Please wait a minute...
Frontiers of Physics

ISSN 2095-0462

ISSN 2095-0470(Online)

CN 11-5994/O4

邮发代号 80-965

2019 Impact Factor: 2.502

Frontiers of Physics  2017, Vol. 12 Issue (3): 127201   https://doi.org/10.1007/s11467-016-0609-y
  本期目录
Quantum transport in topological semimetals under magnetic fields
Hai-Zhou Lu1(),Shun-Qing Shen2
1. Department of Physics, South University of Science and Technology of China, Shenzhen 518055, China
2. Department of Physics, The University of Hong Kong, Pokfulam Road, Hong Kong, China
 全文: PDF(1444 KB)  
Abstract

Topological semimetals are three-dimensional topological states of matter, in which the conduction and valence bands touch at a finite number of points, i.e., the Weyl nodes. Topological semimetals host paired monopoles and antimonopoles of Berry curvature at the Weyl nodes and topologically protected Fermi arcs at certain surfaces. We review our recent works on quantum transport in topological semimetals, according to the strength of the magnetic field. At weak magnetic fields, there are competitions between the positive magnetoresistivity induced by the weak anti-localization effect and negative magnetoresistivity related to the nontrivial Berry curvature. We propose a fitting formula for the magnetoconductivity of the weak anti-localization. We expect that the weak localization may be induced by inter-valley effects and interaction effect, and occur in double-Weyl semimetals. For the negative magnetoresistance induced by the nontrivial Berry curvature in topological semimetals, we show the dependence of the negative magnetoresistance on the carrier density. At strong magnetic fields, specifically, in the quantum limit, the magnetoconductivity depends on the type and range of the scattering potential of disorder. The high-field positive magnetoconductivity may not be a compelling signature of the chiral anomaly. For long-range Gaussian scattering potential and half filling, the magnetoconductivity can be linear in the quantum limit. A minimal conductivity is found at the Weyl nodes although the density of states vanishes there.

Key wordstopological semimetal    magnetoconductivity    magnetoresistance    localization    anti-localization    chiral anomaly
收稿日期: 2016-07-16      出版日期: 2016-10-11
Corresponding Author(s): Hai-Zhou Lu   
 引用本文:   
. [J]. Frontiers of Physics, 2017, 12(3): 127201.
Hai-Zhou Lu,Shun-Qing Shen. Quantum transport in topological semimetals under magnetic fields. Front. Phys. , 2017, 12(3): 127201.
 链接本文:  
https://academic.hep.com.cn/fop/CN/10.1007/s11467-016-0609-y
https://academic.hep.com.cn/fop/CN/Y2017/V12/I3/127201
1 L. Balents, Weyl electrons kiss, Physics 4, 36 (2011)
https://doi.org/10.1103/Physics.4.36
2 G. E. Volovik, The Universe in a Helium Droplet, Oxford: Clarendon Press, 2003
3 X. Wan, A. M. Turner, A. Vishwanath, and S. Y. Savrasov, Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates, Phys. Rev. B 83(20), 205101 (2011)
https://doi.org/10.1103/PhysRevB.83.205101
4 K. Y. Yang, Y. M. Lu, and Y. Ran, Quantum Hall effects in a Weyl semimetal: Possible application in pyrochlore iridates, Phys. Rev. B 84(7), 075129 (2011)
https://doi.org/10.1103/PhysRevB.84.075129
5 A. A. Burkov and L. Balents, Weyl Semimetal in a Topological Insulator Multilayer, Phys. Rev. Lett. 107(12), 127205 (2011)
https://doi.org/10.1103/PhysRevLett.107.127205
6 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(18), 186806 (2011)
https://doi.org/10.1103/PhysRevLett.107.186806
