Journal of High Energy Physics

, 2016:107 | Cite as

On effective holographic Mott insulators

  • Matteo BaggioliEmail author
  • Oriol Pujolàs
Open Access
Regular Article - Theoretical Physics


We present a class of holographic models that behave effectively as prototypes of Mott insulators — materials where electron-electron interactions dominate transport phenomena. The main ingredient in the gravity dual is that the gauge-field dynamics contains self-interactions by way of a particular type of non-linear electrodynamics. The electrical response in these models exhibits typical features of Mott-like states: i) the low-temperature DC conductivity is unboundedly low; ii) metal-insulator transitions appear by varying various parameters; iii) for large enough self-interaction strength, the conductivity can even decrease with increasing doping (density of carriers) — which appears as a sharp manifestation of ‘traffic-jam’-like behaviour; iv) the insulating state becomes very unstable towards superconductivity at large enough doping. We exhibit some of the properties of the resulting insulator-superconductor transition, which is sensitive to the momentum dissipation rate in a specific way. These models imply a clear and generic correlation between Mott behaviour and significant effects in the nonlinear electrical response. We compute the nonlinear current-voltage curve in our model and find that indeed at large voltage the conductivity is largely reduced.


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


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]
    V. Dobrosavljevic, Introduction to Metal-Insulator Transitions, arXiv:1112.6166.
  2. [2]
    E. Abrahams, S.V. Kravchenko and M.P. Sarachik, Metallic behavior and related phenomena in two dimensions, Rev. Mod. Phys. 73 (2001) 251 [cond-mat/0006055].
  3. [3]
    M. Imada, A. Fujimori and Y. Tokura, Metal-insulator transitions, Rev. Mod. Phys. 70 (1998) 1039.ADSCrossRefGoogle Scholar
  4. [4]
    D. Vollhardt, K. Byczuk and M. Kollar, Dynamical Mean-Field Theory, arXiv:1109.4833.
  5. [5]
    P.A. Lee, N. Nagaosa and X.-G. Wen, Doping a Mott insulator: Physics of high-temperature superconductivity, Rev. Mod. Phys. 78 (2006) 17 [INSPIRE].ADSCrossRefGoogle Scholar
  6. [6]
    N.F. Mott, Metal-Insulator Transition, Rev. Mod. Phys. 40 (1968) 677 [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    F. Gebhard, The Mott Metal-Insulator Transition: Models and Methods, Springer Tracts in Modern Physics, Springer, Berlin Germany (1997).Google Scholar
  8. [8]
    P.W. Phillips, Mottness cond-mat/0702348.
  9. [9]
    T. Andrade and B. Withers, A simple holographic model of momentum relaxation, JHEP 05 (2014) 101 [arXiv:1311.5157] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    M. Baggioli and O. Pujolàs, Electron-Phonon Interactions, Metal-Insulator Transitions and Holographic Massive Gravity, Phys. Rev. Lett. 114 (2015) 251602 [arXiv:1411.1003] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    T. Andrade, S.A. Gentle and B. Withers, Drude in D major, JHEP 06 (2016) 134 [arXiv:1512.06263] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  12. [12]
    T. Andrade, A simple model of momentum relaxation in Lifshitz holography, arXiv:1602.00556 [INSPIRE].
  13. [13]
    M. Taylor and W. Woodhead, Inhomogeneity simplified, Eur. Phys. J. C 74 (2014) 3176 [arXiv:1406.4870] [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    V.A. Rubakov and P.G. Tinyakov, Infrared-modified gravities and massive gravitons, Phys. Usp. 51 (2008) 759 [arXiv:0802.4379] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    D. Vegh, Holography without translational symmetry, arXiv:1301.0537 [INSPIRE].
  16. [16]
    R.A. Davison, Momentum relaxation in holographic massive gravity, Phys. Rev. D 88 (2013) 086003 [arXiv:1306.5792] [INSPIRE].ADSGoogle Scholar
  17. [17]
    L. Alberte, M. Baggioli, A. Khmelnitsky and O. Pujolàs, Solid Holography and Massive Gravity, JHEP 02 (2016) 114 [arXiv:1510.09089] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  18. [18]
