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Frontiers of Physics

, 12:127205 | Cite as

Negative magnetoresistance in Weyl semimetals NbAs and NbP: Intrinsic chiral anomaly and extrinsic effects

  • Yupeng Li
  • Zhen Wang
  • Pengshan Li
  • Xiaojun Yang
  • Zhixuan Shen
  • Feng Sheng
  • Xiaodong Li
  • Yunhao Lu
  • Yi Zheng
  • Zhu-An Xu
Review Article
Part of the following topical collections:
  1. Recent Progress on Weyl Semimetals

Abstract

Chiral anomaly-induced negative magnetoresistance (NMR) has been widely used as critical transport evidence for the existence of Weyl fermions in topological semimetals. In this mini-review, we discuss the general observation of NMR phenomena in non-centrosymmetric NbP and NbAs. We show that NMR can arise from the intrinsic chiral anomaly of Weyl fermions and/or extrinsic effects, such as the superimposition of Hall signals; field-dependent inhomogeneous current flow in the bulk, i.e., current jetting; and weak localization (WL) of coexistent trivial carriers. The WL-controlled NMR is heavily dependent on sample quality and is characterized by a pronounced crossover from positive to negative MR growth at elevated temperatures, resulting from the competition between the phase coherence time and the spin-orbital scattering constant of the bulk trivial pockets. Thus, the correlation between the NMR and the chiral anomaly need to be scrutinized without the support of complimentary techniques. Because of the lifting of spin degeneracy, the spin orientations of Weyl fermions are either parallel or antiparallel to the momentum, which is a unique physical property known as helicity. The conservation of helicity provides strong protection for the transport of Weyl fermions, which can only be effectively scattered by magnetic impurities. Chemical doping with magnetic and non-magnetic impurities is thus more convincing than the NMR method for detecting the existence of Weyl fermions.

Keywords

Weyl semimetals chiral anomaly negative magnetoresistance extrinsic effects 

Notes

Acknowledgments

This work was supported by the National Basic Research Program of China (Grant No. 2014CB921203), the National Science Foundation of China (Grant Nos. 11190023, U1332209, 11374009, 61574123, and 11574264), MOE of China (Grant No. 2015KF07), the Fundamental Research Funds for the Central Universities of China, and the National Key R&D Program of the MOST of China (Grant No. 2016YFA0300204). The in-situ high-pressure angle-dispersive X-ray diffraction (ADXRD) measurement was performed at the 4W2 beamline of the Beijing Synchrotron Radiation Facility (BSRF). Y.Z. acknowledges the start funding support from the Thousand Talents Plan.