7 P. Delplace, J. Li, and D. Carpentier, Topological Weyl semi-metal from a lattice model, EPL 97(6), 67004 (2012)
https://doi.org/10.1209/0295-5075/97/67004
8 J. H. Jiang, Tunable topological Weyl semimetal from simple-cubic lattices with staggered fluxes, Phys. Rev. A 85(3), 033640 (2012)
https://doi.org/10.1103/PhysRevA.85.033640
9 S. M. Young, S. Zaheer, J. C. Y. Teo, C. L. Kane, E. J. Mele, and A. M. Rappe, Dirac semimetal in three dimensions, Phys. Rev. Lett. 108(14), 140405 (2012)
https://doi.org/10.1103/PhysRevLett.108.140405
10 Z. Wang, Y. Sun, X. Q. Chen, C. Franchini, G. Xu, H. Weng, X. Dai, and Z. Fang, Dirac semimetal and topological phase transitions in A3Bi (A= Na, K, Rb), Phys. Rev. B 85(19), 195320 (2012)
https://doi.org/10.1103/PhysRevB.85.195320
11 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. B 86(11), 115208 (2012)
https://doi.org/10.1103/PhysRevB.86.115208
12 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)
https://doi.org/10.1103/PhysRevB.88.125427
13 J. Liu and D. Vanderbilt, Weyl semimetals from noncentrosymmetric topological insulators,Phys. Rev. B 90(15), 155316 (2014)
https://doi.org/10.1103/PhysRevB.90.155316
14 D. Bulmash, C. X. Liu, and X. L. Qi, Prediction of a Weyl semimetal in Hg1txtyCdxMnyTe, Phys. Rev. B 89(8), 081106 (2014)
https://doi.org/10.1103/PhysRevB.89.081106
15 M. Brahlek, N. Bansal, N. Koirala, S. Y. Xu, M. Neupane, C. Liu, M. Z. Hasan, and S. Oh, Topologicalmetal to band-insulator transition in (Bi1−xInx)2Se3 thin films, Phys. Rev. Lett. 109(18), 186403 (2012)
https://doi.org/10.1103/PhysRevLett.109.186403
16 Liang Wu, M. Brahlek, R. Valdés Aguilar, 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
17 Z. K. Liu, B. Zhou, Y. Zhang, Z. J. Wang, H. M. Weng, D. Prabhakaran, S. K. Mo, Z. X. Shen, Z. Fang, X. Dai, Z. Hussain, and Y. L. Chen, Discovery of a threedimensional topological Dirac semimetal, Na3Bi, Science 343(6173), 864 (2014)
https://doi.org/10.1126/science.1245085
18 S. Y. Xu, C. Liu, S. K. Kushwaha, R. Sankar, J. W. Krizan, I. Belopolski, M. Neupane, G. Bian, N. Alidoust, T. R. Chang, H. T. Jeng, C. Y. Huang, W. F. Tsai, H. Lin, P. P. Shibayev, F. C. Chou, R. J. Cava, and M. Z. Hasan, Observation of Fermi arc surface states in a topological metal, Science 347(6219), 294 (2015)
https://doi.org/10.1126/science.1256742
19 Z. K. Liu, J. Jiang, B. Zhou, Z. J. Wang, Y. Zhang, H. M. Weng, D. Prabhakaran, S. K. Mo, H. Peng, P. Dudin, T. Kim, M. Hoesch, Z. Fang, X. Dai, Z. X. Shen, D. L. Feng, Z. Hussain, and Y. L. Chen, A stable threedimensional topological Dirac semimetal Cd3As2, Nat. Mater. 13(7), 677 (2014)
https://doi.org/10.1038/nmat3990
20 M. Neupane, S. Y. Xu, R. Sankar, N. Alidoust, G. Bian, C. Liu, I. Belopolski, T. R. Chang, H. T. Jeng, H. Lin, A. Bansil, F. Chou, and M. Z. Hasan, Observation of a three-dimensional topological Dirac semimetal phase in high-mobility Cd3As2, Nat. Commun. 5, 3786 (2014)
https://doi.org/10.1038/ncomms4786
21 H. Yi, Z. Wang, C. Chen, Y. Shi, Y. Feng, A. Liang, Z. Xie, S. He, J. He, Y. Peng, X. Liu, Y. Liu, L. Zhao, G. Liu, X. Dong, J. Zhang, M. Nakatake, M. Arita, K. Shimada, H. Namatame, M. Taniguchi, Z. Xu, C. Chen, X. Dai, Z. Fang, and X. J. Zhou, Evidence of topological surface state in three-dimensional Dirac semimetal Cd3As2, Sci. Rep. 4, 6106 (2014)
https://doi.org/10.1038/srep06106
22 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(2), 027603 (2014)
https://doi.org/10.1103/PhysRevLett.113.027603