    M. Baggioli and D.K. Brattan, Drag phenomena from holographic massive gravity, Class. Quant. Grav. 34 (2017) 015008 [arXiv:1504.07635] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    M. Baggioli and O. Pujolàs, On holographic disorder-driven metal-insulator transitions, arXiv:1601.07897 [INSPIRE].
  20. [20]
    B. Goutéraux, E. Kiritsis and W.-J. Li, Effective holographic theories of momentum relaxation and violation of conductivity bound, JHEP 04 (2016) 122 [arXiv:1602.01067] [INSPIRE].ADSGoogle Scholar
  21. [21]
    S.S. Gubser, Curvature singularities: The Good, the bad and the naked, Adv. Theor. Math. Phys. 4 (2000) 679 [hep-th/0002160] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  22. [22]
    S. Grozdanov, A. Lucas, S. Sachdev and K. Schalm, Absence of disorder-driven metal-insulator transitions in simple holographic models, Phys. Rev. Lett. 115 (2015) 221601 [arXiv:1507.00003] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    M. Edalati, R.G. Leigh and P.W. Phillips, Dynamically Generated Mott Gap from Holography, Phys. Rev. Lett. 106 (2011) 091602 [arXiv:1010.3238] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    M. Edalati, R.G. Leigh, K.W. Lo and P.W. Phillips, Dynamical Gap and Cuprate-like Physics from Holography, Phys. Rev. D 83 (2011) 046012 [arXiv:1012.3751] [INSPIRE].ADSGoogle Scholar
  25. [25]
    J.-P. Wu and H.-B. Zeng, Dynamic gap from holographic fermions in charged dilaton black branes, JHEP 04 (2012) 068 [arXiv:1201.2485] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    Y. Ling, P. Liu, C. Niu, J.-P. Wu and Z.-Y. Xian, Holographic fermionic system with dipole coupling on Q-lattice, JHEP 12 (2014) 149 [arXiv:1410.7323] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    M. Fujita, S. Harrison, A. Karch, R. Meyer and N.M. Paquette, Towards a Holographic Bose-Hubbard Model, JHEP 04 (2015) 068 [arXiv:1411.7899] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  28. [28]
    Y. Ling, P. Liu, C. Niu and J.-P. Wu, Building a doped Mott system by holography, Phys. Rev. D 92 (2015) 086003 [arXiv:1507.02514] [INSPIRE].ADSGoogle Scholar
  29. [29]
    T. Nishioka, S. Ryu and T. Takayanagi, Holographic Superconductor/Insulator Transition at Zero Temperature, JHEP 03 (2010) 131 [arXiv:0911.0962] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  30. [30]
    E. Kiritsis and J. Ren, On Holographic Insulators and Supersolids, JHEP 09 (2015) 168 [arXiv:1503.03481] [INSPIRE].ADSCrossRefGoogle Scholar
  31. [31]
    A. Donos and S.A. Hartnoll, Interaction-driven localization in holography, Nature Phys. 9 (2013) 649 [arXiv:1212.2998] [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    A. Donos and J.P. Gauntlett, Holographic Q-lattices, JHEP 04 (2014) 040 [arXiv:1311.3292] [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    A. Donos and J.P. Gauntlett, Novel metals and insulators from holography, JHEP 06 (2014) 007 [arXiv:1401.5077] [INSPIRE].ADSCrossRefGoogle Scholar
  34. [34]
    M. Rangamani, M. Rozali and D. Smyth, Spatial Modulation and Conductivities in Effective Holographic Theories, JHEP 07 (2015) 024 [arXiv:1505.05171] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  35. [35]
    R.C. Myers, S. Sachdev and A. Singh, Holographic Quantum Critical Transport without Self-Duality, Phys. Rev. D 83 (2011) 066017 [arXiv:1010.0443] [INSPIRE].ADSGoogle Scholar
  36. [36]
    T.N. Ikeda, A. Lucas and Y. Nakai, Conductivity bounds in probe brane models, JHEP 04 (2016) 007 [arXiv:1601.07882] [INSPIRE].ADSMathSciNetGoogle Scholar
  37. [37]
    M. Blake, Universal Charge Diffusion and the Butterfly Effect in Holographic Theories, Phys. Rev. Lett. 117 (2016) 091601 [arXiv:1603.08510] [INSPIRE].ADSCrossRefGoogle Scholar
  38. [38]
    M. Blake, Universal Diffusion in Incoherent Black Holes, Phys. Rev. D 94 (2016) 086014 [arXiv:1604.01754] [INSPIRE].ADSGoogle Scholar
  39. [39]
