 1149 (2016) https://doi.org/10.1038/nmat4741
57	C. Shekhar, et al., Anomalous Hall effect in Weyl semimetal half-Heusler compounds RPtBi (R = Gd and Nd), Proc. Natl. Acad. Sci. USA115, 9140 (2018) https://doi.org/10.1073/pnas.1810842115
58	S.-Q. Shen, Topological Insulators, 2nd Ed., Springer-Verlag, Berlin Heidelberg, 2017
59	R. Okugawa and S. Murakami, Dispersion of Fermi arcs in Weyl semimetals and their evolutions to Dirac cones, Phys. Rev. B89, 235315 (2014) https://doi.org/10.1103/PhysRevB.89.235315
60	H. Z. Lu, S. B. Zhang, and S. Q. Shen, High-field magnetoconductivity of topological semimetals with short-range potential, Phys. Rev. B92, 045203 (2015) https://doi.org/10.1103/PhysRevB.92.045203
61	P. E. C. Ashby and J. P. Carbotte, Theory of magnetic oscillations in Weyl semimetals, Eur. Phys. J. B87 (2014) https://doi.org/10.1140/epjb/e2014-50023-7
62	E. V. Gorbar, V. A. Miransky, and I. A. Shovkovy, Chiral anomaly, dimensional reduction, and magnetoresistivity of Weyl and Dirac semimetals, Phys. Rev. B89, 085126 (2014) https://doi.org/10.1103/PhysRevB.89.085126
63	H. Z. Lu, W. Y. Shan, W. Yao, Q. Niu, and S. Q. Shen, Massive Dirac fermions and spin physics in an ultrathin film of topological insulator, Phys. Rev. B81, 115407 (2010) https://doi.org/10.1103/PhysRevB.81.115407
64	S. Jeon, B. B. Zhou, A. Gyenis, B. E. Feldman, I. Kimchi, A. C. Potter, Q. D. Gibson, R. J. Cava, A. Vishwanath, and A. Yazdani, Landau quantization and quasiparticle interference in the three-dimensional Dirac semimetal Cd3As2, Nat. Mater.13, 851 (2014) https://doi.org/10.1038/nmat4023
65	A. A. Burkov, M. D. Hook, and L. Balents, Topological nodal semimetals, Phys. Rev. B84, 235126 (2011) https://doi.org/10.1103/PhysRevB.84.235126
66	C.-K. Chiu and A. P. Schnyder, Classification of reflection-symmetry-protected topological semimetals and nodal superconductors, Phys. Rev. B90, 205136 (2014) https://doi.org/10.1103/PhysRevB.90.205136
67	C. Fang, H. Weng, X. Dai, and Z. Fang, Topological nodal line semimetals, Chin. Phys. B25, 117106 (2016) https://doi.org/10.1088/1674-1056/25/11/117106
68	B.-J. Yang, T. A. Bojesen, T. Morimoto, and A. Furusaki, Topological semimetals protected by off-centered symmetries in nonsymmorphic crystals, Phys. Rev. B95, 075135 (2017) https://doi.org/10.1103/PhysRevB.95.075135
69	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, 6974 (2015) https://doi.org/10.1021/acs.nanolett.5b02978
70	T. Bzdušek, Q. Wu, A. Rüegg, M. Sigrist, and A. A. Soluyanov, Nodal-chain metals, Nature538, 75 (2016) https://doi.org/10.1038/nature19099
71	X. Feng, C. Yue, Z. Song, Q. Wu, and B. Wen, Topological Dirac nodal-net fermions in AlB2-type TiB2 and ZrB2, Phys. Rev. Mater.2, 014202 (2018) https://doi.org/10.1103/PhysRevMaterials.2.014202
72	C.-J. Yi, et al., Observation of a nodal chain with Dirac surface states in TiB2, Phys. Rev. B97, 201107 (2018) https://doi.org/10.1103/PhysRevB.97.201107
73	W. Chen, K. Luo, L. Li, and O. Zilberberg, Proposal for detecting nodal-line semimetal surface states with resonant spin-flipped reflection, Phys. Rev. Lett.121, 166802 (2018) https://doi.org/10.1103/PhysRevLett.121.166802
74	Z. Zhu, et al., Quasiparticle interference and nonsymmorphic effect on a floating band surface state of ZrSiSe, Nat. Commun.9, 4153 (2018) https://doi.org/10.1038/s41467-018-06661-9
75	W. Chen and J. L. Lado, Interaction driven surface Chern insulator in nodal line semimetals, arXiv: 1807.06916 (2018) https://doi.org/10.1103/PhysRevLett.122.016803
76	H. Weng, Y. Liang, Q. Xu, R. Yu, Z. Fang, X. Dai, and Y. Kawazoe, Topological node-line semimetal in threedimensional graphene networks, Phys. Rev. B92, 045108 (2015) https://doi.org/10.1103/PhysRevB.92.045108
77	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, 036807 (2015) https://doi.org/10.1103/PhysRevLett.115.036807
78	Y. Kim, B. J. Wieder, C. L. Kane, and A. M. Rappe, Dirac line nodes in inversion-symmetric crystals, Phys. Rev. Lett.115, 036806 (2015) https://doi.org/10.1103/PhysRevLett.115.036806
79	C. Fang, Y. Chen, H.-Y. Kee, and L. Fu, Topological nodal line semimetals with and without spin-orbital coupling, Phys. Rev. B92, 081201 (2015) https://doi.org/10.1103/PhysRevB.92.081201
80	Y. Chen, Y.-M. Lu, and H.-Y. Kee, Topological crystalline metal in orthorhombic perovskite iridates, Nat. Commun.6, 6593 (2015) https://doi.org/10.1038/ncomms7593
81	G. Bian, et al., Drumhead surface states and topological nodal-line fermions in TlTaSe2, Phys. Rev. B93, 121113 (2016) https://doi.org/10.1103/PhysRevB.93.121113
82	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, 083602 (2015) https://doi.org/10.1063/1.4926545
83	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. B93, 205132 (2016) https://doi.org/10.1103/PhysRevB.93.205132
84	Y. Du, F. Tang, D. Wang, L. Sheng, E.-j. Kan, C.-G. Duan, S. Y. Savrasov, and X. Wan, CaTe: A new topological node-line and Dirac semimetal, npj Quantum Mater.2, 3 (2017) https://doi.org/10.1038/s41535-016-0005-4
85	J. Zhao, R. Yu, H. Weng, and Z. Fang, Topological nodeline semimetal in compressed black phosphorus, Phys. Rev. B94, 195104 (2016) https://doi.org/10.1103/PhysRevB.94.195104
86	A. Yamakage, Y. Yamakawa, Y. Tanaka, and Y. Okamoto, Line-node Dirac semimetal and topological insulating phase in noncentrosymmetric pnictides CaAgX (X= P, As), J. Phys. Soc. Japan85, 013708 (2015) https://doi.org/10.7566/JPSJ.85.013708
87	Q. Xu, R. Yu, Z. Fang, X. Dai, and H. Weng, Topological nodal line semimetals in the CaP3 family of materials, Phys.Rev. B95, 045136 (2017) https://doi.org/10.1103/PhysRevB.95.045136
88	Y.-J. Jin, R. Wang, J.-Z. Zhao, Y.-P. Du, C.-D. Zheng, L.-Y. Gan, J.-F. Liu, H. Xu, and S. Tong, The prediction of a family group of two-dimensional node-line semimetals, Nanoscale9, 13112 (2017) https://doi.org/10.1039/C7NR03520A
89	Z. Zhu, M. Li, and J. Li, Topological semimetal to insulator quantum phase transition in the Zintl compounds Ba2X (X=Si,Ge), Phys. Rev. B94, 155121 (2016) https://doi.org/10.1103/PhysRevB.94.155121