23 H. M. Weng, C. Fang, Z. Fang, B. A. Bernevig, and X. Dai, Weyl semimetal phase in noncentrosymmetric transition-metal monophosphides, Phys. Rev. X 5(1), 011029 (2015)
https://doi.org/10.1103/PhysRevX.5.011029
24 S. M. Huang, S. Y. Xu, I. Belopolski, C. C. Lee, G. Chang, B. K. Wang, N. Alidoust, G. Bian, M. Neupane, C. Zhang, S. Jia, A. Bansil, H. Lin, and M. Z. Hasan, A Weyl Fermion semimetal with surface Fermi arcs in the transition metal monopnictide TaAs class, Nat. Commun. 6, 7373 (2015)
https://doi.org/10.1038/ncomms8373
25 B. Q. Lv, H. M. Weng, B. B. Fu, X. P. Wang, H. Miao, J. Ma, P. Richard, X. C. Huang, L. X. Zhao, G. F. Chen, Z. Fang, X. Dai, T. Qian, and H. Ding, Experimental discovery of Weyl semimetal TaAs, Phys. Rev. X 5(3), 031013 (2015)
https://doi.org/10.1103/PhysRevX.5.031013
26 S. Y. Xu, I. Belopolski, N. Alidoust, M. Neupane, G. Bian, C. L. Zhang, R. Sankar, G. Q. Chang, Z. J. Yuan, C. C. Lee, S. M. Huang, H. Zheng, J. Ma, D. S. Sanchez, B. K. Wang, A. Bansil, F. C. Chou, P. P. Shibayev, H. Lin, S. Jia, and M. Z. Hasan, Discovery of a Weyl fermion semimetal and topological Fermi arcs, Science 349(6248), 613 (2015)
https://doi.org/10.1126/science.aaa9297
27 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
28 H. B. Nielsen and M. Ninomiya, Absence of neutrinos on a lattice, Nucl. Phys. B 185(1), 20 (1981)
https://doi.org/10.1016/0550-3213(81)90361-8
29 H. B. Nielsen and M. Ninomiya, The Adler-Bell-Jackiw anomaly and Weyl fermions in a crystal, Phys. Lett. B 130(6), 389 (1983)
https://doi.org/10.1016/0370-2693(83)91529-0
30 D. T. Son and B. Z. Spivak, Chiral anomaly and classical negative magnetoresistance of Weyl metals, Phys. Rev. B 88(10), 104412 (2013)
https://doi.org/10.1103/PhysRevB.88.104412
31 A. A. Burkov, Chiral anomaly and diffusive magnetotransport in Weyl metals, Phys. Rev. Lett. 113(24), 247203 (2014)
https://doi.org/10.1103/PhysRevLett.113.247203
32 D. E. Kharzeev and H. U. Yee, Anomaly induced chiral magnetic current in a Weyl semimetal: Chiral electronics, Phys. Rev. B 88(11), 115119 (2013)
https://doi.org/10.1103/PhysRevB.88.115119
33 S. A. Parameswaran, T. Grover, D. A. Abanin, D. A. Pesin, and A. Vishwanath, Probing the chiral anomaly with nonlocal transport in three-dimensional topological semimetals, Phys. Rev. X 4(3), 031035 (2014)
https://doi.org/10.1103/PhysRevX.4.031035
34 J. Zhou, H. R. Chang, and D. Xiao, Plasmon mode as a detection of the chiral anomaly in Weyl semimetals, Phys. Rev. B 91(3), 035114 (2015)
https://doi.org/10.1103/PhysRevB.91.035114
35 D. T. Son and N. Yamamoto, Berry curvature, triangle anomalies, and the chiral magnetic effect in Fermi liquids, Phys. Rev. Lett. 109(18), 181602 (2012)
https://doi.org/10.1103/PhysRevLett.109.181602
36 M. A. Stephanov and Y. Yin, Chiral Kinetic Theory, Phys. Rev. Lett. 109(16), 162001 (2012)
https://doi.org/10.1103/PhysRevLett.109.162001
37 K. Landsteiner, E. Megías, and F. Pena-Benitez, Gravitational anomaly and transport phenomena, Phys. Rev. Lett. 107(2), 021601 (2011)
https://doi.org/10.1103/PhysRevLett.107.021601
38 M. C. Chang and M. F. Yang, Chiral magnetic effect in a two-band lattice model of Weyl semimetal, Phys. Rev. B 91(11), 115203 (2015)
https://doi.org/10.1103/PhysRevB.91.115203
39 Q. D. Jiang, H. Jiang, H. Liu, Q. F. Sun, and X. C. Xie, Topological Imbert–Fedorov shift in Weyl semimetals, Phys. Rev. Lett. 115(15), 156602 (2015)
https://doi.org/10.1103/PhysRevLett.115.156602
40 Q. D. Jiang, H. Jiang, H. Liu, Q. F. Sun, and X. C. Xie, Chiral wave-packet scattering in Weyl semimetals, Phys. Rev. B 93(19), 195165 (2016)