    S.A. Hartnoll, Theory of universal incoherent metallic transport, Nature Phys. 11 (2015) 54 [arXiv:1405.3651] [INSPIRE].ADSCrossRefGoogle Scholar
  40. [40]
    A. Amoretti, A. Braggio, N. Magnoli and D. Musso, Bounds on charge and heat diffusivities in momentum dissipating holography, JHEP 07 (2015) 102 [arXiv:1411.6631] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  41. [41]
    X.-H. Ge, S.-J. Sin and S.-F. Wu, Lower Bound of Electrical Conductivity from Holography, arXiv:1512.01917 [INSPIRE].
  42. [42]
    L. Alberte, M. Baggioli and O. Pujolàs, Viscosity bound violation in holographic solids and the viscoelastic response, JHEP 07 (2016) 074 [arXiv:1601.03384] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  43. [43]
    P. Burikham and N. Poovuttikul, Shear viscosity in holography and effective theory of transport without translational symmetry, Phys. Rev. D 94 (2016) 106001 [arXiv:1601.04624] [INSPIRE].ADSGoogle Scholar
  44. [44]
    S.A. Hartnoll, D.M. Ramirez and J.E. Santos, Entropy production, viscosity bounds and bumpy black holes, JHEP 03 (2016) 170 [arXiv:1601.02757] [INSPIRE].ADSCrossRefGoogle Scholar
  45. [45]
    S. Grozdanov, A. Lucas and K. Schalm, Incoherent thermal transport from dirty black holes, Phys. Rev. D 93 (2016) 061901 [arXiv:1511.05970] [INSPIRE].ADSMathSciNetGoogle Scholar
  46. [46]
    G.W. Gibbons and D.A. Rasheed, SL(2, ) invariance of nonlinear electrodynamics coupled to an axion and a dilaton, Phys. Lett. B 365 (1996) 46 [hep-th/9509141] [INSPIRE].ADSCrossRefGoogle Scholar
  47. [47]
    G.W. Gibbons and D.A. Rasheed, Electric-magnetic duality rotations in nonlinear electrodynamics, Nucl. Phys. B 454 (1995) 185 [hep-th/9506035] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  48. [48]
    A. Karch and A. O’Bannon, Metallic AdS/CFT, JHEP 09 (2007) 024 [arXiv:0705.3870] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  49. [49]
    P.C. West, Automorphisms, nonlinear realizations and branes, JHEP 02 (2000) 024 [hep-th/0001216] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  50. [50]
    F. Gliozzi, Dirac-Born-Infeld action from spontaneous breakdown of Lorentz symmetry in brane-world scenarios, Phys. Rev. D 84 (2011) 027702 [arXiv:1103.5377] [INSPIRE].ADSGoogle Scholar
  51. [51]
    A. Adams, N. Arkani-Hamed, S. Dubovsky, A. Nicolis and R. Rattazzi, Causality, analyticity and an IR obstruction to UV completion, JHEP 10 (2006) 014 [hep-th/0602178] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  52. [52]
    F. Nogueira and J.B. Stang, Density versus chemical potential in holographic field theories, Phys. Rev. D 86 (2012) 026001 [arXiv:1111.2806] [INSPIRE].ADSGoogle Scholar
  53. [53]
    A. Karch and S.L. Sondhi, Non-linear, Finite Frequency Quantum Critical Transport from AdS/CFT, JHEP 01 (2011) 149 [arXiv:1008.4134] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  54. [54]
    J. Sonner and A.G. Green, Hawking Radiation and Non-equilibrium Quantum Critical Current Noise, Phys. Rev. Lett. 109 (2012) 091601 [arXiv:1203.4908] [INSPIRE].ADSCrossRefGoogle Scholar
  55. [55]
    G.T. Horowitz, N. Iqbal and J.E. Santos, Simple holographic model of nonlinear conductivity, Phys. Rev. D 88 (2013) 126002 [arXiv:1309.5088] [INSPIRE].ADSGoogle Scholar
  56. [56]
    S. Gopalakrishnan, M. Mueller, V. Khemani, M. Knap, E. Demler and D.A. Huse, Low-frequency conductivity in many-body localized systems, Phys. Rev. B 92 (2015) 104202 [arXiv:1502.07712].ADSCrossRefGoogle Scholar
  57. [57]
    J. Jing, Q. Pan and S. Chen, Holographic Superconductor/Insulator Transition with logarithmic electromagnetic field in Gauss-Bonnet gravity, Phys. Lett. B 716 (2012) 385 [arXiv:1209.0893] [INSPIRE].ADSCrossRefGoogle Scholar
  58. [58]
    R.A. Davison and B. Goutéraux, Momentum dissipation and effective theories of coherent and incoherent transport, JHEP 01 (2015) 039 [arXiv:1411.1062] [INSPIRE].ADSCrossRefGoogle Scholar
  59. [59]
    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