90	Q.-F. Liang, J. Zhou, R. Yu, Z. Wang, and H. Weng, Node-surface and node-line fermions from nonsymmorphic lattice symmetries, Phys. Rev. B93, 085427 (2016) https://doi.org/10.1103/PhysRevB.93.085427
91	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: 1504.03492 (2015)
92	M. Hirayama, R. Okugawa, T. Miyake, and S. Murakami, Topological Dirac nodal lines and surface charges in fcc alkaline earth metals, Nat Commun.8, 14022 (2017) https://doi.org/10.1038/ncomms14022
93	H. Huang, J. Liu, D. Vanderbilt, and W. Duan, Topological nodal-line semimetals in alkaline-earth stannides, germanides, and silicides, Phys. Rev. B93, 201114 (2016) https://doi.org/10.1103/PhysRevB.93.201114
94	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, 096401 (2016) https://doi.org/10.1103/PhysRevLett.117.096401
95	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, 195501 (2016) https://doi.org/10.1103/PhysRevLett.116.195501
96	Y. Sun, Y. Zhang, C.-X. Liu, C. Felser, and B. Yan, Dirac nodal lines and induced spin Hall effect in metallic rutile oxides, Phys. Rev. B95, 235104 (2017) https://doi.org/10.1103/PhysRevB.95.235104
97	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) https://doi.org/10.1038/ncomms11696
98	M. Neupane, et al., Observation of topological nodal fermion semimetal phase in ZrSiS, Phys. Rev. B93, 201104 (2016) https://doi.org/10.1103/PhysRevB.93.201104
99	C. Chen, et al., Dirac line nodes and effect of spin-orbit coupling in the nonsymmorphic critical semimetals MSiS (M=Hf,Zr), Phys. Rev. B95, 125126 (2017) https://doi.org/10.1103/PhysRevB.95.125126
100	G. Bian, et al., Topological nodal-line fermions in spinorbit metal PbTaSe2, Nat. Commun.7, 10556 (2016) https://doi.org/10.1038/ncomms10556
101	T.-R. Chang, et al., Topological Dirac surface states and superconducting pairing correlations in PbTaSe2, Phys. Rev. B93, 245130 (2016) https://doi.org/10.1103/PhysRevB.93.245130
102	S. A. Ekahana, et al., Observation of nodal line in nonsymmorphic topological semimetal InBi, New J. Phys.19, 065007 (2017) https://doi.org/10.1088/1367-2630/aa75a1
103	Y. Wu, L.-L. Wang, E. Mun, D. D. Johnson, D. Mou, L. Huang, Y. Lee, S. L. Bud’ko, P. C. Canfield, and A. Kaminski, Dirac node arcs in PtSn4, Nat. Phys.12, 667 (2016) https://doi.org/10.1038/nphys3712
104	A. Alexandradinata and L. Glazman, Semiclassical theory of Landau levels and magnetic breakdown in topological metals, Phys. Rev. B97, 144422 (2018) https://doi.org/10.1103/PhysRevB.97.144422
105	H. Zhang, C.-X. Liu, X.-L. Qi, X. Dai, Z. Fang, and S.-C. Zhang, Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface, Nat. Phys.5, 438 (2009) https://doi.org/10.1038/nphys1270
106	I. A. Nechaev and E. E. Krasovskii, Relativistic k·p Hamiltonians for centrosymmetric topological insulators from ab initio wave functions, Phys. Rev. B94, 201410 (2016) https://doi.org/10.1103/PhysRevB.94.201410
107	W.-Y. Shan, H.-Z. Lu, and S.-Q. Shen, Effective continuous model for surface states and thin films of threedimensional topological insulators, New J. Phys.12, 043048 (2010) https://doi.org/10.1088/1367-2630/12/4/043048
108	Y. Zhang, et al., Crossover of the three-dimensional topological insulator Bi2Se3 to the two-dimensional limit, Nat. Phys.6, 584 (2010) https://doi.org/10.1038/nphys1689
109	J. Wang, et al., Anomalous anisotropic magnetoresistance in topological insulator films, Nano Res.5, 739 (2012) https://doi.org/10.1007/s12274-012-0260-z
110	H. T. He, H. C. Liu, B. K. Li, X. Guo, Z. J. Xu, M. H. Xie, and J. N. Wang, Disorder-induced linear magnetoresistance in (221) topological insulator Bi2Se3 films, Appl. Phys. Lett.103, 031606 (2013) https://doi.org/10.1063/1.4816078
111	S. Wiedmann, et al., Anisotropic and strong negative magnetoresistance in the three-dimensional topological insulator Bi2Se3, Phys. Rev. B94, 081302 (2016) https://doi.org/10.1103/PhysRevB.94.081302
112	L.-X. Wang, Y. Yan, L. Zhang, Z.-M. Liao, H.-C. Wu, and D.-P. Yu, Zeeman effect on surface electron transport in topological insulator Bi2Se3 nanoribbons, Nanoscale7, 16687 (2015) https://doi.org/10.1039/C5NR05250E
113	S. L. Adler, Axial-vector vertex in spinor electrodynamics, Phys. Rev.177, 2426 (1969) https://doi.org/10.1103/PhysRev.177.2426
114	J. S. Bell and R. Jackiw, A PCAC puzzle: π0→γγ in the σ-model, Il Nuovo Cimento A60, 47 (1969) https://doi.org/10.1007/BF02823296
115	H. B. Nielsen and M. Ninomiya, Absence of neutrinos on a lattice (i): Proof by homotopy theory, Nucl. Phys. B185, 20 (1981) https://doi.org/10.1016/0550-3213(81)90361-8
116	H. J. Kim, K. S. Kim, J. F. Wang, M. Sasaki, N. Satoh, A. Ohnishi, M. Kitaura, M. Yang, and L. Li, Dirac versus Weyl fermions in topological insulators: Adler-Bell-Jackiw anomaly in transport phenomena, Phys. Rev. Lett.111, 246603 (2013) https://doi.org/10.1103/PhysRevLett.111.246603
117	K.-S. Kim, H.-J. Kim, and M. Sasaki, Boltzmann equation approach to anomalous transport in a Weyl metal, Phys. Rev. B89, 195137 (2014) https://doi.org/10.1103/PhysRevB.89.195137
118	Q. Li, D. E. Kharzeev, C. Zhang, Y. Huang, I. Pletikosic, A. V. Fedorov, R. D. Zhong, J. A. Schneeloch, G. D. Gu, and T. Valla, Chiral magnetic effect in ZrTe5, Nat. Phys.12, 550 (2016) https://doi.org/10.1038/nphys3648
119	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, Science350, 413 (2015) https://doi.org/10.1126/science.aac6089
120	F. Arnold, et al., Negative magnetoresistance without well-defined chirality in the Weyl semimetal TaP, Nat. Commun.7, 11615 (2016) https://doi.org/10.1038/ncomms11615
121	X. J. Yang, Y. P. Liu, Z. Wang, Y. Zheng, and Z. A. Xu, Chiral anomaly induced negative magnetoresistance in topological Weyl semimetal NbAs, arXiv: 1506.03190 (2015)
122	X. Yang, Y. Li, Z. Wang, Y. Zhen, and Z.-A. Xu, Observation of negative magnetoresistance and nontrivial π Berry’s phase in 3D Weyl semi-metal NbAs, arXiv: 1506.02283 (2015)
123	H. Wang, et al., Chiral anomaly and ultrahigh mobility in crystalline HfTe5, Phys. Rev. B93, 165127 (2016) https://doi.org/10.1103/PhysRevB.93.165127
