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

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

References

[1] P. R. Wallace, The band theory of graphite, Phys. Rev. 71(9), 622 (1947)

[2] H. Weyl, Elektron und gravitation. I, Z. Phys. 56(5–6), 330 (1929)

[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)

[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)

[5] M. Z. Hasan and C. L. Kane, Colloquium: Topological insulators, Rev. Mod. Phys. 82(4), 3045 (2010)

[6] X. L. Qi and S. C. Zhang, Topological insulators and superconductors, Rev. Mod. Phys. 83(4), 1057 (2011)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[14] G. B. Halász and L. Balents, Time-reversal invariant realization of the Weyl semimetal phase, Phys. Rev. B 85(3), 035103 (2012)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[24] P. Hosur and X. L. Qi, Recent developments in transport phenomena in Weyl semimetals, C. R. Phys. 14(9– 10), 857 (2013)

[25] I. A. Luk’yanchuk and Y. Kopelevich, Phase analysis of quantum oscillation in graphite, Phys. Rev. Lett. 93(16), 166402 (2004)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[33] D. T. Son and B. Z. Spivak, Chiral anomaly and classical negative magnetoresistance of Weyl metals, Phys. Rev. B 88(10), 104412 (2013)

[34] A. A. Burkov, Negative longitudinal magnetoresistance in Dirac and Weyl metals, Phys. Rev. B 91(24), 245157 (2015)

[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)

[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)

[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)

[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)

[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)

[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: 1606.05178

[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)

[42] K. Y. Bliokh, Weak antilocalization of ultrarelativistic fermions, Phys. Lett. A 344(2–4), 127 (2005)

[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)

[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)

[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)

[46] A. Kawabata, Theory of negative magnetoresistance i. application to heavily doped semiconductors, J. Phys. Soc. Jpn. 49(2), 628 (1980)

[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)

[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)

[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)

[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)

[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)

[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)

[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)

[54] A. K. Mitchell and L. Fritz, Kondo effect in threedimensional Dirac and Weyl systems, Phys. Rev. B 92, 121109(R) (2015)

RIGHTS & PERMISSIONS

2017 Higher Education Press and Springer-Verlag Berlin Heidelberg