https://doi.org/10.1103/PhysRevB.93.195165
41 C. Z. Chen, J. Song, H. Jiang, Q. F. Sun, Z. Wang, and X. C. Xie, Disorder and metal-insulator transitions in Weyl semimetals, Phys. Rev. Lett. 115(24), 246603 (2015)
https://doi.org/10.1103/PhysRevLett.115.246603
42 C. Z. Chen, H. Liu, H. Jiang, and X. C. Xie, Positive magnetoconductivity of Weyl semimetals in the ultraquantum limit, Phys. Rev. B 93(16), 165420 (2016)
https://doi.org/10.1103/PhysRevB.93.165420
43 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(24), 246603 (2013)
https://doi.org/10.1103/PhysRevLett.111.246603
44 K. S. Kim, H. J. Kim, and M. Sasaki, Boltzmann equation approach to anomalous transport in a Weyl metal, Phys. Rev. B 89(19), 195137 (2014)
https://doi.org/10.1103/PhysRevB.89.195137
45 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(6), 550 (2016)
https://doi.org/10.1038/nphys3648
46 R. Y. Chen, Z. G. Chen, X. Y. Song, J. A. Schneeloch, G. D. Gu, F. Wang, and N. L. Wang, Magnetoinfrared spectroscopy of Landau levels and Zeeman splitting of three-dimensional massless Dirac fermions in ZrTe5, Phys. Rev. Lett. 115(17), 176404 (2015)
https://doi.org/10.1103/PhysRevLett.115.176404
47 G. Zheng, J. Lu, X. Zhu, W. Ning, Y. Han, H. Zhang, J. Zhang, C. Xi, J. Yang, H. Du, K. Yang, Y. Zhang, and M. Tian, Transport evidence for the three-dimensional Dirac semimetal phase in ZrTe5, Phys. Rev. B 93(11), 115414 (2016)
https://doi.org/10.1103/PhysRevB.93.115414
48 J. Xiong, S. K. Kushwaha, T. Liang, J. W. Krizan, M. Hirschberger, W. Wang, R. J. Cava, and N. P. Ong, Evidence for the chiral anomaly in the Dirac semimetal Na3Bi, Science 350(6259), 413 (2015)
https://doi.org/10.1126/science.aac6089
49 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(9), 851 (2014)
https://doi.org/10.1038/nmat4023
50 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(3), 280 (2015)
https://doi.org/10.1038/nmat4143
51 J. Feng, Y. Pang, D. Wu, Z. Wang, H. Weng, J. Li, X. Dai, Z. Fang, Y. Shi, and L. Lu, Large linear magnetoresistance in Dirac semimetal Cd3As2 with Fermi surfaces close to the Dirac points, Phys. Rev. B 92(8), 081306 (2015)
https://doi.org/10.1103/PhysRevB.92.081306
52 L. P. He, X. C. Hong, J. K. Dong, J. Pan, Z. Zhang, J. Zhang, and S. Y. Li, Quantum transport evidence for the three-dimensional Dirac semimetal phase in Cd3As2, Phys. Rev. Lett. 113(24), 246402 (2014)
https://doi.org/10.1103/PhysRevLett.113.246402
53 Y. F. Zhao, H. W. Liu, C. L. Zhang, H. C. Wang, J. F. Wang, Z. Q. Lin, Y. Xing, H. Lu, J. Liu, Y. Wang, S. M. Brombosz, Z. L. Xiao, S. Jia, X. C. Xie, and J. Wang, Anisotropic Fermi surface and quantum limit transport in high mobility three-dimensional Dirac semimetal Cd3As2, Phys. Rev. X 5(3), 031037 (2015)
https://doi.org/10.1103/PhysRevX.5.031037
54 J. Cao, S. Liang, C. Zhang, Y. Liu, J. Huang, Z. Jin, Z. G. Chen, Z. Wang, Q. Wang, J. Zhao, S. Li, X. Dai, J. Zou, Z. Xia, L. Li, and F. Xiu, Landau level splitting in Cd3As2 under high magnetic fields, Nat. Commun. 6, 7779 (2015)
https://doi.org/10.1038/ncomms8779
55 C. Shekhar, A. K. Nayak, Y. Sun, M. Schmidt, M. Nicklas, I. Leermakers, U. Zeitler, W. Schnelle, J. Grin, C. Felser, and B. Yan, Extremely large magnetoresistance and ultrahigh mobility in the topological Weyl semimetal candidate NbP, Nature Phys. 11, 645 (2015)
https://doi.org/10.1038/nphys3372
56 A. Narayanan, M. D. Watson, S. F. Blake, N. Bruyant, L. Drigo, Y. L. Chen, D. Prabhakaran, B. Yan, C. Felser, T. Kong, P. C. Canfield, and A. I. Coldea, Linear Magnetoresistance Caused by Mobility Fluctuations in n-Doped Cd3As2, Phys. Rev. Lett. 114, 117201 (2015)