124	O. Breunig, Z. Wang, A. A. Taskin, J. Lux, A. Rosch, and Y. Ando, Gigantic negative magnetoresistance in the bulk of a disordered topological insulator, Nat. Commun.8, 15545 (2017) https://doi.org/10.1038/ncomms15545
125	B. A. Assaf, et al., Negative longitudinal magnetoresistance from the anomalous N = 0 Landau level in topological materials, Phys. Rev. Lett.119, 106602 (2017) https://doi.org/10.1103/PhysRevLett.119.106602
126	M. Zhang, et al., Topological phase transition-induced triaxial vector magnetoresistance in (Bi1-xInx)2Se3 nanodevices, ACS Nano12, 1537 (2018) https://doi.org/10.1021/acsnano.7b08054
127	C. Fleckenstein, N. Traverso Ziani, and B. Trauzettel, Chiral anomaly in real space from stable fractional charges at the edge of a quantum spin hall insulator, Phys. Rev. B94, 241406 (2016) https://doi.org/10.1103/PhysRevB.94.241406
128	A. Wolos, et al., g-factors of conduction electrons and holes in Bi2Se3 three-dimensional topological insulator, Phys. Rev. B93, 155114 (2016) https://doi.org/10.1103/PhysRevB.93.155114
129	D. Culcer, Transport in three-dimensional topological insulators: Theory and experiment, Physica E44, 860 (2012) https://doi.org/10.1016/j.physe.2011.11.003
130	G. Sundaram and Q. Niu, Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects, Phys. Rev. B59, 14915 (1999) https://doi.org/10.1103/PhysRevB.59.14915
131	D. Xiao, M. C. Chang, and Q. Niu, Berry phase effects on electronic properties, Rev. Mod. Phys.82, 1959 (2010) https://doi.org/10.1103/RevModPhys.82.1959
132	G. D. Mahan, Many-Particle Physics, Plenum Press, 1990 https://doi.org/10.1007/978-1-4613-1469-1
133	D. T. Son and B. Z. Spivak, Chiral anomaly and classical negative magnetoresistance of Weyl metals, Phys. Rev. B88, 104412 (2013) https://doi.org/10.1103/PhysRevB.88.104412
134	S.-K. Yip, Kinetic equation and magneto-conductance for Weyl metal in the clean limit, arXiv: 1508.01010 (2015)
135	A. A. Burkov, Chiral anomaly and diffusive magnetotransport in Weyl metals, Phys. Rev. Lett.113, 247203 (2014) https://doi.org/10.1103/PhysRevLett.113.247203
136	S. Mao, A. Yamakage, and Y. Kuramoto, Tight-binding model for topological insulators: Analysis of helical surface modes over the whole Brillouin zone, Phys. Rev. B84, 115413 (2011) https://doi.org/10.1103/PhysRevB.84.115413
137	J. G. Checkelsky, Y. S. Hor, M.-H. Liu, D.-X. Qu, R. J. Cava, and N. P. Ong, Quantum interference in macroscopic crystals of nonmetallic Bi2Se3, Phys. Rev. Lett.103, 246601 (2009) https://doi.org/10.1103/PhysRevLett.103.246601
138	J.Chen, et al., Gate-voltage control of chemical potential and weak antilocalization in Bi2Se3, Phys. Rev. Lett.105, 176602 (2010) https://doi.org/10.1103/PhysRevLett.105.176602
139	J. Wang, A. M. DaSilva, C.-Z. Chang, K. He, J. K. Jain, N. Samarth, X.-C. Ma, Q.-K. Xue, and M. H. W. Chan, Evidence for electron-electron interaction in topological insulator thin films, Phys. Rev. B83, 245438 (2011) https://doi.org/10.1103/PhysRevB.83.245438
140	H.-T. He, G. Wang, T. Zhang, I.-K. Sou, G. K. L. Wong, J.-N. Wang, H.-Z. Lu, S.-Q. Shen, and F.-C. Zhang, Impurity effect on weak antilocalization in the topological insulator Bi2Te3, Phys. Rev. Lett.106, 166805 (2011) https://doi.org/10.1103/PhysRevLett.106.166805
141	H. Köhler and E. Wöchner, The g-factor of the conduction electrons in Bi2Se3, physica status solidi (b)67, 665 (1975) https://doi.org/10.1002/pssb.2220670229
142	A. Srinivasan, K. L. Hudson, D. Miserev, L. A. Yeoh, O. Klochan, K. Muraki, Y. Hirayama, O. P. Sushkov, and A. R. Hamilton, Electrical control of the sign of the g factor in a GaAs hole quantum point contact, Phys. Rev. B94, 041406 (2016) https://doi.org/10.1103/PhysRevB.94.041406
143	T. Morimoto, S. Zhong, J. Orenstein, and J. E. Moore, Semiclassical theory of nonlinear magneto-optical responses with applications to topological Dirac/Weyl semimetals, Phys. Rev. B94, 245121 (2016) https://doi.org/10.1103/PhysRevB.94.245121
144	Y. Gao, S. A. Yang, and Q. Niu, Intrinsic relative magnetoconductivity of nonmagnetic metals, Phys. Rev. B95, 165135 (2017) https://doi.org/10.1103/PhysRevB.95.165135
145	Y. Gao, S. A. Yang, and Q. Niu, Field induced positional shift of Bloch electrons and its dynamical implications, Phys. Rev. Lett.112, 166601 (2014) https://doi.org/10.1103/PhysRevLett.112.166601
146	Y. Gao, S. A. Yang, and Q. Niu, Geometrical effects in orbital magnetic susceptibility, Phys. Rev. B91, 214405 (2015) https://doi.org/10.1103/PhysRevB.91.214405
147	P. Goswami, J. H. Pixley, and S. Das Sarma, Axial anomaly and longitudinal magnetoresistance of a generic three-dimensional metal, Phys. Rev. B92, 075205 (2015) https://doi.org/10.1103/PhysRevB.92.075205
148	R. D. dos Reis, M. O. Ajeesh, N. Kumar, F. Arnold, C. Shekhar, M. Naumann, M. Schmidt, M. Nicklas, and E. Hassinger, On the search for the chiral anomaly in Weyl semimetals: the negative longitudinal magnetoresistance, New J. Phys.18, 085006 (2016) https://doi.org/10.1088/1367-2630/18/8/085006
149	A. V. Andreev and B. Z. Spivak, Longitudinal negative magnetoresistance and magnetotransport phenomena in conventional and topological conductors, Phys. Rev. Lett.120, 026601 (2018) https://doi.org/10.1103/PhysRevLett.120.026601
150	H. Ishizuka and N. Nagaosa, Robustness of anomalyrelated magnetoresistance in doped Weyl semimetals, arXiv: 1808.09093 (2018)
151	D. Shoenberg, Magnetic Oscillations in Metals, Cambridge University Press, 1984 https://doi.org/10.1017/CBO9780511897870
152	G. P. Mikitik and Y. V. Sharlai, Manifestation of Berry’s phase in metal physics, Phys. Rev. Lett.82, 2147 (1999) https://doi.org/10.1103/PhysRevLett.82.2147
153	I. M. Lifshitz and A. M. Kosevich, Theory of magnetic susceptibility in metals at low temperatures, Sov. Phys. JETP2, 636 (1956)
154	D. Shoenberg, The Fermi surfaces of copper, silver and gold. I. the de Haas–van Alphen effect, Phil. Trans. R. Soc. Lond. A255, 85 (1962) https://doi.org/10.1098/rsta.1962.0011
155	P. T. Coleridge and I. M. Templeton, High precision de Haas–van Alphen measurements in the noble metals, J. Phys. F: Metal Phys.2, 643 (1972) https://doi.org/10.1088/0305-4608/2/4/009
