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Journal of High Energy Physics

, 2018:69 | Cite as

Magnetotransport in multi-Weyl semimetals: a kinetic theory approach

  • Renato M. A. DantasEmail author
  • Francisco Peña-Benitez
  • Bitan Roy
  • Piotr Surówka
Open Access
Regular Article - Theoretical Physics

Abstract

We study the longitudinal magnetotransport in three-dimensional multi-Weyl semimetals, constituted by a pair of (anti)-monopole of arbitrary integer charge (n), with n = 1,2 and 3 in a crystalline environment. For any n > 1, even though the distribution of the underlying Berry curvature is anisotropic, the corresponding intrinsic component of the longitudinal magnetoconductivity (LMC), bearing the signature of the chiral anomaly, is insensitive to the direction of the external magnetic field (B) and increases as B2, at least when it is sufficiently weak (the semi-classical regime). In addition, the LMC scales as n3 with the monopole charge. We demonstrate these outcomes for two distinct scenarios, namely when inter-particle collisions in the Weyl medium are effectively described by (a) a single and (b) two (corresponding to inter- and intra-valley) scattering times. While in the former situation the contribution to LMC from chiral anomaly is inseparable from the non-anomalous ones, these two contributions are characterized by different time scales in the later construction. Specifically for sufficiently large inter-valley scattering time the LMC is dominated by the anomalous contribution, arising from the chiral anomaly. The predicted scaling of LMC and the signature of chiral anomaly can be observed in recently proposed candidate materials, accommodating multi-Weyl semimetals in various solid state compounds.