https://doi.org/10.1103/PhysRevLett.114.117201
57 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
58 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
59 C. Zhang, E. Zhang, Y. Liu, Z.G. Chen, S. Liang, J. Cao, X. Yuan, L. Tang, Q. Li, T. Gu, Y. Wu, J. Zou, and F. Xiu, Detection of chiral anomaly and valley transport in Dirac semimetals, arXiv: 1504.07698
60 H. Wang, H. Wang, H. Liu, H. Lu, W. Yang, S. Jia, X. J. Liu, X. C. Xie, J. Wei, and J. Wang, Observation of superconductivity induced by a point contact on 3D Dirac semimetal Cd3As2 crystals, Nat. Mater. 15(1), 38 (2016)
https://doi.org/10.1038/nmat4456
61 L. Aggarwal, A. Gaurav, G. S. Thakur, Z. Haque, A. K. Ganguli, and G. Sheet, Unconventional superconductivity at mesoscopic point contacts on the 3D Dirac semimetal Cd3As2, Nat. Mater. 15(1), 32 (2016)
https://doi.org/10.1038/nmat4455
62 X. C. Huang, L. X. Zhao, Y. J. Long, P. P. Wang, D. Chen, Z. H. Yang, H. Liang, M. Q. Xue, H. M. Weng, Z. Fang, X. Dai, and G. F. Chen, Observation of the chiral-anomaly-induced negative magnetoresistance in 3D Weyl semimetal TaAs, Phys. Rev. X 5(3), 031023 (2015)
https://doi.org/10.1103/PhysRevX.5.031023
63 C. Zhang, S. Y. Xu, I. Belopolski, Z. Yuan, Z. Lin, B. Tong, N. Alidoust, C. C. Lee, S. M. Huang, T. R. Chang, H. T. Jeng, H. Lin, M. Neupane, D. S. Sanchez, H. Zheng, G. Bian, J. Wang, C. Zhang, H. Z. Lu, S. Q. Shen, T. Neupert, M. Z. Hasan, and S. Jia, Signatures of the Adler–Bell–Jackiw chiral anomaly in a Weyl fermion semimetal, Nat. Commun. 7, 10735 (2016)
https://doi.org/10.1038/ncomms10735
64 C. Zhang, C. Guo, H. Lu, X. Zhang, Z. Yuan, Z. Lin, J. Wang, and S. Jia, Large magnetoresistance over an extended temperature regime in monophosphides of tantalum and niobium, Phys. Rev. B 92(4), 041203 (2015)
https://doi.org/10.1103/PhysRevB.92.041203
65 F. Arnold, C. Shekhar, S. C. Wu, Y. Sun, R. D. dos Reis, N. Kumar, M. Naumann, M. O. Ajeesh, M. Schmidt, A. G. Grushin, J. H. Bardarson, M. Baenitz, D. Sokolov, H. Borrmann, M. Nicklas, C. Felser, E. Hassinger, and B. Yan, Negative magnetoresistance without well-defined chirality in the Weyl semimetal TaP, Nat. Commun. 7, 11615 (2016)
https://doi.org/10.1038/ncomms11615
66 C. Zhang, Z. Lin, C. Guo, S.Y. Xu, C.C. Lee, H. Lu, S.M. Huang, G. Chang, C.H. Hsu, H. Lin, L. Li, C. Zhang, T. Neupert, M. Z. Hasan, J. Wang, and S. Jia, Quantum phase transitions in Weyl semimetal tantalum monophosphide, arXiv: 1507.06301
67 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
68 X. Yang, Y. Li, Z. Wang, Y. Zhen, and Z.A. Xu, Observation of negative magnetoresistance and nontrivial π Berrys phase in 3D Weyl semi-metal NbAs, arXiv: 1506.02283
69 Z. Wang, Y. Zheng, Z. Shen, Y. Lu, H. Fang, F. Sheng, Y. Zhou, X. Yang, Y. Li, C. Feng, and Z.-A. Xu, Helicity-protected ultrahigh mobility Weyl fermions in NbP, Phys. Rev. B 93, 121112(R) (2016)
70 H. Wang, C. K. Li, H. Liu, J. Yan, J. Wang, J. Liu, Z. Lin, Y. Li, Y. Wang, L. Li, D. Mandrus, X. C. Xie, J. Feng, and J. Wang, Chiral anomaly and ultrahigh mobility in crystalline HfTe5, Phys. Rev. B 93(16), 165127 (2016)
https://doi.org/10.1103/PhysRevB.93.165127
71 H. Z. Lu and S. Q. Shen, Weak antilocalization and localization in disordered and interacting Weyl semimetals, Phys. Rev. B 92(3), 035203 (2015)
https://doi.org/10.1103/PhysRevB.92.035203