156	I. A. Luk’yanchuk and Y. Kopelevich, Phase analysis of quantum oscillations in graphite, Phys. Rev. Lett.93, 166402 (2004) https://doi.org/10.1103/PhysRevLett.93.166402
157	G. E. Volovik, The Universe in a Helium Droplet, Clarendon Press, Oxford, 2003
158	Y. Zhang, Y.-W. Tan, H. L. Stormer, and P. Kim, Experimental observation of the quantum Hall effect and Berry’s phase in graphene, Nature438, 201 (2005) https://doi.org/10.1038/nature04235
159	H. Murakawa, M. S. Bahramy, M. Tokunaga, Y. Kohama, C. Bell, Y. Kaneko, N. Nagaosa, H. Y. Hwang, and Y. Tokura, Detection of Berry’s phase in a bulk Rashba semiconductor, Science342, 1490 (2013) https://doi.org/10.1126/science.1242247
160	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, 246402 (2014)` https://doi.org/10.1103/PhysRevLett.113.246402
161	M. Novak, S. Sasaki, K. Segawa, and Y. Ando, Large linear magnetoresistance in the Dirac semimetal TlBiSSe, Phys. Rev. B91, 041203(R) (2015) https://doi.org/10.1103/PhysRevB.91.041203
162	Y. F. Zhao, et al., Anisotropic Fermi surface and quantum limit transport in high mobility three-dimensional Dirac semimetal Cd3As2, Phys. Rev. X5, 031037 (2015) https://doi.org/10.1103/PhysRevX.5.031037
163	J. Du, et al., Large unsaturated positive and negative magnetoresistance in Weyl semimetal TaP, Sci. China-Phys. Mech. Astron.59, 657406 (2016) https://doi.org/10.1007/s11433-016-5798-4
164	Z. Wang, et al., Helicity-protected ultrahigh mobility Weyl fermions in NbP, Phys. Rev. B93, 121112(R) (2016) https://doi.org/10.1103/PhysRevB.93.121112
165	J. Cao, et al., Landau level splitting in Cd3As2 under high magnetic fields, Nat. Commun.6, 7779 (2015) https://doi.org/10.1038/ncomms8779
166	C. Zhang, Z. Yuan, S. Xu, Z. Lin, B. Tong, M. Z. Hasan, J. Wang, C. Zhang, and S. Jia, Tantalum monoarsenide: an exotic compensated semimetal, arXiv: 1502.00251 (2015)
167	A. Narayanan, et al., Linear magnetoresistance caused by mobility fluctuations in n-doped Cd3As2, Phys. Rev. Lett.114, 117201 (2015) https://doi.org/10.1103/PhysRevLett.114.117201
168	J. Park, et al., Anisotropic Dirac Fermions in a Bi square net of SrMnBi2, Phys. Rev. Lett.107, 126402 (2011) https://doi.org/10.1103/PhysRevLett.107.126402
169	F.-X. Xiang, X.-L. Wang, M. Veldhorst, S.-X. Dou, and M. S. Fuhrer, Observation of topological transition of Fermi surface from a spindle torus to a torus in bulk Rashba spin-split BiTeCl, Phys. Rev. B92, 035123 (2015) https://doi.org/10.1103/PhysRevB.92.035123
170	F. F. Tafti, Q. D. Gibson, S. K. Kushwaha, N. Haldolaarachchige, and R. J. Cava, Resistivity plateau and extreme magnetoresistance in LaSb, Nat. Phys.12, 272 (2016) https://doi.org/10.1038/nphys3581
171	Y. Luo, N. J. Ghimire, M. Wartenbe, H. Choi, M. Neupane, R. D. McDonald, E. D. Bauer, J. Zhu, J. D. Thompson, and F. Ronning, Electron–hole compensation effect between topologically trivial electrons and nontrivial holes in NbAs, Phys. Rev. B92, 205134 (2015) https://doi.org/10.1103/PhysRevB.92.205134
172	F. Arnold, M. Naumann, S.-C. Wu, Y. Sun, M. Schmidt, H. Borrmann, C. Felser, B. Yan, and E. Hassinger, Chiral Weyl pockets and Fermi surface topology of the Weyl semimetal TaAs, Phys. Rev. Lett.117, 146401 (2016) https://doi.org/10.1103/PhysRevLett.117.146401
173	J. Klotz, et al., Quantum oscillations and the Fermi surface topology of the Weyl semimetal NbP, Phys. Rev. B93, 121105 (2016) https://doi.org/10.1103/PhysRevB.93.121105
174	R. D. dos Reis, S. C. Wu, Y. Sun, M. O. Ajeesh, C. Shekhar, M. Schmidt, C. Felser, B. Yan, and M. Nicklas, Pressure tuning the Fermi surface topology of the Weyl semimetal NbP, Phys. Rev. B93, 205102 (2016) https://doi.org/10.1103/PhysRevB.93.205102
175	P. Sergelius, et al., Berry phase and band structure analysis of the Weyl semimetal NbP, Sci. Rep.6, 33859 (2016) https://doi.org/10.1038/srep33859
176	N. Kumar, K. Manna, Y. Qi, S.-C. Wu, L. Wang, B. Yan, C. Felser, and C. Shekhar, Unusual magnetotransport from Si-square nets in topological semimetal HfSiS, Phys. Rev. B95, 121109 (2017) https://doi.org/10.1103/PhysRevB.95.121109
177	R. Singha, A. K. Pariari, B. Satpati, and P. Mandal, Large nonsaturating magnetoresistance and signature of nondegenerate Dirac nodes in ZrSiS, Proc. Natl. Acad. Sci. USA114, 2468 (2017) https://doi.org/10.1073/pnas.1618004114
178	M. N. Ali, L. M. Schoop, C. Garg, J. M. Lippmann, E. Lara, B. Lotsch, and S. S. P. Parkin, Butterfly magnetoresistance, quasi-2D Dirac Fermi surface and topological phase transition in ZrSiS, Sci. Adv.2, e1601742 (2016) https://doi.org/10.1126/sciadv.1601742
179	X. Wang, et al., Evidence of both surface and bulk Dirac bands and anisotropic nonsaturating magnetoresistance in ZrSiS, Adv. Electron. Mater.2, 1600228 (2016) https://doi.org/10.1002/aelm.201600228
180	Y.-Y. Lv, B.-B. Zhang, X. Li, S.-H. Yao, Y. B. Chen, J. Zhou, S.-T. Zhang, M.-H. Lu, and Y.-F. Chen, Extremely large and significantly anisotropic magnetoresistance in ZrSiS single crystals, App. Phys. Lett.108, 244101 (2016) https://doi.org/10.1063/1.4953772
181	J. Hu, Z. Tang, J. Liu, Y. Zhu, J. Wei, and Z. Mao, Nearly massless Dirac fermions and strong Zeeman splitting in the nodal-line semimetal ZrSiS probed by de Haas–van Alphen quantum oscillations, Phys. Rev. B96, 045127 (2017) https://doi.org/10.1103/PhysRevB.96.045127
182	H. Pan, et al., Three-dimensional anisotropic magnetoresistance in the Dirac node-line material ZrSiSe, Sci. Rep.8, 9340 (2018) https://doi.org/10.1038/s41598-018-27148-z
183	J. Hu, et al., Evidence of topological nodal-line fermions in ZrSiSe and ZrSiTe, Phys. Rev. Lett. 117, 016602 (2016) https://doi.org/10.1103/PhysRevLett.117.016602
184	J. Hu, Y. L. Zhu, D. Graf, Z. J. Tang, J. Y. Liu, and Z. Q. Mao, Quantum oscillation studies of the topological semimetal candidate ZrGeM (M=S, Se, Te), Phys. Rev. B95, 205134 (2017) https://doi.org/10.1103/PhysRevB.95.205134
185	M. Charbonneau, K. M. van Vliet, and P. Vasilopoulos, Linear response theory revisited III: One-body response formulas and generalized Boltzmann equations, J. Math. Phys.23, 318 (1982) https://doi.org/10.1063/1.525355