  60. [60]
    S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Holographic Superconductors, JHEP 12 (2008) 015 [arXiv:0810.1563] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  61. [61]
    M. Baggioli and M. Goykhman, Phases of holographic superconductors with broken translational symmetry, JHEP 07 (2015) 035 [arXiv:1504.05561] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  62. [62]
    E. Kiritsis and L. Li, Holographic Competition of Phases and Superconductivity, JHEP 01 (2016) 147 [arXiv:1510.00020] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  63. [63]
    M. Baggioli and M. Goykhman, Under The Dome: Doped holographic superconductors with broken translational symmetry, JHEP 01 (2016) 011 [arXiv:1510.06363] [INSPIRE].ADSCrossRefGoogle Scholar
  64. [64]
    J.-W. Chen, S.-H. Dai, D. Maity and Y.-L. Zhang, Engineering holographic phase diagrams, Phys. Rev. D 94 (2016) 086004 [arXiv:1603.08259] [INSPIRE].ADSGoogle Scholar
  65. [65]
    F. Rullier-Albenque1, H. Alloul, F. Balakirev and C. Proust, Disorder, metal-insulator crossover and phase diagram in high-Tc cuprates, EPL 81 (2008) 37008.Google Scholar
  66. [66]
    W. Ebeling, D. Blaschke, R. Redmer, H. Reinholz and G. Ropke, The Influence of Pauli blocking effects on the properties of dense hydrogen, J. Phys. A 42 (2009) 214033 [arXiv:0810.3336] [INSPIRE].ADSzbMATHGoogle Scholar
  67. [67]
    S. Gangopadhyay and D. Roychowdhury, Analytic study of properties of holographic superconductors in Born-Infeld electrodynamics, JHEP 05 (2012) 002 [arXiv:1201.6520] [INSPIRE].ADSCrossRefGoogle Scholar
  68. [68]
    A. Amoretti, M. Baggioli, N. Magnoli and D. Musso, Chasing the cuprates with dilatonic dyons, JHEP 06 (2016) 113 [arXiv:1603.03029] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  69. [69]
    Z.Q. Liu et al., Nonlinear Insulator in Complex Oxides, Phys. Rev. B 84 (2010) 165106 [arXiv:1011.2629].ADSGoogle Scholar
  70. [70]
    H. Kishida et al., Gigantic optical nonlinearity in one-dimensional Mott d Hubbard insulators, Nature 405 (2000) 929.ADSCrossRefGoogle Scholar
  71. [71]
    Y. Takahide et al., Highly nonlinear current-voltage characteristics of the organic Mott insulator κ − (BEDTT T F )2 Cu[N (CN )2]Cl, Phys. Rev. B 84 (2011) 035129.ADSCrossRefGoogle Scholar
  72. [72]
    D.V. Khveshchenko, Demystifying the Holographic Mystique, Lith. J. Phys. 56 (2016) 125 [arXiv:1603.09741] [INSPIRE].CrossRefGoogle Scholar
  73. [73]
    M. Kulaxizi and R. Rahman, Fermion Dipole Moment and Holography, JHEP 12 (2015) 146 [arXiv:1507.08284] [INSPIRE].ADSMathSciNetGoogle Scholar
  74. [74]
    S.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav. 26 (2009) 224002 [arXiv:0903.3246] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  75. [75]
    H. Kodama and A. Ishibashi, Master equations for perturbations of generalized static black holes with charge in higher dimensions, Prog. Theor. Phys. 111 (2004) 29 [hep-th/0308128] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  76. [76]
    M. Blake and D. Tong, Universal Resistivity from Holographic Massive Gravity, Phys. Rev. D 88 (2013) 106004 [arXiv:1308.4970] [INSPIRE].ADSGoogle Scholar
  77. [77]
    A. Donos and J.P. Gauntlett, Thermoelectric DC conductivities from black hole horizons, JHEP 11 (2014) 081 [arXiv:1406.4742] [INSPIRE].ADSCrossRefGoogle Scholar
  78. [78]
    D.A. Roberts and B. Swingle, Lieb-Robinson Bound and the Butterfly Effect in Quantum Field Theories, Phys. Rev. Lett. 117 (2016) 091602 [arXiv:1603.09298] [INSPIRE].ADSCrossRefGoogle Scholar
  79. [79]
    M. Baggioli, O. Pujolas, S. Renaux-Petel and K. Yang, in preparation.Google Scholar

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© The Author(s) 2016

Authors and Affiliations

  1. 1.Institut de Física d’Altes Energies (IFAE)Universitat Autònoma de Barcelona, The Barcelona Institute of Science and TechnologyBellaterra (Barcelonav)Spain

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