72 H. Z. Lu, S. B. Zhang, and S. Q. Shen, High-field magnetoconductivity of topological semimetals with shortrange potential, Phys. Rev. B 92(4), 045203 (2015)
https://doi.org/10.1103/PhysRevB.92.045203
73 X. Dai, H.-Z. Lu, S.-Q. Shen, and H. Yao, Detecting monopole charge in Weyl semimetals via quantum interference transport, Phys. Rev. B 93, 161110(R) (2016)
74 S. B. Zhang, H. Z. Lu, and S. Q. Shen, Linear magnetoconductivity in an intrinsic topological Weyl semimetal, New J. Phys. 18(5), 053039 (2016)
https://doi.org/10.1088/1367-2630/18/5/053039
75 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
76 H.Z. Lu, and S.Q. Shen, Weak localization and weak anti-localization in topological insulators, Proc. SPIE 9167, Spintronics VII, 91672E (2014)
77 H.-Z. Lu and S.-Q. Shen, Weak antilocalization and interaction-induced localization of Dirac and Weyl fermions in topological insulators and semimetals, Chin. Phys. B 25(11), 117202 (2016)
78 P. Hosur and X. Qi, Recent developments in transport phenomena in Weyl semimetals, C. R. Phys. 14(9-10), 857 (2013)
https://doi.org/10.1016/j.crhy.2013.10.010
79 S. Q. Shen, Topological Insulators, Berlin Heidelberg: Springer-Verlag, 2012
https://doi.org/10.1007/978-3-642-32858-9
80 D. Xiao, M. C. Chang, and Q. Niu, Berry phase effects on electronic properties, Rev. Mod. Phys. 82(3), 1959 (2010)
https://doi.org/10.1103/RevModPhys.82.1959
81 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. B 81(11), 115407 (2010)
https://doi.org/10.1103/PhysRevB.81.115407
82 Y. Hatsugai, Chern number and edge states in the integer quantum Hall effect, Phys. Rev. Lett. 71(22), 3697 (1993)
https://doi.org/10.1103/PhysRevLett.71.3697
83 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(4), 043048 (2010)
https://doi.org/10.1088/1367-2630/12/4/043048
84 S. Q. Shen, W. Y. Shan, and H. Z. Lu, Topological insulator and the Dirac equation, SPIN 01(01), 33 (2011)
https://doi.org/10.1142/S2010324711000057
85 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(25), 256603 (2004)
https://doi.org/10.1103/PhysRevLett.92.256603
86 S. Q. Shen, Y. J. Bao, M. Ma, X. C. Xie, and F. C. Zhang, Resonant spin Hall conductance in quantum Hall systems lacking bulk and structural inversion symmetry, Phys. Rev. B 71(15), 155316 (2005)
https://doi.org/10.1103/PhysRevB.71.155316
87 J. J. Sakurai, Modern Quantum Mechanics (Revised Edition), Addison Wesley, 1993
88 L. X. Yang, Z. K. Liu, Y. Sun, H. Peng, H. F. Yang, T. Zhang, B. Zhou, Y. Zhang, Y. F. Guo, M. Rahn, D. Prabhakaran, Z. Hussain, S. K. Mo, C. Felser, B. Yan, and Y. L. Chen, Weyl semimetal phase in the noncentrosymmetric compound TaAs, Nat. Phys. 11(9), 728 (2015)
https://doi.org/10.1038/nphys3425
89 S. Y. Xu, N. Alidoust, I. Belopolski, Z. Yuan, G. Bian, T. R. Chang, H. Zheng, V. N. Strocov, D. S. Sanchez, G. Chang, C. Zhang, D. Mou, Y. Wu, L. Huang, C. C. Lee, S. M. Huang, B. Wang, A. Bansil, H. T. Jeng, T. Neupert, A. Kaminski, H. Lin, S. Jia, and M. Zahid Hasan, Discovery of a Weyl fermion state with Fermi arcs in niobium arsenide, Nat. Phys. 11(9), 748 (2015)
https://doi.org/10.1038/nphys3437
90 N. Xu, H. M. Weng, B. Q. Lv, C. E. Matt, J. Park, F. Bisti, V. N. Strocov, D. Gawryluk, E. Pomjakushina, K. Conder, N. C. Plumb, M. Radovic, G. Autes, O. V. Yazyev, Z. Fang, X. Dai, T. Qian, J. Mesot, H. Ding, and M. Shi, Observation of Weyl nodes and Fermi arcs in tantalum phosphide, Nat. Commun. 7, 11006 (2016)
https://doi.org/10.1038/ncomms11006
91 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)
https://doi.org/10.1103/PhysRevLett.108.266802