186	P. Vasilopoulos and C. Van Vliet, Linear response theory revisited (IV): Applications, J. Math. Phys.25, 1391 (1984) https://doi.org/10.1063/1.526309
187	C. M. Wang and X. L. Lei, Linear magnetoresistance on the topological surface, Phys. Rev. B86, 035442 (2012) https://doi.org/10.1103/PhysRevB.86.035442
188	C. M. Wang and X. L. Lei, Linear magnetotransport in monolayer MoS2, Phys. Rev. B92, 125303 (2015) https://doi.org/10.1103/PhysRevB.92.125303
189	D.-X. Qu, Y. S. Hor, J. Xiong, R. J. Cava, and N. P. Ong, Quantum oscillations and hall anomaly of surface states in the topological insulator Bi2Te3, Science329, 821 (2010) https://doi.org/10.1126/science.1189792
190	S. Datta, Electronic Transport in Mesoscopic Systems, Cambridge University Press, 1997
191	F. T. Vasko and O. E. Raichev, Quantum Kinetic Theory and Applications: Electrons, Photons, Phonons, Springer Science & Business Media, 2006
192	A. A. Abrikosov, Quantum magnetoresistance, Phys. Rev. B58, 2788 (1998) https://doi.org/10.1103/PhysRevB.58.2788
193	J. Xiong, S. Kushwaha, J. Krizan, T. Liang, R. J. Cava, and N. P. Ong, Anomalous conductivity tensor in the Dirac semimetal Na3Bi, EPL114, 27002 (2016) https://doi.org/10.1209/0295-5075/114/27002
194	J. Hu, et al., π Berry phase and Zeeman splitting of TaP probed by high field magnetotransport measurements, Sci. Rep.6, 18674 (2016) https://doi.org/10.1038/srep18674
195	L. Onsager, Interpretation of the de Haas–van Alphen effect, Philos. Mag.43, 1006 (1952) https://doi.org/10.1080/14786440908521019
196	M. Phillips and V. Aji, Tunable line node semimetals, Phys. Rev. B90, 115111 (2014) https://doi.org/10.1103/PhysRevB.90.115111
197	W. Chen, H.-Z. Lu, and O. Zilberberg, Weak localization and antilocalization in nodal-line semimetals: Dimensionality and topological effects, arXiv: 1902.06921 (2019)
198	K. v. 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, 494 (1980) https://doi.org/10.1103/PhysRevLett.45.494
199	D. J. Thouless, M. Kohmoto, M. P. Nightingale, and M. den Nijs, Quantized Hall conductance in a twodimensional periodic potential, Phys. Rev. Lett.49, 405 (1982) https://doi.org/10.1103/PhysRevLett.49.405
200	K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, Two-dimensional gas of massless Dirac fermions in graphene, Nature438, 197 (2005) https://doi.org/10.1038/nature04233
201	Y. Xu, I. Miotkowski, C. Liu, J. Tian, H. Nam, N. Alidoust, J. Hu, C.-K. Shih, M. Z. Hasan, and Y. P. Chen, Observation of topological surface state quantum Hall effect in an intrinsic three-dimensional topological insulator, Nat. Phys.10, 956 (2014) https://doi.org/10.1038/nphys3140
202	R. Yoshimi, K. Yasuda, A. Tsukazaki, K. S. Takahashi, N. Nagaosa, M. Kawasaki, and Y. Tokura, Quantum Hall states stabilized in semi-magnetic bilayers of topological insulators, Nat. Commun.6, 8530 (2015) https://doi.org/10.1038/ncomms9530
203	M. Brahlek, N. Bansal, N. Koirala, S. Y. Xu, M. Neupane, C. Liu, M. Z. Hasan, and S. Oh, Topological-metal to band-insulator transition in (Bi1-xInx)2Se3 thin films, Phys. Rev. Lett.109, 186403 (2012) https://doi.org/10.1103/PhysRevLett.109.186403
204	L. Wu, M. Brahlek, R. Valdes Aquilar, A. V. Stier, C. M. Morris, Y. Lubashevsky, L. S. Bilbro, N. Bansal, S. Oh, and N. P. Armitage, A sudden collapse in the transport lifetime across the topological phase transition in (Bi1-xInx)2Se3, Nat. Phys.9, 410 (2013) https://doi.org/10.1038/nphys2647
205	P. Hosur, Friedel oscillations due to Fermi arcs in Weyl semimetals, Phys. Rev. B86, 195102 (2012) https://doi.org/10.1103/PhysRevB.86.195102
206	Y. Baum, E. Berg, S. A. Parameswaran, and A. Stern, Current at a distance and resonant transparency in Weyl semimetals, Phys. Rev. X5, 041046 (2015) https://doi.org/10.1103/PhysRevX.5.041046
207	E. V. Gorbar, V. A. Miransky, I. A. Shovkovy, and P. O. Sukhachov, Origin of dissipative Fermi arc transport in Weyl semimetals, Phys. Rev. B93, 235127 (2016) https://doi.org/10.1103/PhysRevB.93.235127
208	Y. Ominato and M. Koshino, Magnetotransport in Weyl semimetals in the quantum limit: Role of topological surface states, Phys. Rev. B93, 245304 (2016) https://doi.org/10.1103/PhysRevB.93.245304
209	T. M. McCormick, S. J. Watzman, J. P. Heremans, and N. Trivedi, Fermi arc mediated entropy transport in topological semimetals, Phys. Rev. B97, 195152 (2018) https://doi.org/10.1103/PhysRevB.97.195152
210	C. Shekhar, et al., Extremely large magnetoresistance and ultrahigh mobility in the topological Weyl semimetal NbP, Nat. Phys.11, 645 (2015) https://doi.org/10.1038/nphys3372
211	T. Liang, Q. Gibson, M. N. Ali, M. H. Liu, R. J. Cava, and N. P. Ong, Ultrahigh mobility and giant magnetoresistance in the Dirac semimetal Cd3As2, Nat. Mater.14, 280 (2015) https://doi.org/10.1038/nmat4143
212	P. J. W. Moll, N. L. Nair, T. Helm, A. C. Potter, I. Kimchi, A. Vishwanath, and J. G. Analytis, Transport evidence for Fermi-arc-mediated chirality transfer in the Dirac semimetal Cd3As2, Nature535, 266 (2016) https://doi.org/10.1038/nature18276
213	G. Rosenberg, H.-M. Guo, and M. Franz, Wormhole effect in a strong topological insulator, Phys. Rev. B82, 041104 (2010) https://doi.org/10.1103/PhysRevB.82.041104
214	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) https://doi.org/10.1038/ncomms11136
215	A. C. Potter, I. Kimchi, and A. Vishwanath, Quantum oscillations from surface Fermi arcs in Weyl and Dirac semimetals, Nat. Commun.5, 5161 (2014) https://doi.org/10.1038/ncomms6161
216	M. Uchida, et al., Quantum Hall effect in Cd3As2 films, APS March Meeting A44.00005 (2017)
217	M. Uchida, et al., Quantum Hall states observed in thin films of Dirac semimetal Cd3As2, Nat. Commun8, 2274 (2017) https://doi.org/10.1038/s41467-017-02423-1
218	T. Schumann, L. Galletti, D. A. Kealhofer, H. Kim, M. Goyal, and S. Stemmer, Observation of the quantum Hall effect in confined films of the three-dimensional Dirac semimetal Cd3As2, Phys. Rev. Lett.120, 016801 (2018) https://doi.org/10.1103/PhysRevLett.120.016801