Keywords

Anomalies in Field and String Theories Topological States of Matter 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    A. Vilenkin, Macroscopic parity violating effects: neutrino fluxes from rotating black holes and in rotating thermal radiation, Phys. Rev. D 20 (1979) 1807 [INSPIRE].MathSciNetGoogle Scholar
  2. [2]
    A. Vilenkin, Equilibrium parity violating current in a magnetic field, Phys. Rev. D 22 (1980) 3080 [INSPIRE].
  3. [3]
    K. Fukushima, D.E. Kharzeev and H.J. Warringa, The chiral magnetic effect, Phys. Rev. D 78 (2008) 074033 [arXiv:0808.3382] [INSPIRE].
  4. [4]
    J. Erdmenger, M. Haack, M. Kaminski and A. Yarom, Fluid dynamics of R-charged black holes, JHEP 01 (2009) 055 [arXiv:0809.2488] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    N. Banerjee et al., Hydrodynamics from charged black branes, JHEP 01 (2011) 094 [arXiv:0809.2596] [INSPIRE].CrossRefzbMATHGoogle Scholar
  6. [6]
    D.T. Son and P. Surowka, Hydrodynamics with triangle anomalies, Phys. Rev. Lett. 103 (2009) 191601 [arXiv:0906.5044] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  7. [7]
    K. Landsteiner, E. Megias and F. Pena-Benitez, Gravitational anomaly and transport, Phys. Rev. Lett. 107 (2011) 021601 [arXiv:1103.5006] [INSPIRE].
  8. [8]
    R.A. Bertlmann, Anomalies in quantum field theory, International Series of Monographs on Physics, Clarendon Press, U.K. (2001).Google Scholar
  9. [9]
    K. Fujikawa and H. Suzuki, Path Integrals and Quantum Anomalies, International Series of Monographs on Physics, Clarendon Press, U.K. (2004).Google Scholar
  10. [10]
    S.L. Adler, Axial vector vertex in spinor electrodynamics, Phys. Rev. 177 (1969) 2426 [INSPIRE].CrossRefGoogle Scholar
  11. [11]
    J.S. Bell and R. Jackiw, A PCAC puzzle: π 0γγ in the σ model, Nuovo Cim. A 60 (1969) 47 [INSPIRE].
  12. [12]
    R. Delbourgo and A. Salam, The gravitational correction to P CAC, Phys. Lett. B 40 (1972) 381.Google Scholar
  13. [13]
    A. Lucas, R.A. Davison and S. Sachdev, Hydrodynamic theory of thermoelectric transport and negative magnetoresistance in Weyl semimetals, Proc. Nat. Acad. Sci. 113 (2016) 9463 [arXiv:1604.08598] [INSPIRE].CrossRefGoogle Scholar
  14. [14]
    K. Landsteiner, Y. Liu and Y.-W. Sun, Odd viscosity in the quantum critical region of a holographic Weyl semimetal, Phys. Rev. Lett. 117 (2016) 081604 [arXiv:1604.01346] [INSPIRE].
  15. [15]
    J. Gooth et al., Experimental signatures of the mixed axial-gravitational anomaly in the Weyl semimetal NbP, Nature 547 (2017) 324 [arXiv:1703.10682] [INSPIRE].CrossRefGoogle Scholar
  16. [16]
    J. Liao, Chiral magnetic effect in heavy ion collisions, Nucl. Phys. A 956 (2016) 99 [arXiv:1601.00381] [INSPIRE].
  17. [17]
    N.P. Armitage, E.J. Mele and A. Vishwanath, Weyl and dirac semimetals in three-dimensional solids, Rev. Mod. Phys. 90 (2018) 015001.Google Scholar
  18. [18]
    H.B. Nielsen and M. Ninomiya, No go theorem for regularizing chiral fermions, Phys. Lett. B 105 (1981) 219.Google Scholar
  19. [19]
    K. Landsteiner, Anomalous transport of Weyl fermions in Weyl semimetals, Phys. Rev. B 89 (2014) 075124 [arXiv:1306.4932] [INSPIRE].
  20. [20]
    G. Basar, D.E. Kharzeev and H.-U. Yee, Triangle anomaly in Weyl semimetals, Phys. Rev. B 89 (2014) 035142 [arXiv:1305.6338] [INSPIRE].
  21. [21]
    M.M. Vazifeh and M. Franz, Electromagnetic response of Weyl semimetals, Phys. Rev. Lett. 111 (2013) 027201.Google Scholar
  22. [22]
    H. Nielsen and M. Ninomiya, The Adler-Bell-Jackiw anomaly and Weyl fermions in a crystal, Phys. Lett. B 130 (1983) 389.Google Scholar
  23. [23]
    D.T. Son and N. Yamamoto, Berry curvature, triangle anomalies and the chiral magnetic effect in Fermi liquids, Phys. Rev. Lett. 109 (2012) 181602 [arXiv:1203.2697] [INSPIRE].CrossRefGoogle Scholar
  24. [24]
    T. Hayata, Y. Kikuchi and Y. Tanizaki, Topological properties of the chiral magnetic effect in multi-Weyl semimetals, Phys. Rev. B 96 (2017) 085112.Google Scholar
  25. [25]
    D.T. Son and B.Z. Spivak, Chiral anomaly and classical negative magnetoresistance of Weyl metals, Phys. Rev. B 88 (2013) 104412 [arXiv:1206.1627] [INSPIRE].
  26. [26]
    T. Osada, Negative interlayer magnetoresistance and zero-mode Landau level in multilayer dirac electron systems, J. Phys. Soc. Japan 77 (2008) 084711.Google Scholar
  27. [27]