92 T. Guan, C. J. Lin, C. L. Yang, Y. G. Shi, C. Ren, Y. Q. Li, H. M. Weng, X. Dai, Z. Fang, S. S. Yan, and P. Xiong, Evidence for half-metallicity in n-type HgCr2Se4, Phys. Rev. Lett. 115(8), 087002 (2015)
https://doi.org/10.1103/PhysRevLett.115.087002
93 S. M. Huang, S. Y. Xu, I. Belopolski, C. C. Lee, G. Chang, T. R. Chang, B. Wang, N. Alidoust, G. Bian, M. Neupane, D. Sanchez, H. Zheng, H. T. Jeng, A. Bansil, T. Neupert, H. Lin, and M. Z. Hasan, New type of Weyl semimetal with quadratic double Weyl fermions, Proc. Natl. Acad. Sci. USA 113(5), 1180 (2016)
https://doi.org/10.1073/pnas.1514581113
94 P. A. Lee and T. V. Ramakrishnan, Disordered electronic systems, Rev. Mod. Phys. 57(2), 287 (1985)
https://doi.org/10.1103/RevModPhys.57.287
95 F. J. Dyson, Statistical theory of the energy levels of complex systems (I), J. Math. Phys. 3(1), 140 (1962)
https://doi.org/10.1063/1.1703773
96 S. Hikami, A. I. Larkin, and Y. Nagaoka, Spin-orbit interaction and magnetoresistance in the two dimensional random system, Prog. Theor. Phys. 63(2), 707 (1980)
https://doi.org/10.1143/PTP.63.707
97 E. McCann, K. Kechedzhi, V. I. Fal’ko, H. Suzuura, T. Ando, and B. L. Altshuler, Weak-localization magnetoresistance and valley symmetry in graphene, Phys. Rev. Lett. 97(14), 146805 (2006)
https://doi.org/10.1103/PhysRevLett.97.146805
98 B. L. Altshuler, A. G. Aronov, and P. A. Lee, Interaction effects in disordered Fermi systems in two dimensions, Phys. Rev. Lett. 44(19), 1288 (1980)
https://doi.org/10.1103/PhysRevLett.44.1288
99 H. Fukuyama, Effects of interactions on non-metallic behaviors in two-dimensional disordered systems, J. Phys. Soc. Jpn. 48(6), 2169 (1980)
https://doi.org/10.1143/JPSJ.48.2169
100 H. Z. Lu, J. Shi, and S. Q. Shen, Competition between weak localization and antilocalization in topological surface states, Phys. Rev. Lett. 107(7), 076801 (2011)
https://doi.org/10.1103/PhysRevLett.107.076801
101 W. Y. Shan, H. Z. Lu, and S. Q. Shen, Spin-orbit scattering in quantum diffusion of massive Dirac fermions, Phys. Rev. B 86(12), 125303 (2012)
https://doi.org/10.1103/PhysRevB.86.125303
102 H. Z. Lu and S. Q. Shen, Finite-temperature conductivity and magnetoconductivity of topological insulators, Phys. Rev. Lett. 112(14), 146601 (2014)
https://doi.org/10.1103/PhysRevLett.112.146601
103 S. Pancharatnam, Proc. Indian Acad. Sci. A 44, 247 (1956)
104 M. V. Berry, Quantal phase factors accompanying adiabatic changes, Proc. R. Soc. Lond. A 392(1802), 45 (1984)
105 N. H. Shon and T. Ando, Quantum transport in twodimensional graphite system, J. Phys. Soc. Jpn. 67(7), 2421 (1998)
https://doi.org/10.1143/JPSJ.67.2421
106 H. Suzuura and T. Ando, Crossover from symplectic to orthogonal class in a two-dimensional honeycomb lattice, Phys. Rev. Lett. 89(26), 266603 (2002)
https://doi.org/10.1103/PhysRevLett.89.266603
107 A. Altland and M. R. Zirnbauer, Nonstandard symmetry classes in mesoscopic normal-superconducting hybrid structures, Phys. Rev. B 55(2), 1142 (1997)
https://doi.org/10.1103/PhysRevB.55.1142
108 S. L. Adler, Axial-vector vertex in spinor electrodynamics, Phys. Rev. 177(5), 2426 (1969)
https://doi.org/10.1103/PhysRev.177.2426
109 J. S. Bell and R. Jackiw, A PCAC puzzle: π0→γγ in the σ-model, Nuovo Cim. A 60(1), 47 (1969)
https://doi.org/10.1007/BF02823296
110 J. Wang, H. Li, C. Chang, K. He, J. Lee, H. Lu, Y. Sun, X. Ma, N. Samarth, S. Shen, Q. Xue, M. Xie, and M. H. Chan, Anomalous anisotropic magnetoresistance in topological insulator films, Nano Res. 5(10), 739 (2012)