219	C. Zhang, et al., Quantum Hall effect based on Weyl orbit in Cd3As2, Nature565, 331 (2019) https://doi.org/10.1038/s41586-018-0798-3
220	V. P. Gusynin and S. G. Sharapov, Unconventional integer quantum Hall effect in graphene, Phys. Rev. Lett.95, 146801 (2005) https://doi.org/10.1103/PhysRevLett.95.146801
221	A. A. Zyuzin and A. A. Burkov, Thin topological insulator film in a perpendicular magnetic field, Phys. Rev. B83, 195413 (2011) https://doi.org/10.1103/PhysRevB.83.195413
222	S. B. Zhang, Y. Y. Zhang, and S. Q. Shen, Robustness of quantum spin Hall effect in an external magnetic field, Phys. Rev. B90, 115305 (2014) https://doi.org/10.1103/PhysRevB.90.115305
223	S. B. Zhang, H. Z. Lu, and S. Q. Shen, Edge states and integer quantum Hall effect in topological insulator thin films, Sci. Rep.5, 13277 (2015) https://doi.org/10.1038/srep13277
224	A. Pertsova, C. M. Canali, and A. H. MacDonald, Quantum Hall edge states in topological insulator nanoribbons, Phys. Rev. B94, 121409 (2016) https://doi.org/10.1103/PhysRevB.94.121409
225	H. Zheng, et al., Atomic-scale visualization of quantum interference on a Weyl semimetal surface by scanning tunneling microscopy, ACS Nano10, 1378 (2016) https://doi.org/10.1021/acsnano.5b06807
226	E. Y. Ma, et al., Unexpected edge conduction in mercury telluride quantum wells under broken time-reversal symmetry, Nat. Commun.6, 7252 (2015) https://doi.org/10.1038/ncomms8252
227	M. Kargarian, M. Randeria, and Y.-M. Lu, Are the surface Fermi arcs in Dirac semimetals topologically protected? Proc. Natl. Acad. Sci. USA113, 8648 (2016) https://doi.org/10.1073/pnas.1524787113
228	J. Cano, B. Bradlyn, Z. Wang, M. Hirschberger, N. P. Ong, and B. A. Bernevig, Chiral anomaly factory: Creating Weyl fermions with a magnetic field, Phys. Rev. B95, 161306 (2017) https://doi.org/10.1103/PhysRevB.95.161306
229	S. Q. Shen, M. Ma, X. C. Xie, and F. C. Zhang, Resonant spin Hall conductance in two-dimensional electron systems with a Rashba interaction in a perpendicular magnetic field, Phys. Rev. Lett.92, 256603 (2004) https://doi.org/10.1103/PhysRevLett.92.256603
230	M. Z. Hasan and C. L. Kane, Colloquium: Topological insulators, Rev. Mod. Phys.82, 3045 (2010) https://doi.org/10.1103/RevModPhys.82.3045
231	X.-L. Qi and S.-C. Zhang, Topological insulators and superconductors, Rev. Mod. Phys.83, 1057 (2011) https://doi.org/10.1103/RevModPhys.83.1057
232	R. Yu, W. Zhang, H.-J. Zhang, S.-C. Zhang, X. Dai, and Z. Fang, Quantized anomalous Hall effect in magnetic topological insulators, Science329, 61 (2010) https://doi.org/10.1126/science.1187485
233	C.-Z. Chang, et al., Experimental observation of the quantum anomalous Hall effect in a magnetic topological insulator, Science340, 167 (2013) https://doi.org/10.1126/science.1234414
234	L. Fu and C. L. Kane, Superconducting proximity effect and Majorana fermions at the surface of a topological insulator, Phys. Rev. Lett.100, 096407 (2008) https://doi.org/10.1103/PhysRevLett.100.096407
235	A. R. Akhmerov, J. Nilsson, and C. W. J. Beenakker, Electrically detected interferometry of Majorana fermions in a topological insulator, Phys. Rev. Lett.102, 216404 (2009) https://doi.org/10.1103/PhysRevLett.102.216404
236	I. Belopolski, et al., A novel artificial condensed matter lattice and a new platform for one-dimensional topological phases, Sci. Adv.3, 3 (2017) https://doi.org/10.1126/sciadv.1501692
237	C.-K. Chiu, G. Bian, H. Zheng, J.-X. Yin, S. S. Zhang, D. S. Sanchez, I. Belopolski, S.-Y. Xu, and M. Z. Hasan, Chiral majorana fermion modes on the surface of superconducting topological insulators, EPL123, 47005 (2018) https://doi.org/10.1209/0295-5075/123/47005
238	M. König, S. Wiedmann, C. Brüne, A. Roth, H. Buhmann, L. W. Molenkamp, X.-L. Qi, and S.-C. Zhang, Quantum spin Hall insulator state in HgTe quantum wells, Science318, 766 (2007) https://doi.org/10.1126/science.1148047
239	B. Büttner, et al., Single valley Dirac fermions in zero-gap HgTe quantum wells, Nat. Phys.7, 418 (2011) https://doi.org/10.1038/nphys1914
240	A. Mani and C. Benjamin, Probing helicity and the topological origins of helicity via non-local Hanbury–Brown and Twiss correlations, Sci. Rep.7, 6954 (2017) https://doi.org/10.1038/s41598-017-06820-w
241	H. Weng, X. Dai, and Z. Fang, Transition-metal pentatelluride ZrTe5 and HfTe5: A paradigm for large-gap quantum spin Hall insulators, Phys. Rev. X4, 011002 (2014) https://doi.org/10.1103/PhysRevX.4.011002
242	Y. Liu, et al., Zeeman splitting and dynamical mass generation in Dirac semimetal ZrTe5, Nat. Commun.7, 12516 (2016) https://doi.org/10.1038/ncomms12516
243	W. Zhang, R. Yu, W. Feng, Y. Yao, H. Weng, X. Dai, and Z. Fang, Topological aspect and quantum magnetoresistance of β-Ag2Te, Phys. Rev. Lett.106, 156808 (2011) https://doi.org/10.1103/PhysRevLett.106.156808
244	H.-Z. Lu, J. Shi, and S.-Q. Shen, Competition between weak localization and antilocalization in topological surface states, Phys. Rev. Lett.107, 076801 (2011) https://doi.org/10.1103/PhysRevLett.107.076801
245	H.-W. Wang, B. Fu, and S.-Q. Shen, Intrinsic magnetoresistance in three-dimensional Dirac materials with low carrier density, Phys. Rev. B98, 081202 (2018) https://doi.org/10.1103/PhysRevB.98.081202
246	A. Alexandradinata and L. Glazman, Geometric phase and orbital moment in quantization rules for magnetic breakdown, Phys. Rev. Lett.119, 256601 (2017) https://doi.org/10.1103/PhysRevLett.119.256601
247	A. Alexandradinata, C. Wang, W. Duan, and L. Glazman, Revealing the topology of fermi-surface wave functions from magnetic quantum oscillations, Phys. Rev. X8, 011027 (2018) https://doi.org/10.1103/PhysRevX.8.011027
248	J. Höller and A. Alexandradinata, Topological Bloch oscillations, Phys. Rev. B98, 024310 (2018) https://doi.org/10.1103/PhysRevB.98.024310
249	T. E. O’Brien, M. Diez, and C. W. J. Beenakker, Magnetic breakdown and Klein tunneling in a type-II Weyl semimetal, Phys. Rev. Lett.116, 236401 (2016) https://doi.org/10.1103/PhysRevLett.116.236401
250	F. Fei, et al., Nontrivial berry phase and type-ii dirac transport in the layered material PdTe2, Phys. Rev. B96, 041201 (2017) https://doi.org/10.1103/PhysRevB.96.041201