References

  1. 1.
    P. R. Wallace, The band theory of graphite, Phys. Rev. 71(9), 622 (1947)ADSCrossRefMATHGoogle Scholar
  2. 2.
    H. Weyl, Elektron und gravitation. I, Z. Phys. 56(5–6), 330 (1929)ADSCrossRefMATHGoogle Scholar
  3. 3.
    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, Nature 438(7065), 197 (2005)ADSCrossRefGoogle Scholar
  4. 4.
    Y. B. Zhang, Y. W. Tan, H. L. Stormer, and P. Kim, Experimental observation of the quantum Hall effect and Berry’s phase in graphene, Nature 438(7065), 201 (2005)ADSCrossRefGoogle Scholar
  5. 5.
    M. Z. Hasan and C. L. Kane, Colloquium: Topological insulators, Rev. Mod. Phys. 82(4), 3045 (2010)ADSCrossRefGoogle Scholar
  6. 6.
    X. L. Qi and S. C. Zhang, Topological insulators and superconductors, Rev. Mod. Phys. 83(4), 1057 (2011)ADSCrossRefGoogle Scholar
  7. 7.
    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)ADSCrossRefGoogle Scholar
  8. 8.
    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)ADSCrossRefGoogle Scholar
  9. 9.
    L. Tian, Q. Gibson, M. N. Ali, M. Liu, R. J. Cava, and N. P. Ong, Ultrahigh mobility and giant magnetoresistance in the Dirac semimetal Cd3As2, Nat. Mater. 14, 280 (2015)ADSGoogle Scholar
  10. 10.
    X. G. Wan, A. M. Turner, A. Vishwanath, and S. Y. Savrasov, Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates, Phys. Rev. B 83(20), 205101 (2011)ADSCrossRefGoogle Scholar
  11. 11.
    H. Weng, C. Fang, Z. Fang, B. A. Bernevig, and X. Dai, Weyl semimetal phase in noncentrosymmetric transition-metal monophosphides, Phys. Rev. X 5(1), 011029 (2015)Google Scholar
  12. 12.
    S. Huang, S. Y. Xu, I. Belopolski, C. Lee, G. Chang, B. Wang, N. Alidoust, G. Bian, M. Neupane, C. Zhang, S. Jia, A. Bansil, H. Lin, and M. Z. Hasan, A Weyl Fermion semimetal with surface Fermi arcs in the transition metal monopnictide TaAs class, Nat. Commun. 6, 7373 (2015)CrossRefGoogle Scholar
  13. 13.
    G. Bian, T. R. Chang, R. Sankar, S. Y. Xu, H. Zheng, T. Neupert, C. K. Chiu, S. M. Huang, G. Chang, I. Belopolski, D. S. Sanchez, M. Neupane, N. Alidoust, C. Liu, B.K. Wang, C.-C. Lee, H.- T. Jeng, A. Bansil, F. Chou, H. Lin, and M. Z. Hasan, Topological nodalline fermions in the non-centrosymmetric superconductor compound PbTaSe2, arXiv: 1505.03069 (2015)Google Scholar
  14. 14.
    G. B. Halász and L. Balents, Time-reversal invariant realization of the Weyl semimetal phase, Phys. Rev. B 85(3), 035103 (2012)ADSCrossRefGoogle Scholar
  15. 15.
    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. K. Wang, A. Bansil, H.T. Jeng, T. Neupert, A. Kaminski, H. Lin, S. Jia, and M. Z. Hasan, Discovery of a Weyl fermion state with Fermi arcs in niobium arsenide, Nat. Phys. 11(9), 748 (2015)CrossRefGoogle Scholar
  16. 16.
    B. Q. Lv, H. M. Weng, B. B. Fu, X. P. Wang, H. Miao, J. Ma, P. Richard, X. C. Huang, L. X. Zhao, G. F. Chen, Z. Fang, X. Dai, T. Qian, and H. Ding, Experimental discovery of Weyl semimetal TaAs, Phys. Rev. X 5(3), 031013 (2015)Google Scholar
  17. 17.
    B. Q. Lv, S. Muff, T. Qian, Z. D. Song, S. M. Nie, N. Xu, P. Richard, C. E. Matt, N. C. Plumb, L. X. Zhao, G. F. Chen, Z. Fang, X. Dai, J. H. Dil, J. Mesot, M. Shi, H. M. Weng, and H. Ding, Observation of Fermiarc spin texture in TaAs, Phys. Rev. Lett. 115, 217601 (2015)ADSCrossRefGoogle Scholar
  18. 18.
    S. Xu, I. Belopolski, N. Alidoust, M. Neupane, G. Bian, C. Zhang, R. Sankar, G. Chang, Z. Yuan, C. C. Lee, S. M. Huang, H. Zheng, J. Ma, D. S. Sanchez, B. Wang, A. Bansil, F. Chou, P. P. Shibayev, H. Lin, S. Jia, and M. Z. Hasan, Discovery of a Weyl fermion semimetal and topological Fermi arcs, Science 349(6248), 613 (2015)ADSCrossRefGoogle Scholar
  19. 19.
    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)Google Scholar
  20. 20.
    X. Huang, L. Zhao, Y. Long, P. Wang, D. Chen, Z. Yang, H. Liang, M. Xue, H. M. Weng, Z. Fang, X. Dai, and G. Chen, Observation of the chiral anomaly induced negative magnetoresistance in 3D Weyl semimetal TaAs, Phys. Rev. X 5(3), 031023 (2015)Google Scholar
