Journal of High Energy Physics

, 2018:109 | Cite as

AC conductivities of a holographic Dirac semimetal

  • Gianluca Grignani
  • Andrea MariniEmail author
  • Lorenzo Papini
  • Adriano-Costantino Pigna
Open Access
Regular Article - Theoretical Physics


We use the AdS/CFT correspondence to compute the AC conductivities for a (2+1)-dimensional system of massless fundamental fermions coupled to (3+1)-dimensional Super Yang-Mills theory at strong coupling. We consider the system at finite charge density, with a constant electric field along the defect and an orthogonal magnetic field. The holographic model we employ is the well studied D3/probe-D5-brane system. There are two competing phases in this model: a phase with broken chiral symmetry favored when the magnetic field dominates over the charge density and the electric field and a chirally symmetric phase in the opposite regime. The presence of the electric field induces Ohm and Hall currents, which can be straightforwardly computed by means of the Karch-O’Bannon technique. Studying the fluctuations around the stable configurations in linear response theory, we are able to derive the full frequency dependence of longitudinal and Hall conductivities in all the regions of the phase space.


AdS-CFT Correspondence D-branes 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 [hep-th/9711200] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    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].CrossRefzbMATHGoogle Scholar
  3. [3]
    E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    J. Crossno et al., Observation of the Dirac fluid and the breakdown of the Wiedemann-Franz law in graphene, Science 351 (2016) 1058 [arXiv:1509.04713].CrossRefGoogle Scholar
  5. [5]
    R.V. Gorbachev et al., Strong Coulomb drag and broken symmetry in double-layer graphene, Nature Phys. 8 (2012) 896.CrossRefGoogle Scholar
  6. [6]
    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].CrossRefGoogle Scholar
  7. [7]
    M. Rogatko and K.I. Wysokinski, Two interacting current model of holographic Dirac fluid in graphene, Phys. Rev. D 97 (2018) 024053 [arXiv:1708.08051] [INSPIRE].Google Scholar
  8. [8]
    M. Rogatko and K.I. Wysokinski, Holographic calculation of the magneto-transport coefficients in Dirac semimetals, JHEP 01 (2018) 078 [arXiv:1712.01608] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    O. DeWolfe, D.Z. Freedman and H. Ooguri, Holography and defect conformal field theories, Phys. Rev. D 66 (2002) 025009 [hep-th/0111135] [INSPIRE].MathSciNetGoogle Scholar
  10. [10]
    A. Karch and L. Randall, Open and closed string interpretation of SUSY CFTs on branes with boundaries, JHEP 06 (2001) 063 [hep-th/0105132] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  11. [11]
    J. Erdmenger, Z. Guralnik and I. Kirsch, Four-dimensional superconformal theories with interacting boundaries or defects, Phys. Rev. D 66 (2002) 025020 [hep-th/0203020] [INSPIRE].MathSciNetGoogle Scholar
  12. [12]
    V.G. Filev, C.V. Johnson, R.C. Rashkov and K.S. Viswanathan, Flavoured large N gauge theory in an external magnetic field, JHEP 10 (2007) 019 [hep-th/0701001] [INSPIRE].CrossRefGoogle Scholar
  13. [13]
    V.G. Filev, C.V. Johnson and J.P. Shock, Universal Holographic Chiral Dynamics in an External Magnetic Field, JHEP 08 (2009) 013 [arXiv:0903.5345] [INSPIRE].CrossRefGoogle Scholar
  14. [14]
    N. Evans, A. Gebauer, K.-Y. Kim and M. Magou, Phase diagram of the D3/D5 system in a magnetic field and a BKT transition, Phys. Lett. B 698 (2011) 91 [arXiv:1003.2694] [INSPIRE].CrossRefGoogle Scholar
  15. [15]
    D.B. Kaplan, J.-W. Lee, D.T. Son and M.A. Stephanov, Conformality Lost, Phys. Rev. D 80 (2009) 125005 [arXiv:0905.4752] [INSPIRE].zbMATHGoogle Scholar
  16. [16]
    K. Jensen, A. Karch, D.T. Son and E.G. Thompson, Holographic Berezinskii-Kosterlitz-Thouless Transitions, Phys. Rev. Lett. 105 (2010) 041601 [arXiv:1002.3159] [INSPIRE].CrossRefGoogle Scholar
  17. [17]