    A.G. Grushin, Consequences of a condensed matter realization of Lorentz violating QED in Weyl semi-metals, Phys. Rev. D 86 (2012) 045001 [arXiv:1205.3722] [INSPIRE].
  28. [28]
    V. Aji, Adler-Bell-Jackiw anomaly in Weyl semimetals: application to pyrochlore iridates, Phys. Rev. B 85 (2012) 241101.Google Scholar
  29. [29]
    A.A. Zyuzin and A.A. Burkov, Topological response in Weyl semimetals and the chiral anomaly, Phys. Rev. B 86 (2012) 115133 [arXiv:1206.1868] [INSPIRE].
  30. [30]
    P. Goswami and S. Tewari, Axionic field theory of (3 + 1)-dimensional Weyl semimetals, Phys. Rev. B 88 (2013) 245107 [arXiv:1210.6352] [INSPIRE].
  31. [31]
    M.M. Vazifeh and M. Franz, Electromagnetic response of weyl semimetals, Phys. Rev. Lett. 111 (2013) 027201.Google Scholar
  32. [32]
    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 (2014) 085126 [arXiv:1312.0027] [INSPIRE].
  33. [33]
    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 (2015) 174202.Google Scholar
  34. [34]
    A. Jimenez-Alba, K. Landsteiner, Y. Liu and Y.-W. Sun, Anomalous magnetoconductivity and relaxation times in holography, JHEP 07 (2015) 117 [arXiv:1504.06566] [INSPIRE].CrossRefGoogle Scholar
  35. [35]
    V.A. Zyuzin, Magnetotransport of Weyl semimetals due to the chiral anomaly, Phys. Rev. B 95 (2017) 245128 [arXiv:1608.01286] [INSPIRE].
  36. [36]
    X. Huang et al., Observation of the chiral-anomaly-induced negative magnetoresistance in 3d Weyl semimetal TaAs, Phys. Rev. X 5 (2015) 031023.Google Scholar
  37. [37]
    Y.-Y. Wang et al., Resistivity plateau and extremely large magnetoresistance in N bAs 2 and T aAs 2, Phys. Rev. B 94 (2016) 041103.Google Scholar
  38. [38]
    G. Zheng et al., Transport evidence for the three-dimensional dirac semimetal phase in ZrTe5, Phys. Rev. B 93 (2016) 115414.Google Scholar
  39. [39]
    C.-L. Zhang et al., Signatures of the Adler-Bell-Jackiw chiral anomaly in a Weyl fermion semimetal, Nature Commun. 7 (2016) 10735.Google Scholar
  40. [40]
    Q. Li et al., Chiral magnetic effect in ZrT e 5, Nature Phys. 12 (2016) 550.Google Scholar
  41. [41]
    G. Xu, H. Weng, Z. Wang, X. Dai and Z. Fang, Chern semi-metal and Quantized Anomalous Hall Effect in HgCr 2 Se 4, Phys. Rev. Lett. 107 (2011) 186806 [arXiv:1106.3125] [INSPIRE].
  42. [42]
    C. Fang, M.J. Gilbert, X. Dai and B.A. Bernevig, Multi-Weyl topological semimetals stabilized by point group symmetry, Phys. Rev. Lett. 108 (2012) 266802.CrossRefGoogle Scholar
  43. [43]
    S.M. Huang et al., New type of Weyl semimetal with quadratic double weyl fermions, Proc. Nat. Acad. Sci. 113 (2016) 1180.CrossRefGoogle Scholar
  44. [44]
    B.J. Yang and N. Nagaosa, Classification of stable three-dimensional Dirac semimetals with nontrivial topology, Nature Commun. 5 (2014) 4898.CrossRefGoogle Scholar
  45. [45]
    M.Z. Hasan, S.Y. Xu, I. Belopolski and S.M. Huang, Discovery of Weyl fermion semimetals and topological fermi arc states, Ann. Rev. Cond. Mat. Phys. 8 (2017) 289.CrossRefGoogle Scholar
  46. [46]
    B. Yan and C. Felser, Topological materials: Weyl semimetals, Ann. Rev. Cond. Mat. Phys. 8 (2017) 337.CrossRefGoogle Scholar
  47. [47]
    Q. Liu and A. Zunger, Predicted realization of cubic Dirac fermion in quasi-one-dimensional transition-metal monochalcogenides, Phys. Rev. X 7 (2017) 021019.Google Scholar
  48. [48]
    G.E. Volovik, The universe in a Helium droplet, International Series of Monographs on Physics. Clarendon Press U.K. (2003).Google Scholar
  49. [49]
    P. Goswami and L. Balicas, Topological properties of possible Weyl superconducting states of URu 2 Si 2, arXiv:1312.3632 [INSPIRE].
  50. [50]
    P. Goswami and A.H. Nevidomskyy, Double Berry monopoles and topological surface states in the superconducting B-phase of UPt 3, Phys. Rev. B 92 (2015) 214504 [arXiv:1403.0924] [INSPIRE].
  51. [51]
    M.H. Fischer et al., Chiral d-wave superconductivity in SrP tAs, Phys. Rev. B 89 (2014) 020509.Google Scholar
  52. [52]
    B. Roy, S.A.A. Ghorashi, M.S. Foster and A.H. Nevidomskyy, Topological superconductivity of spin-3/2 carriers in a three-dimensional doped Luttinger semimetal, arXiv:1708.07825 [INSPIRE].
  53. [53]
    M. Stephanov, H.-U. Yee and Y. Yin, Collective modes of chiral kinetic theory in a magnetic field, Phys. Rev. D 91 (2015) 125014.Google Scholar
  54. [54]
    X.-N. Wang, Role of multiple mini-jets in high-energy hadronic reactions, Phys. Rev. D 43 (1991) 104 [INSPIRE].