  21. 21.
    C. Shekhar, A. K. Nayak, Y. Sun, M. Schmidt, M. Nicklas, I. Leermakers, U. Zeitler, Y. Skourski, J. Wosnitza, Z. Liu, Y. Chen, W. Schnelle, H. Borrmann, Y. Grin, C. Felser, and B. H. Yan, Extremely large magnetoresistance and ultrahigh mobility in the topological Weyl semimetal candidate NbP, Nat. Phys. 11(8), 645 (2015)CrossRefGoogle Scholar
  22. 22.
    Z. Wang, Y. Zheng, Z. X. Shen, Y. Zhou, X. J. Yang, Y. P. Li, C. M. Feng, and Z. A. Xu, Helicity protected ultrahigh mobility Weyl fermions in NbP, Phys. Rev. B 93, 121112(R) (2016)ADSCrossRefGoogle Scholar
  23. 23.
    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(11), 117201 (2015)ADSCrossRefGoogle Scholar
  24. 24.
    P. Hosur and X. L. Qi, Recent developments in transport phenomena in Weyl semimetals, C. R. Phys. 14(9–10), 857 (2013)ADSCrossRefGoogle Scholar
  25. 25.
    I. A. Luk’yanchuk and Y. Kopelevich, Phase analysis of quantum oscillation in graphite, Phys. Rev. Lett. 93(16), 166402 (2004)ADSCrossRefGoogle Scholar
  26. 26.
    H. B. Nielsen and M. Ninomiya, The Adler-Bell-Jackiw anomaly and Weyl fermions in a crystal, Phys. Lett. B 130(6), 389 (1983)ADSMathSciNetCrossRefGoogle Scholar
  27. 27.
    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)ADSMathSciNetCrossRefMATHGoogle Scholar
  28. 28.
    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 topoogical insulators: Adler–Bell–Jackiw anomaly in transport phenomena, Phys. Rev. Lett. 111(24), 246603 (2013)ADSCrossRefGoogle Scholar
  29. 29.
    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, Observation of the chiral magnetic effect in ZrTe5, arXiv: 1412.6543 (2014)Google Scholar
  30. 30.
    F. Arnold, C. Shekhar, S.- C. Wu, Y. Sun, R. Donizeth 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, Large and unsaturated negative magnetoresistance induced by the chiral anomaly in the Weyl semimetal TaP, arXiv: 1506.06577 (2015)Google Scholar
  31. 31.
    X. J. Yang, Y. P. Li, Z. Wang, Y. Zheng, and Z. A. Xu, Chiral anomaly induced negative magnetoresistance in topological Weyl semimetal NbAs, arXiv: 1506.03190 (2015)Google Scholar
  32. 32.
    M. Hirschberger, S. Kushwaha, Z. Wang, Q. Gibson, S. Liang, C. A. Belvin, B. A. Bernevig, R. J. Cava, and N. P. Ong, The chiral anomaly and thermopower of Weyl fermions in the half-Heusler GdPtBi, Nat. Mater. 15(11), 1161 (2016)ADSCrossRefGoogle Scholar
  33. 33.
    D. T. Son and B. Z. Spivak, Chiral anomaly and classical negative magnetoresistance of Weyl metals, Phys. Rev. B 88(10), 104412 (2013)ADSCrossRefGoogle Scholar
  34. 34.
    A. A. Burkov, Negative longitudinal magnetoresistance in Dirac and Weyl metals, Phys. Rev. B 91(24), 245157 (2015)ADSCrossRefGoogle Scholar
  35. 35.
    B. Z. Spivak and A. V. Andreev, Magneto-transport phenomena related to the chiral anomaly in Weyl semimetals, Phys. Rev. B 93(8), 085107 (2016)ADSCrossRefGoogle Scholar
  36. 36.
    J. S. Hu, T. F. Rosenbaum, and J. B. Betts, Current jets, disorder, and linear magnetoresistance in the silver chalcogenides, Phys. Rev. Lett. 95(18), 186603 (2005)ADSGoogle Scholar
  37. 37.
    J. S. Hu, M. M. Parish, and T. F. Rosenbaum, Nonsaturating magnetoresistance of inhomogeneous conductors: Comparison of experiment and simulation, Phys. Rev. B 75(21), 214203 (2007)ADSCrossRefGoogle Scholar
  38. 38.
    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, arXiv: 1606.03389 (2016)Google Scholar
  39. 39.
    C. L. Zhang, S. Y. Xu, I. Belopolski, Z. Yuan, Z. Lin, B. Tong, G. Bian, N. Alidoust, C. C. Lee, S. M. Huang, T. R. Chang, G. Chang, C. H. Hsu, H. T. Jeng, M. Neupane, D. S. Sanchez, H. Zheng, J. Wang, H. Lin, 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)ADSCrossRefGoogle Scholar
  40. 40.
    T. Besara, D. A. Rhodes, K. W. Chen, S. Das, Q. R. Zhang, J. F. Sun, B. Zeng, Y. Xin, L. Balicas, R. E. Baumbach, E. Manousakis, D. J. Singh, and T. Siegrist, Coexistence of Weyl physics and planar defects in semimetals TaP and TaAs, Phys. Rev. B 93, 245152 (2016), arXiv: 1606.05178ADSCrossRefGoogle Scholar