    N. Evans and K.-Y. Kim, Vacuum alignment and phase structure of holographic bi-layers, Phys. Lett. B 728 (2014) 658 [arXiv:1311.0149] [INSPIRE].CrossRefzbMATHGoogle Scholar
  18. [18]
    G. Grignani, N. Kim, A. Marini and G.W. Semenoff, Holographic D3-probe-D5 Model of a Double Layer Dirac Semimetal, JHEP 12 (2014) 091 [arXiv:1410.4911] [INSPIRE].CrossRefGoogle Scholar
  19. [19]
    G. Grignani, A. Marini, A.-C. Pigna and G.W. Semenoff, Phase structure of a holographic double monolayer Dirac semimetal, JHEP 06 (2016) 141 [arXiv:1603.02583] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    A. Karch and A. O’Bannon, Metallic AdS/CFT, JHEP 09 (2007) 024 [arXiv:0705.3870] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  21. [21]
    N. Evans, K.-Y. Kim, J.P. Shock and J.P. Shock, Chiral phase transitions and quantum critical points of the D3/D7(D5) system with mutually perpendicular E and B fields at finite temperature and density, JHEP 09 (2011) 021 [arXiv:1107.5053] [INSPIRE].CrossRefzbMATHGoogle Scholar
  22. [22]
    S.A. Hartnoll, J. Polchinski, E. Silverstein and D. Tong, Towards strange metallic holography, JHEP 04 (2010) 120 [arXiv:0912.1061] [INSPIRE].CrossRefzbMATHGoogle Scholar
  23. [23]
    S.R. Das, T. Nishioka and T. Takayanagi, Probe Branes, Time-dependent Couplings and Thermalization in AdS/CFT, JHEP 07 (2010) 071 [arXiv:1005.3348] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  24. [24]
    A. O’Bannon, Hall Conductivity of Flavor Fields from AdS/CFT, Phys. Rev. D 76 (2007) 086007 [arXiv:0708.1994] [INSPIRE].Google Scholar
  25. [25]
    D. Mateos, R.C. Myers and R.M. Thomson, Holographic phase transitions with fundamental matter, Phys. Rev. Lett. 97 (2006) 091601 [hep-th/0605046] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  26. [26]
    S. Kobayashi, D. Mateos, S. Matsuura, R.C. Myers and R.M. Thomson, Holographic phase transitions at finite baryon density, JHEP 02 (2007) 016 [hep-th/0611099] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  27. [27]
    J. Mas, J.P. Shock, J. Tarrio and D. Zoakos, Holographic Spectral Functions at Finite Baryon Density, JHEP 09 (2008) 009 [arXiv:0805.2601] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  28. [28]
    K.-Y. Kim, J.P. Shock and J. Tarrio, The open string membrane paradigm with external electromagnetic fields, JHEP 06 (2011) 017 [arXiv:1103.4581] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  29. [29]
    N. Seiberg and E. Witten, String theory and noncommutative geometry, JHEP 09 (1999) 032 [hep-th/9908142] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  30. [30]
    G.W. Gibbons and C.A.R. Herdeiro, Born-Infeld theory and stringy causality, Phys. Rev. D 63 (2001) 064006 [hep-th/0008052] [INSPIRE].MathSciNetGoogle Scholar
  31. [31]
    S. Ryu, T. Takayanagi and T. Ugajin, Holographic Conductivity in Disordered Systems, JHEP 04 (2011) 115 [arXiv:1103.6068] [INSPIRE].CrossRefGoogle Scholar
  32. [32]
    C.-F. Chen and A. Lucas, Origin of the Drude peak and of zero sound in probe brane holography, Phys. Lett. B 774 (2017) 569 [arXiv:1709.01520] [INSPIRE].CrossRefzbMATHGoogle Scholar
  33. [33]
    S. Grozdanov, A. Lucas and N. Poovuttikul, Holography and hydrodynamics with weakly broken symmetries, arXiv:1810.10016 [INSPIRE].
  34. [34]
    S.A. Hartnoll, A. Lucas and S. Sachdev, Holographic quantum matter, arXiv:1612.07324 [INSPIRE].
  35. [35]
    P. Bøggild et al., Mapping the electrical properties of large-area graphene, 2D Materials 4 (2017) 042003.Google Scholar
  36. [36]
    J. Horng et al., Drude conductivity of Dirac fermions in graphene, Phys. Rev. B 83 (2011) 165113.CrossRefGoogle Scholar
  37. [37]
    S.A. Hartnoll and P. Kovtun, Hall conductivity from dyonic black holes, Phys. Rev. D 76 (2007) 066001 [arXiv:0704.1160] [INSPIRE].Google Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Dipartimento di Fisica e Geologia, Università di Perugia, I.N.F.N. Sezione di PerugiaPerugiaItaly
  2. 2.Dipartimento di Fisica e Astronomia “G. Galilei”, Università di Padova I.N.F.N. Sezione di PadovaPadovaItaly

Personalised recommendations