  55. [55]
    S. Bera, J.D. Sau and B. Roy, Dirty weyl semimetals: Stability, phase transition, and quantum criticality, Phys. Rev. B 93 (2016) 201302.Google Scholar
  56. [56]
    B. Roy, P. Goswami and V. Juricic, Interacting Weyl fermions: phases, phase transitions and global phase diagram, Phys. Rev. B 95 (2017) 201102 [arXiv:1610.05762] [INSPIRE].
  57. [57]
    G. Sundaram and Q. Niu, Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects, Phys. Rev. B 59 (1999) 14915 [INSPIRE].
  58. [58]
    D. Xiao, M.-C. Chang and Q. Niu, Berry phase effects on electronic properties, Rev. Mod. Phys. 82 (2010) 1959.MathSciNetCrossRefzbMATHGoogle Scholar
  59. [59]
    E.V. Gorbar et al., Anomalous maxwell equations for inhomogeneous chiral plasma, Phys. Rev. D 93 (2016) 105028.Google Scholar
  60. [60]
    E.V. Gorbar, D.O. Rybalka and I.A. Shovkovy, Second-order dissipative hydrodynamics for plasma with chiral asymmetry and vorticity, Phys. Rev. D 95 (2017) 096010 [arXiv:1702.07791] [INSPIRE].
  61. [61]
    Y. Hidaka, S. Pu and D.-L. Yang, Nonlinear responses of chiral fluids from kinetic theory, Phys. Rev. D 97 (2018) 016004 [arXiv:1710.00278] [INSPIRE].
  62. [62]
    D.O. Rybalka, E.V. Gorbar and I.A. Shovkovy, Hydrodynamic modes in magnetized chiral plasma with vorticity, arXiv:1807.07608 [INSPIRE].
  63. [63]
    R. Soto, Kinetic theory and transport phenomena, Oxford Master Series in Physics. Oxford University Press, Oxford U.K. (2016).Google Scholar
  64. [64]
    C. Duval et al., Berry phase correction to electron density in solids and ‘exotic’ dynamics, Mod. Phys. Lett. B 20 (2006) 373 [cond-mat/0506051] [INSPIRE].
  65. [65]
    R. Loganayagam and P. Surowka, Anomaly/transport in an ideal Weyl gas, JHEP 04 (2012) 097 [arXiv:1201.2812] [INSPIRE].CrossRefzbMATHGoogle Scholar
  66. [66]
    M.A. Stephanov and Y. Yin, Chiral kinetic theory, Phys. Rev. Lett. 109 (2012) 162001 [arXiv:1207.0747] [INSPIRE].CrossRefGoogle Scholar
  67. [67]
    B.Z. Spivak and A.V. Andreev, Magnetotransport phenomena related to the chiral anomaly in weyl semimetals, Phys. Rev. B 93 (2016) 085107.Google Scholar
  68. [68]
    A.A. Burkov, Chiral anomaly and diffusive magnetotransport in Weyl metals, Phys. Rev. Lett. 113 (2014) 247203.CrossRefGoogle Scholar
  69. [69]
    A.H. Castro Neto et al., The electronic properties of graphene, Rev. Mod. Phys. 81 (2009) 109.CrossRefGoogle Scholar
  70. [70]
    X. Dai, Z.Z. Du and H.-Z. Lu, Negative magnetoresistance without chiral anomaly in topological insulators, Phys. Rev. Lett. 119 (2017) 166601 [arXiv:1705.02724] [INSPIRE].CrossRefGoogle Scholar
  71. [71]
    K. Fujikawa, Quantum anomaly and geometric phase: their basic differences, Phys. Rev. D 73 (2006) 025017 [hep-th/0511142] [INSPIRE].
  72. [72]
    N. Mueller and R. Venugopalan, The chiral anomaly, Berry’s phase and chiral kinetic theory, from world-lines in quantum field theory, Phys. Rev. D 97 (2018) 051901 [arXiv:1701.03331] [INSPIRE].
  73. [73]
    K. Fujikawa, Characteristics of chiral anomaly in view of various applications, Phys. Rev. D 97 (2018) 016018 [arXiv:1709.08181] [INSPIRE].
  74. [74]
    G. Bergmann, Weak localization in thin films: a time-of-flight experiment with conduction electrons, Phys. Rept. 107 (1984) 1.CrossRefGoogle Scholar
  75. [75]
    D.T. Son and N. Yamamoto, Kinetic theory with Berry curvature from quantum field theories, Phys. Rev. D 87 (2013) 085016 [arXiv:1210.8158] [INSPIRE].
  76. [76]
    J.-Y. Chen et al., Lorentz invariance in chiral kinetic theory, Phys. Rev. Lett. 113 (2014) 182302 [arXiv:1404.5963] [INSPIRE].CrossRefGoogle Scholar
  77. [77]
    X. Li, B. Roy and S. Das Sarma, Weyl fermions with arbitrary monopoles in magnetic fields: Landau levels, longitudinal magnetotransport and density-wave ordering, Phys. Rev. B 94 (2016) 195144 [arXiv:1608.06632] [INSPIRE].
  78. [78]
    B. Roy and J.D. Sau, Magnetic catalysis and axionic charge-density-wave in Weyl semimetals, Phys. Rev. B 92 (2015) 125141 [arXiv:1406.4501] [INSPIRE].

Copyright information

© The Author(s) 2018

Authors and Affiliations

  • Renato M. A. Dantas
    • 1
    Email author
  • Francisco Peña-Benitez
    • 1
  • Bitan Roy
    • 1
  • Piotr Surówka
    • 1
  1. 1.Max-Planck-Institut für Physik komplexer SystemeDresdenGermany

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