  41. 41.
    J. Jiang, F. Tang, X. C. Pan, H. M. Liu, X. H. Niu, Y. X. Wang, D. F. Xu, H. F. Yang, B. P. Xie, F. Q. Song, P. Dudin, T. K. Kim, M. Hoesch, P. K. Das, I. Vobornik, X. G. Wan, and D. L. Feng, Signature of strong spin-orbital coupling in the large nonsaturating magnetoresistance material WTe2, Phys. Rev. Lett. 115(16), 166601 (2015)ADSCrossRefGoogle Scholar
  42. 42.
    K. Y. Bliokh, Weak antilocalization of ultrarelativistic fermions, Phys. Lett. A 344(2–4), 127 (2005)ADSCrossRefMATHGoogle Scholar
  43. 43.
    S. Hikami, A. I. Larkin, and Y. Nagaoka, Spinorbital interaction and magnetoresistance in the twodimensional random system, Prog. Theor. Phys. 63(2), 707 (1980)ADSCrossRefGoogle Scholar
  44. 44.
    H. Wang, H. Liu, C. Z. Chang, H. Zuo, Y. Zhao, Y. Sun, Z. Xia, K. He, X. Ma, X. C. Xie, Q. K. Xue, and J. Wang, Crossover between weak antilocalization and weak localization of bulk states in ultrathin Bi2Se3 films, Sci. Rep. 4, 5817 (2014)CrossRefGoogle Scholar
  45. 45.
    C. J. Lin, X. Y. He, J. Liao, X. X. Wang, V. Sacksteder IV, W. M. Yang, T. Guan, Q. M. Zhang, L. Gu, G. Y. Zhang, C. G. Zeng, X. Dai, K. H. Wu, and Y. Q. Li, Parallel field magnetoresistance in topological insulator thin films, Phys. Rev. B 88, 041307(R) (2013)ADSCrossRefGoogle Scholar
  46. 46.
    A. Kawabata, Theory of negative magnetoresistance i. application to heavily doped semiconductors, J. Phys. Soc. Jpn. 49(2), 628 (1980)ADSCrossRefGoogle Scholar
  47. 47.
    Y. Kopelevich, J. H. S. Torres, R. R. da Silva, F. Mrowka, H. Kempa, and P. Esquinazi, Reentrant metallic behavior of graphite in the quantum limit, Phys. Rev. Lett. 90(15), 156402 (2003)ADSCrossRefGoogle Scholar
  48. 48.
    B. Fauqué, B. Vignolle, C. Proust, J. P. Issi, and K. Behnia, Electronic instability in bismuth far beyond the quantum limit, New J. Phys. 11(11), 113012 (2009)ADSCrossRefGoogle Scholar
  49. 49.
    Y. P. Li, Z. Wang, Y. H. Lu, X. J. Yang, Z. X. Shen, F. Sheng, C. Feng, Y. Zheng, and Z.-A. Xu, Negative magnetoresistance in topological semimetals of transitionmetal dipnictides with non-trivial Z2 indices, arXiv: 1603.04056 (2016)Google Scholar
  50. 50.
    B. Shen, X. Y. Deng, G. Kotliar, and N. Ni, Fermi surface topology and negative longitudinal magnetoresistance observed in centrosymmetric NbAs2 semimetal, arXiv: 1602.01795 (2016)Google Scholar
  51. 51.
    Y. K. Luo, R. D. McDonald, P. F. S. Rosa, B. Scott, N. Wakeham, N. J. Ghimire, E. D. Bauer, J. D. Thompson, and F. Ronning, Anomalous magnetoresistance in TaAs2, arXiv: 1601.05524 (2016)Google Scholar
  52. 52.
    Z. Wang, Y. P. Li, Y. H. Lu, Z. X. Shen, F. Sheng, C. M. Feng, Y. Zheng, and Z. A. Xu, Topological phase transition induced extreme magnetoresistance in TaSb2, arXiv: 1603.01717 (2016)Google Scholar
  53. 53.
    V. K. Dugaev and D. E. Khmelnitskii, Magnetoresistance of metal films with low impurity concentration in a parallel magnetic field, Sov. Phys. JETP 59, 1038 (1984)Google Scholar
  54. 54.
    A. K. Mitchell and L. Fritz, Kondo effect in threedimensional Dirac and Weyl systems, Phys. Rev. B 92, 121109(R) (2015)ADSCrossRefGoogle Scholar

Copyright information

© Higher Education Press and Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Yupeng Li
    • 1
  • Zhen Wang
    • 1
    • 2
  • Pengshan Li
    • 3
  • Xiaojun Yang
    • 1
    • 2
  • Zhixuan Shen
    • 1
  • Feng Sheng
    • 1
  • Xiaodong Li
    • 3
  • Yunhao Lu
    • 2
  • Yi Zheng
    • 1
    • 4
    • 5
  • Zhu-An Xu
    • 1
    • 2
    • 4
    • 5
  1. 1.Department of PhysicsZhejiang UniversityHangzhouChina
  2. 2.State Key Lab of Silicon MaterialsZhejiang UniversityHangzhouChina
  3. 3.Institute of High Energy PhysicsChinese Academy of SciencesBeijingChina
  4. 4.Zhejiang California International NanoSystems InstituteZhejiang UniversityHangzhouChina
  5. 5.Collaborative Innovation Centre of Advanced MicrostructuresNanjingChina

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