https://doi.org/10.1007/s12274-012-0260-z
111 M. C. Chang and Q. Niu, Berry phase, hyperorbits, and the Hofstadter spectrum, Phys. Rev. Lett. 75(7), 1348 (1995)
https://doi.org/10.1103/PhysRevLett.75.1348
112 G. Sundaram and Q. Niu, Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects, Phys. Rev. B 59(23), 14915 (1999)
https://doi.org/10.1103/PhysRevB.59.14915
113 J. H. Zhou, H. Jiang, Q. Niu, and J. R. Shi, Topological invariants of metals and the related physical effects, Chin. Phys. Lett. 30(2), 027101 (2013)
https://doi.org/10.1088/0256-307X/30/2/027101
114 P. Goswami and S. Tewari, Axionic field theory of (3+ 1)-dimensional Weyl semimetals, Phys. Rev. B 88(24), 245107 (2013)
https://doi.org/10.1103/PhysRevB.88.245107
115 A. A. Zyuzin and A. A. Burkov, Topological response in Weyl semimetals and the chiral anomaly, Phys. Rev. B 86(11), 115133 (2012)
https://doi.org/10.1103/PhysRevB.86.115133
116 S.-K. Yip, Kinetic equation and magneto-conductance for Weyl metal in the clean limit, arXiv: 1508.01010
117 E. V. Gorbar, V. A. Miransky, and I. A. Shovkovy, Chiral anomaly, dimensional reduction, and magnetoresistivity of Weyl and Dirac semimetals, Phys. Rev. B 89(8), 085126 (2014)
https://doi.org/10.1103/PhysRevB.89.085126
118 V. Aji, Adler–Bell–Jackiw anomaly in Weyl semimetals: Application to pyrochlore iridates, Phys. Rev. B 85(24), 241101 (2012)
https://doi.org/10.1103/PhysRevB.85.241101
119 A. A. Abrikosov, Quantum magnetoresistance, Phys. Rev. B 58(5), 2788 (1998)
https://doi.org/10.1103/PhysRevB.58.2788
120 Y. Ominato and M. Koshino, Quantum transport in a three-dimensional Weyl electron system, Phys. Rev. B 89(5), 054202 (2014)
https://doi.org/10.1103/PhysRevB.89.054202
121 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)
https://doi.org/10.1103/PhysRevB.92.075205
122 J. C. W. Song, G. Refael, and P. A. Lee, Linear magnetoresistance in metals: Guiding center diffusion in a smooth random potential, Phys. Rev. B 92(18), 180204 (2015)
https://doi.org/10.1103/PhysRevB.92.180204
123 G. D. Mahan, Many-Particle Physics, Plenum Press, 1990
https://doi.org/10.1007/978-1-4613-1469-1
124 M. E. Raikh and T. V. Shahbazyan, High Landau levels in a smooth random potential for two-dimensional electrons, Phys. Rev. B 47(3), 1522 (1993)
https://doi.org/10.1103/PhysRevB.47.1522
125 S. S. Murzin, Electron transport in the extreme quantum limit in applied magnetic field, Physics-Uspekhi 43(4), 349 (2000)
https://doi.org/10.1070/PU2000v043n04ABEH000691
126 D. A. Pesin, E. G. Mishchenko, and A. Levchenko, Density of states and magnetotransport in Weyl semimetals with long-range disorder, Phys. Rev. B 92(17), 174202 (2015)
https://doi.org/10.1103/PhysRevB.92.174202
127 M. M. Parish and P. B. Littlewood, Non-saturating magnetoresistance in heavily disordered semiconductors, Nature 426(6963), 162 (2003)
https://doi.org/10.1038/nature02073
128 P. S. Alekseev, A. P. Dmitriev, I. V. Gornyi, V. Y. Kachorovskii, B. N. Narozhny, M. Schütt, and M. Titov, Magnetoresistance in two-component systems, Phys. Rev. Lett. 114(15), 156601 (2015)
https://doi.org/10.1103/PhysRevLett.114.156601
129 N. Ramakrishnan, M. Milletari, and S. Adam, Transport and magnetotransport in three-dimensional Weyl semimetals, Phys. Rev. B 92(24), 245120 (2015)
https://doi.org/10.1103/PhysRevB.92.245120
130 Y. Pan, H. Wang, P. Lu, J. Sun, B. Wang, and D. Y. Xing, The large unsaturated magnetoresistance of Weyl semimetals, arXiv: 1509.03975
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed