Holographic calculation of the magneto-transport coefficients in Dirac semimetals

  • Marek RogatkoEmail author
  • Karol I. Wysokinski
Open Access
Regular Article - Theoretical Physics


Based on the gauge/gravity correspondence we have calculated the thermoelectric kinetic and transport characteristics of the strongly interacting materials in the presence of perpendicular magnetic field. The 3+1 dimensional system with Dirac-like spectrum is considered as a strongly interacting one if it is close to the particle-hole symmetry point. Transport in such system has been modeled by the two interacting vector fields. In the holographic theory the momentum relaxation is caused by axion field and leads to finite values of the direct current transport coefficients. We have calculated conductivity tensor in the presence of mutually perpendicular electric and magnetic fields and temperature gradient. The geometry differs from that in which magnetic field lies in the same plane as an electric one and temperature gradient.


AdS-CFT Correspondence Holography and condensed matter physics (AdS/CMT) 


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.


  1. [1]
    J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [Adv. Theor. Math. Phys. 2 (1998) 231] [hep-th/9711200] [INSPIRE].
  2. [2]
    E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  4. [4]
    J. Zaanen et al., Holographic duality in condensed matter physics, Cambridge University Press, Camrbidge U.K. (2015).CrossRefGoogle Scholar
  5. [5]
    S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Building a holographic superconductor, Phys. Rev. Lett. 101 (2008) 031601 [arXiv:0803.3295] [INSPIRE].ADSCrossRefGoogle Scholar
  6. [6]
    E. Gubankova, M. Cubrovic and J. Zaanen, Exciton-driven quantum phase transitions in holography, Phys. Rev. D 92 (2015) 086004 [arXiv:1412.2373] [INSPIRE].ADSGoogle Scholar
  7. [7]
    P. Kovtun, D.T. Son and A.O. Starinets, Viscosity in strongly interacting quantum field theories from black hole physics, Phys. Rev. Lett. 94 (2005) 111601 [hep-th/0405231] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    M. Blake and D. Tong, Universal resistivity from holographic massive gravity, Phys. Rev. D 88 (2013) 106004 [arXiv:1308.4970] [INSPIRE].ADSGoogle Scholar
  9. [9]
    R.A. Davison, Momentum relaxation in holographic massive gravity, Phys. Rev. D 88 (2013) 086003 [arXiv:1306.5792] [INSPIRE].ADSGoogle Scholar
  10. [10]
    M. Blake, D. Tong and D. Vegh, Holographic lattices give the graviton an effective mass, Phys. Rev. Lett. 112 (2014) 071602 [arXiv:1310.3832] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    A. Donos and J.P. Gauntlett, Holographic Q-lattices, JHEP 04 (2014) 040 [arXiv:1311.3292] [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    A. Donos and J.P. Gauntlett, Novel metals and insulators from holography, JHEP 06 (2014) 007 [arXiv:1401.5077] [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    T. Andrade and B. Withers, A simple holographic model of momentum relaxation, JHEP 05 (2014) 101 [arXiv:1311.5157] [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    A. Donos and J.P. Gauntlett, Thermoelectric DC conductivities from black hole horizons, JHEP 11 (2014) 081 [arXiv:1406.4742] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    A. Amoretti et al., Thermo-electric transport in gauge/gravity models with momentum dissipation, JHEP 09 (2014) 160 [arXiv:1406.4134] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    A. Amoretti et al., Analytic dc thermoelectric conductivities in holography with massive gravitons, Phys. Rev. D 91 (2015) 025002 [arXiv:1407.0306] [INSPIRE].ADSGoogle Scholar
  17. [17]
    A. Donos and J.P. Gauntlett, Navier-Stokes equations on black hole horizons and DC thermoelectric conductivity, Phys. Rev. D 92 (2015) 121901 [arXiv:1506.01360] [INSPIRE].ADSzbMATHGoogle Scholar
  18. [18]