251	H. Yang, R. Moessner, and L.-K. Lim, Quantum oscillations in nodal line systems, Phys. Rev. B97, 165118 (2018) https://doi.org/10.1103/PhysRevB.97.165118
252	L. Oroszlány, B. Dóra, J. Cserti, and A. Cortijo, Topological and trivial magnetic oscillations in nodal loop semimetals, Phys. Rev. B97, 205107 (2018) https://doi.org/10.1103/PhysRevB.97.205107
253	C. Zhang, et al., Evolution of Weyl orbit and quantum Hall effect in Dirac semimetal Cd3As2, Nat. Commun.8, 1272 (2017) https://doi.org/10.1038/s41467-017-01438-y
254	Y. Zhang, D. Bulmash, P. Hosur, A. C. Potter, and A. Vishwanath, Quantum oscillations from generic surface Fermi arcs and bulk chiral modes in Weyl semimetals, Sci. Rep.6, 23741 (2016) https://doi.org/10.1038/srep23741
255	B. I. Halperin, Possible states for a three-dimensional electron gas in a strong magnetic field, Japanese J. Appl. Phys.26, 1913 (1987) https://doi.org/10.7567/JJAPS.26S3.1913
256	F. Tang, et al., Three-dimensional quantum Hall effect and metal-insulator transition in ZrTe5, arXiv: 1807.02678 (2018)
257	H.-Z. Lu, Perspective: 3D quantum Hall effect, Natl. Sci. Rev., nwy082 (2018)
258	H. Wang, et al., Discovery of log-periodic oscillations in ultraquantum topological materials, Sci. Adv.4, 11 (2018) https://doi.org/10.1126/sciadv.aau5096
259	H. Wang, et al., Log-periodic quantum magnetooscillations and discrete scale invariance in topological material HfTe5, arXiv: 1810.03109 (2018)
260	P. Zhang and H. Zhai, Efimov effect in Dirac semi-metals, Front. Phys.13, 137204 (2018) https://doi.org/10.1007/s11467-018-0800-4
261	H. Liu, H. Jiang, Z. Wang, R. Joynt, and X. C. Xie, Discrete scale invariance in topological semimetals, arXiv: 1807.02459 (2018)
262	H. Weng, C. Fang, Z. Fang, and X. Dai, Topological semimetals with triply degenerate nodal points in θ-phase tantalum nitride, Phys. Rev. B93, 241202 (2016) https://doi.org/10.1103/PhysRevB.93.241202
263	H. Weng, C. Fang, Z. Fang, and X. Dai, Coexistence of Weyl fermion and massless triply degenerate nodal points, Phys. Rev. B94, 165201 (2016) https://doi.org/10.1103/PhysRevB.94.165201
264	B. Bradlyn, J. Cano, Z. Wang, M. G. Vergniory, C. Felser, R. J. Cava, and B. A. Bernevig, Beyond Dirac and Weyl fermions: Unconventional quasiparticles in conventional crystals, Science353 (2016) https://doi.org/10.1126/science.aaf5037
265	G. Chang, et al., Nexus fermions in topological symmorphic crystalline metals, Sci. Rep.7, 1688 (2017) https://doi.org/10.1038/s41598-017-01523-8
266	B. Q. Lv, et al., Observation of three-component fermions in the topological semimetal molybdenum phosphide, Nature546, 627 (2017) https://doi.org/10.1038/nature22390
267	J.-Z. Ma, et al., Three-component fermions with surface Fermi arcs in tungsten carbide, Nat. Phys.14, 349 (2018) https://doi.org/10.1038/s41567-017-0021-8
268	J. B. He, D. Chen, W. L. Zhu, S. Zhang, L. X. Zhao, Z. A. Ren, and G. F. Chen, Magnetotransport properties of the triply degenerate node topological semimetal tungsten carbide, Phys. Rev. B95, 195165 (2017) https://doi.org/10.1103/PhysRevB.95.195165
269	W. L. Zhu, J. B. He, S. Zhang, D. Chen, L. Shan, Z. A. Ren, and G. F. Chen, Magnetotransport properties of the new-type topological semimetal ZrTe, arXiv: 1707.00942 (2017)
270	C. Shekhar, et al., Extremely high conductivity observed in the unconventional triple point fermion material MoP, arXiv: 1703.03736 (2017)
271	A. K. Nayak, et al., Large anomalous Hall effect driven by a nonvanishing Berry curvature in the noncolinear antiferromagnet Mn3Ge, Sci. Adv.2, 4 (2016) https://doi.org/10.1126/sciadv.1501870
272	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-reversalbreaking Weyl fermions in magnetic Heusler alloys, Phys. Rev. Lett.117, 236401 (2016) https://doi.org/10.1103/PhysRevLett.117.236401
273	G. Chang, et al., Room-temperature magnetic topological Weyl fermion and nodal line semimetal states in halfmetallic Heusler Co2TiX (X=Si, Ge, or Sn), Sci. Rep.6, 38839 (2016) https://doi.org/10.1038/srep38839
274	S. Nie, G. Xu, F. B. Prinz, and S.-C. Zhang, Topological semimetal in honeycomb lattice LnSI, Proc. Natl. Acad. Sci. USA114, 10596 (2017) https://doi.org/10.1073/pnas.1713261114
275	H. Yang, Y. Sun, Y. Zhang, W.-J. Shi, S. S. P. Parkin, and B. Yan, Topological Weyl semimetals in the chiral antiferromagnetic materials Mn3Ge and Mn3Sn, New J. Phys.19, 015008 (2017) https://doi.org/10.1088/1367-2630/aa5487
276	E. Liu, et al., Giant anomalous Hall effect in a ferromagnetic kagome-lattice semimetal, Nat. Phys.14, 1125 (2018) https://doi.org/10.1038/s41567-018-0234-5
277	Q. Wang, Y. Xu, R. Lou, Z. Liu, M. Li, Y. Huang, D. Shen, H. Weng, S. Wang, and H. Lei, Large intrinsic anomalous Hall effect in half-metallic ferromagnet Co3Sn2S2 with magnetic Weyl fermions, Nat. Commun.9, 3681 (2018) https://doi.org/10.1038/s41467-018-06088-2
278	S. N. Guin, et al., Anomalous Nernst effect beyond the magnetization scaling relation in the ferromagnetic Heusler compound Co2MnGa, arXiv: 1806.06753 (2018)
279	G. Chang, et al., Magnetic and noncentrosymmetric weyl fermion semimetals in the RAlGe family of compounds (R=rare earth), Phys. Rev. B97, 041104 (2018) https://doi.org/10.1103/PhysRevB.97.041104
280	J.-X. Yin, et al., Giant and anisotropic many-body spinorbit tunability in a strongly correlated kagome magnet, Nature562, 91 (2018) https://doi.org/10.1038/s41586-018-0502-7
281	S.-M. Huang, et al., New type of Weyl semimetal with quadratic double Weyl fermions, Proc. Natl. Acad. Sci. USA113, 1180 (2016) https://doi.org/10.1073/pnas.1514581113
282	A. A. Soluyanov, D. Gresch, Z. Wang, Q. Wu, M. Troyer, X. Dai, and B. A. Bernevig, Type-II Weyl semimetals, Nature527, 495 (2015) https://doi.org/10.1038/nature15768
283	K. Deng, et al., Experimental observation of topological fermi arcs in type-II Weyl semimetal MoTe2, Nat. Phys.12, 1105 (2016) https://doi.org/10.1038/nphys3871
284	J. Jiang, et al., Signature of type-II Weyl semimetal phase in MoTe2, Nat. Commun.8, 13973 (2017) https://doi.org/10.1038/ncomms13973
