Optical conductivity with holographic lattices



We add a gravitational background lattice to the simplest holographic model of matter at finite density and calculate the optical conductivity. With the lattice, the zero frequency delta function found in previous calculations (resulting from translation invariance) is broadened and the DC conductivity is finite. The optical conductivity exhibits a Drude peak with a cross-over to power-law behavior at higher frequencies. Surprisingly, these results bear a strong resemblance to the properties of some of the cuprates.


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


  1. [1]
    S.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav. 26 (2009) 224002 [arXiv:0903.3246] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  2. [2]
    C.P. Herzog, Lectures on holographic superfluidity and superconductivity, J. Phys. A 42 (2009) 343001 [arXiv:0904.1975] [INSPIRE].Google Scholar
  3. [3]
    J. McGreevy, Holographic duality with a view toward many-body physics, Adv. High Energy Phys. 2010 (2010) 723105 [arXiv:0909.0518] [INSPIRE].Google Scholar
  4. [4]
    S. Sachdev, Condensed matter and AdS/CFT, arXiv:1002.2947 [INSPIRE].
  5. [5]
    S.A. Hartnoll, Horizons, holography and condensed matter, arXiv:1106.4324 [INSPIRE].
  6. [6]
    S. Kachru, A. Karch and S. Yaida, Holographic lattices, dimers and glasses, Phys. Rev. D 81 (2010) 026007 [arXiv:0909.2639] [INSPIRE].MathSciNetADSGoogle Scholar
  7. [7]
    S. Kachru, A. Karch and S. Yaida, Adventures in holographic dimer models, New J. Phys. 13 (2011) 035004 [arXiv:1009.3268] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    S. Hellerman, Lattice gauge theories have gravitational duals, hep-th/0207226 [INSPIRE].
  9. [9]
    A. Karch and A. O’Bannon, Metallic AdS/CFT, JHEP 09 (2007) 024 [arXiv:0705.3870] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  10. [10]
    T. Faulkner, N. Iqbal, H. Liu, J. McGreevy and D. Vegh, From black holes to strange metals, arXiv:1003.1728 [INSPIRE].
  11. [11]
    S.A. Hartnoll, J. Polchinski, E. Silverstein and D. Tong, Towards strange metallic holography, JHEP 04 (2010) 120 [arXiv:0912.1061] [INSPIRE].ADSCrossRefGoogle Scholar
  12. [12]
    D. van der Marel et al., Quantum critical behaviour in a high-T c superconductor, Nature 425 (2003) 271 [cond-mat/0309172].ADSCrossRefGoogle Scholar
  13. [13]
    S.A. Hartnoll and D.M. Hofman, Locally critical umklapp scattering and holography, arXiv:1201.3917 [INSPIRE].
  14. [14]
    M. Headrick, S. Kitchen and T. Wiseman, A new approach to static numerical relativity and its application to Kaluza-Klein black holes, Class. Quant. Grav. 27 (2010) 035002 [arXiv:0905.1822] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  15. [15]
    P. Figueras, J. Lucietti and T. Wiseman, Ricci solitons, Ricci flow and strongly coupled CFT in the Schwarzschild Unruh or Boulware vacua, Class. Quant. Grav. 28 (2011) 215018 [arXiv:1104.4489] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  16. [16]
    C.P. Herzog, P. Kovtun, S. Sachdev and D.T. Son, Quantum critical transport, duality and M-theory, Phys. Rev. D 75 (2007) 085020 [hep-th/0701036] [INSPIRE].MathSciNetADSGoogle Scholar
  17. [17]
    K. Damle and S. Sachdev, Nonzero-temperature transport near quantum critical points, Phys. Rev. B 56 (1997) 8714 [cond-mat/9705206].ADSGoogle Scholar
  18. [18]
    S. Sachdev, Nonzero-temperature transport near fractional quantum Hall critical points, Phys. Rev. B 57 (1998) 7157 [cond-mat/9709243].ADSGoogle Scholar
  19. [19]
    A. El. Azrak et. al., Infrared properties of YBa 2 Cu 3 O 7 and Bi 2 Sr 2 Ca n−1 Cu n O 2n+4 thin films, Phys. Rev. B 49 (1994) 9846.ADSGoogle Scholar
  20. [20]
    D. van der Marel, F. Carbone, A.B. Kuzmenko and E. Giannini, Scaling properties of the optical conductivity of Bi-based cuprates, Ann. Phys. 321 (2006) 1716 [cond-mat/0604037].ADSCrossRefGoogle Scholar
  21. [21]
    T. Kato and M. Imada, Thermodynamics and optical conductivity of a dissipative carrier in a tight binding model, J. Phys. Soc. Japan 67 (1998) 2828 [cond-mat/9711208].ADSCrossRefGoogle Scholar
  22. [22]
    P.W. Anderson, Infrared conductivity of cuprate metals: detailed fit using luttinger liquid theory, cond-mat/9506140.
  23. [23]
    M.R. Norman and A.V. Chubukov, High-frequency behavior of the infrared conductivity of cuprates, Phys. Rev. B 73 (2006) 140501 [cond-mat/0511584].ADSGoogle Scholar
  24. [24]
    M. Edalati, J.I. Jottar and R.G. Leigh, Holography and the sound of criticality, JHEP 10 (2010) 058 [arXiv:1005.4075] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    R. Flauger, E. Pajer and S. Papanikolaou, A striped holographic superconductor, Phys. Rev. D 83 (2011) 064009 [arXiv:1010.1775] [INSPIRE].ADSGoogle Scholar
  26. [26]
    K. Maeda, T. Okamura and J.-i. Koga, Inhomogeneous charged black hole solutions in asymptotically Anti-de Sitter spacetime, Phys. Rev. D 85 (2012) 066003 [arXiv:1107.3677] [INSPIRE].ADSGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2012

Authors and Affiliations

  • Gary T. Horowitz
    • 1
  • Jorge E. Santos
    • 1
  • David Tong
    • 2
  1. 1.Department of PhysicsUCSBSanta BarbaraUSA
  2. 2.DAMTPUniversity of CambridgeCambridgeUK

Personalised recommendations