    E. Banks, A. Donos and J.P. Gauntlett, Thermoelectric DC conductivities and Stokes flows on black hole horizons, JHEP 10 (2015) 103 [arXiv:1507.00234] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    A. Donos, J.P. Gauntlett, T. Griffin and L. Melgar, DC conductivity of magnetised holographic matter, JHEP 01 (2016) 113 [arXiv:1511.00713] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    A. Donos, J.P. Gauntlett, T. Griffin and L. Melgar, DC conductivity and higher derivative gravity, Class. Quant. Grav. 34 (2017) 135015 [arXiv:1701.01389] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  21. [21]
    L. Cheng, X.-H. Ge and Z.-Y. Sun, Thermoelectric DC conductivities with momentum dissipation from higher derivative gravity, JHEP 04 (2015) 135 [arXiv:1411.5452] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  22. [22]
    M. Blake, A. Donos and N. Lohitsiri, Magnetothermoelectric response from holography, JHEP 08 (2015) 124 [arXiv:1502.03789] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  23. [23]
    M. Blake and A. Donos, Quantum critical transport and the Hall angle, Phys. Rev. Lett. 114 (2015) 021601 [arXiv:1406.1659] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    A. Amoretti and D. Musso, Magneto-transport from momentum dissipating holography, JHEP 09 (2015) 094 [arXiv:1502.02631] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  25. [25]
    A. Lucas and S. Sachdev, Memory matrix theory of magnetotransport in strange metals, Phys. Rev. B 91 (2015) 195122 [arXiv:1502.04704] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    K.-Y. Kim, K.K. Kim, Y. Seo and S.-J. Sin, Thermoelectric conductivities at finite magnetic field and the Nernst effect, JHEP 07 (2015) 027 [arXiv:1502.05386] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  27. [27]
    M.S. Foster and I.L. Aleiner, Slow imbalance relaxation and thermoelectric transport in graphene, Phys. Rev. B 79 (2009) 085415.ADSCrossRefGoogle Scholar
  28. [28]
    Y. Seo, G. Song, P. Kim, S. Sachdev and S.-J. Sin, Holography of the Dirac Fluid in Graphene with two currents, Phys. Rev. Lett. 118 (2017) 036601 [arXiv:1609.03582] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    J. Crossno et al., Observation of the Dirac fluid and the breakdown of the Wiedemann-Franz law in graphene, Science 351 (2016) 1058.ADSCrossRefGoogle Scholar
  30. [30]
    S.M. Young et al., Dirac semimetal in three dimensions, Phys. Rev. Lett. 108 (2012) 140405.ADSCrossRefGoogle Scholar
  31. [31]
    A.H. Castro Neto et al., The electronic properties of graphene, Rev. Mod. Phys. 81 (2009) 109 [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    C. Fang, M.J. Gilbert, X.Dai and B.A. Bernevig, Topological semimetals stabilized by point group symmetry, Phys. Rev. Lett. 108 (2012) 266802.ADSCrossRefGoogle Scholar
  33. [33]
    B.J. Yang and N. Nagaosa, Classification of stable three-dimensional Dirac semimetals with nontrivial topology, Nature Commun. 5 (2014) 4989.CrossRefGoogle Scholar
  34. [34]
    N.P. Armitage, E.J. Mele and A. Vishvanath, Weyl and Dirac semimetals in three dimensional solids, arXiv:1705:01111.
  35. [35]
    L. Levitov and G. Falkovich, Electron viscosity, current vortices and negative nonlocal resistance in graphene, Nature Phys. 12 (2016) 672.ADSCrossRefGoogle Scholar
  36. [36]
    T. Liang et al., Ultrahigh mobility and giant magnetoresistance in the Dirac semimetal Cd 3 As 2, Nature Math. 14 (2015) 280.ADSCrossRefGoogle Scholar
  37. [37]
    T. Liang et al., Anomalous Nernst effect in the Dirac semimetal Cd 3 As 2, Phys. Rev. Lett. 118 (2017) 136601 [arXiv:1610.02459] [INSPIRE].ADSCrossRefGoogle Scholar
  38. [38]
    L.P. He and S.Y. Li, Quantum transport properties of the three-dimensional Dirac semimetal Cd 3 As 2 single crystals, Chin. Phys. B 25 (2016) 117105.ADSCrossRefGoogle Scholar
  39. [39]
    S. Murakami, Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase, New J. Phys. 9 (2007) 356.ADSCrossRefGoogle Scholar
  40. [40]