285	Y. Wang, et al., Gate-tunable negative longitudinal magnetoresistance in the predicted type-II Weyl semimetal WTe2, Nat. Commun.7, 13142 (2016) https://doi.org/10.1038/ncomms13142
286	E. Zhang, et al., Tunable positive to negative magnetoresistance in atomically thin WTe2, Nano Lett.17, 878 (2017) https://doi.org/10.1021/acs.nanolett.6b04194
287	D. Chen, et al., Magnetotransport properties of the type-II Weyl semimetal candidate Ta3S2, Phys. Rev. B94, 174411 (2016)
288	S. Khim, et al., Magnetotransport and de Haas–van Alphen measurements in the type-II Weyl semimetal TaIrTe4, Phys. Rev. B94, 165145 (2016) https://doi.org/10.1103/PhysRevB.94.165145
289	S.-Y. Xu, et al., Discovery of lorentz-violating type II Weyl fermions in laalge, Sci. Adv.3, 6 (2017) https://doi.org/10.1126/sciadv.1603266
290	I. Belopolski, et al., Discovery of a new type of topological Weyl fermion semimetal state in MoxW1–xTe2, Nat. Commun.7, 13643 (2016) https://doi.org/10.1038/ncomms13643
291	G. Chang, et al., A strongly robust type II Weyl fermion semimetal state in Ta3S2, Sci. Adv.2, 6 (2016) https://doi.org/10.1126/sciadv.1600295
292	C. Zhong, Y. Chen, Z.-M. Yu, Y. Xie, H. Wang, S. A. Yang, and S. Zhang, Three-dimensional pentagon carbon with a genesis of emergent fermions, Nat. Commun.8, 15641 (2017) https://doi.org/10.1038/ncomms15641
293	W. Chen, H.-Z. Lu, and J.-M. Hou, Topological semimetals with a double-helix nodal link, Phys. Rev. B96, 041102 (2017) https://doi.org/10.1103/PhysRevB.96.041102
294	Z. Yan, R. Bi, H. Shen, L. Lu, S.-C. Zhang, and Z. Wang, Nodal-link semimetals, Phys. Rev. B96, 041103 (2017) https://doi.org/10.1103/PhysRevB.96.041103
295	M. Ezawa, Topological semimetals carrying arbitrary Hopf numbers: Fermi surface topologies of a Hopf link, Solomon’s knot, trefoil knot, and other linked nodal varieties, Phys. Rev. B96, 041202 (2017) https://doi.org/10.1103/PhysRevB.96.041202
296	L.-X. Wang, C.-Z. Li, D.-P. Yu, and Z.-M. Liao, Aharonov–Bohm oscillations in Dirac semimetal Cd3As2 nanowires, Nat. Commun.7, 10769 (2016) https://doi.org/10.1038/ncomms10769
297	H. Zheng, et al., Atomic-scale visualization of quasiparticle interference on a type-II Weyl semimetal surface, Phys. Rev. Lett.117, 266804 (2016) https://doi.org/10.1103/PhysRevLett.117.266804
298	H. Zheng and M. Z. Hasan, Quasiparticle interference on type-I and type-II Weyl semimetal surfaces: A review, Advances in Physics: X3, 1466661 (2018) https://doi.org/10.1080/23746149.2018.1466661
299	H. Zheng, et al., Mirror protected Dirac fermions on a Weyl semimetal NbP surface, Phys. Rev. Lett.119, 196403 (2017) https://doi.org/10.1103/PhysRevLett.119.196403
300	G. Chang, et al., Signatures of Fermi arcs in the quasiparticle interferences of the Weyl semimetals TaAs and NbP, Phys. Rev. Lett.116, 066601 (2016) https://doi.org/10.1103/PhysRevLett.116.066601
301	S. Wang, B.-C. Lin, W.-Z. Zheng, D. Yu, and Z.-M. Liao, Fano interference between bulk and surface states of a Dirac semimetal Cd3As2 nanowire, Phys. Rev. Lett.120, 257701 (2018) https://doi.org/10.1103/PhysRevLett.120.257701
302	J. Gooth, et al., Experimental signatures of the mixed axial-gravitational anomaly in the Weyl semimetal NbP, Nature547, 324 (2017) https://doi.org/10.1038/nature23005

[1]	Chen-Xiao Zhao (赵晨晓), Jin-Feng Jia (贾金锋). Stanene: A good platform for topological insulator and topological superconductor[J]. Front. Phys. , 2020, 15(5): 53201-.
[2]	Chang-Yong Zhu, Shi-Han Zheng, Hou-Jian Duan, Ming-Xun Deng, Rui-Qiang Wang. Double Andreev reflections at surface states of the topological insulators with hexagonal warping[J]. Front. Phys. , 2020, 15(2): 23602-.
[3]	Y. X. Zhao. Equivariant PT-symmetric real Chern insulators[J]. Front. Phys. , 2020, 15(1): 13603-.
[4]	Jun-Ran Zhang, Bo Liu, Ming Gao, Yong-Bing Xu, Rong Zhang. Evidence of anisotropic Landau level splitting in topological semimetal ZrSiS under high magnetic fields[J]. Front. Phys. , 2019, 14(6): 63602-.
[5]	Mengyun He, Huimin Sun, Qing Lin He. Topological insulator: Spintronics and quantum computations[J]. Front. Phys. , 2019, 14(4): 43401-.
[6]	Junjie Qi, Haiwen Liu, Hua Jiang, X. C. Xie. Dephasing effects in topological insulators[J]. Front. Phys. , 2019, 14(4): 43403-.
[7]	Ali Ebrahimian, Mehrdad Mehrdad Dadsetaniz. Alkali-metal-induced topological nodal line semimetalin layered XN₂ (X= Cr, Mo, W)[J]. Front. Phys. , 2018, 13(5): 137309-.
[8]	Yupeng Li,Zhen Wang,Pengshan Li,Xiaojun Yang,Zhixuan Shen,Feng Sheng,Xiaodong Li,Yunhao Lu,Yi Zheng,Zhu-An Xu. Negative magnetoresistance in Weyl semimetals NbAs and NbP: Intrinsic chiral anomaly and extrinsic effects[J]. Front. Phys. , 2017, 12(3): 127205-.
[9]	Rui Yu,Zhong Fang,Xi Dai,Hongming Weng. Topological nodal line semimetals predicted from first-principles calculations[J]. Front. Phys. , 2017, 12(3): 127202-.
[10]	Hai-Zhou Lu,Shun-Qing Shen. Quantum transport in topological semimetals under magnetic fields[J]. Front. Phys. , 2017, 12(3): 127201-.
[11]	Dingping Li, Baruch Rosenstein, B. Ya. Shapiro, I. Shapiro. Chiral universality class of normal-superconducting and exciton condensation transitions on surface of topological insulator[J]. Front. Phys. , 2015, 10(3): 107402-.
[12]	Ming Yang, Xiao-Long Zhang, Wu-Ming Liu. Tunable topological quantum states in three- and two-dimensional materials[J]. Front. Phys. , 2015, 10(2): 108102-.
[13]	Yi-Bin Hu, Yong-Hong Zhao, Xue-Feng Wang. A computational investigation of topological insulator Bi₂Se₃ film[J]. Front. Phys. , 2014, 9(6): 760-767.
[14]	Ying Xing (邢颖), Yi Sun (孙祎), Meenakshi Singh, Yan-Fei Zhao (赵弇斐), Moses H. W. Chan, Jian Wang (王健). Electronic transport properties of topological insulator films and low dimensional superconductors[J]. Front. Phys. , 2013, 8(5): 491-508.
[15]	Hui Li (李辉), Hailin Peng (彭海琳), Wenhui Dang (党文辉), Lili Yu (余力立), Zhongfan Liu (刘忠范). Topological insulator nanostructures: Materials synthesis, Raman spectroscopy, and transport properties[J]. Front. Phys. , 2012, 7(2): 208-217.

Viewed

Full text

Abstract

Cited

Shared

Discussed