    D. Hsieh et al., A topological Dirac insulator in a quantum spin Hall phase, Nature 452 (2008) 970.ADSCrossRefGoogle Scholar
  41. [41]
    M. Neupane et al., Observation of a three-dimensional topological Dirac semimetal phase in high-mobility Cd 3 As 2, Nature Commun. 5 (2014) 3786.CrossRefGoogle Scholar
  42. [42]
    M. Neupane et al., Observation of topological nodal fermion semimetal phase in ZrSiS, Phys. Rev. B 93 (2016) 201104.ADSCrossRefGoogle Scholar
  43. [43]
    Z. Wang et al., Dirac semimetal and topological phase transitions in A 3 Bi (A = Na, K, Rb), Phys. Rev. B 85 (2012) 195320.ADSCrossRefGoogle Scholar
  44. [44]
    Z. Wang et al., Three-dimensional Dirac semimetal and quantum transport in Cd 3 As 2, Phys. Rev. B 88 (2013) 125427.ADSCrossRefGoogle Scholar
  45. [45]
    M. Brahlek et al., Topological metal to band-insulator transition in (Bi 1−x In x ) 2 Se 3 thin films, Phys. Rev. Lett. 109 (2013) 186403.ADSCrossRefGoogle Scholar
  46. [46]
    L. Wu et al., A sudden collapse in the transport lifetime across the topological phase transition in (Bi 1−x In x ) 2 Se 3, Nature Phys. 9 (2013) 410.ADSCrossRefGoogle Scholar
  47. [47]
    Z.K. Liu et al., Discovery of a three-dimensional topological Dirac semimetal, Na 3 Bi, Science 343 (2014) 864.ADSCrossRefGoogle Scholar
  48. [48]
    S.Y. Xu et al., Observation of Fermi arc surface states in a topological metal, Science 347 (2015) 294.ADSCrossRefGoogle Scholar
  49. [49]
    Z.K. Liu et al., A stable threedimensional topological Dirac semimetal Cd 3 As 2, Nature Math. 13 (2014) 677.ADSCrossRefGoogle Scholar
  50. [50]
    H.Z. Lu and S.Q. Shen, Quantum transport in topological semimetals under magnetic fields, Front. Phys. 12 (2017) 127201.CrossRefGoogle Scholar
  51. [51]
    R. Lundgren, P. Laurell and G.A. Fiete, Thermoelectric properties of Weyl and Dirac semimetals, Phys. Rev. B 90 (2014) 165115 [arXiv:1407.1435] [INSPIRE].ADSCrossRefGoogle Scholar
  52. [52]
    V. Aji, Adler Bell Jackiw anomaly in Weyl semi-metals: application to pyrochlore iridates, Phys. Rev. B 85 (2012) 241101.ADSCrossRefGoogle Scholar
  53. [53]
    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].ADSCrossRefGoogle Scholar
  54. [54]
    A. Donos and J. P. Gauntlett, Holographic Q lattices, JHEP 04 (2014) 040.ADSCrossRefGoogle Scholar
  55. [55]
    S.S. Yazadjiev, Generating dyonic solutions in 5D Einstein-dilaton gravity with antisymmetric forms and dyonic black rings, Phys. Rev. D 73 (2006) 124032 [hep-th/0512229] [INSPIRE].ADSGoogle Scholar
  56. [56]
    G.W. Gibbons and K.I. Maeda, Black holes and membranes in higher dimensional theories with dilaton fields, Nucl. Phys. B 298 (1988) 741 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  57. [57]
    S.Sachdev, What can gauge-gravity duality teach us about condensed matter physics?, Annu. Rev. Cond. Mat. Phys. 3 (2012) 9.CrossRefGoogle Scholar
  58. [58]
    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].ADSCrossRefGoogle Scholar
  59. [59]
    M. Ammon, J. Erdmenger, P. Kerner and M. Strydom, Black hole instability induced by a magnetic field, Phys. Lett. B 706 (2011) 94 [arXiv:1106.4551] [INSPIRE].ADSCrossRefGoogle Scholar
  60. [60]
    S.A. Hartnoll, P.K. Kovtun, M. Muller and S. Sachdev, Theory of the Nernst effect near quantum phase transitions in condensed matter and in dyonic black holes, Phys. Rev. B 76 (2007) 144502 [arXiv:0706.3215] [INSPIRE].ADSCrossRefGoogle Scholar
  61. [61]
    F.C. Adams, G. Laughlin, M. Mbonye and M.J. Perry, Gravitational demise of cold degenerate stars, Phys. Rev. D 58 (1998) 083003 [astro-ph/9808250] [INSPIRE].
  62. [62]
    J. Xiong et al., Anomalous conductivity tensor in the Dirac semimetal Na3Bi, Eur. Phys. Lett. 114 (2016) 27002.ADSCrossRefGoogle Scholar

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Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  1. 1.Institute of PhysicsMaria Curie-Sklodowska UniversityLublinPoland

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