Friedel oscillations in holographic metals

  • V. Giangreco M. Puletti
  • S. Nowling
  • L. Thorlacius
  • T. Zingg


In this article we study the conditions under which holographic metallic states display Friedel oscillations. We focus on systems where the bulk charge density is not hidden behind a black hole horizon. Understanding holographic Friedel oscillations gives a clean way to characterize the boundary system, complementary to probe fermion calculations. We find that fermions in a “hard wall” AdS geometry unambiguously display Friedel oscillations. However, similar oscillations are washed out for electron stars, suggesting a smeared continuum of Fermi surfaces.


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


  1. [1]
    S.A. Hartnoll, Horizons, holography and condensed matter, arXiv:1106.4324 [INSPIRE].
  2. [2]
    S. Sachdev, What can gauge-gravity duality teach us about condensed matter physics?, arXiv:1108.1197 [INSPIRE].
  3. [3]
    N. Iqbal, H. Liu and M. Mezei, Lectures on holographic non-Fermi liquids and quantum phase transitions, arXiv:1110.3814 [INSPIRE].
  4. [4]
    J. Polchinski, Effective field theory and the Fermi surface, hep-th/9210046 [INSPIRE].
  5. [5]
    R. Shankar, Renormalization-group approach to interacting fermions, Rev. Mod. Phys. 66 (1994) 129 [cond-mat/9307009].MathSciNetADSCrossRefGoogle Scholar
  6. [6]
    S.-S. Lee, Low-energy effective theory of Fermi surface coupled with U(1) gauge field in 2 + 1 dimensions, Phys. Rev. B 80 (2009) 165102 [arXiv:0905.4532].ADSGoogle Scholar
  7. [7]
    M.A. Metlitski and S. Sachdev, Quantum phase transitions of metals in two spatial dimensions: I. Ising-nematic order, Phys. Rev. B 82 (2010) 075127 [arXiv:1001.1153] [INSPIRE].ADSGoogle Scholar
  8. [8]
    M.A. Metlitski and S. Sachdev, Quantum phase transitions of metals in two spatial dimensions: II. Spin density wave order, Phys. Rev. B 82 (2010) 075128 [arXiv:1005.1288] [INSPIRE].ADSGoogle Scholar
  9. [9]
    S.-S. Lee, A non-Fermi liquid from a charged black hole: a critical Fermi ball, Phys. Rev. D 79 (2009) 086006 [arXiv:0809.3402] [INSPIRE].ADSGoogle Scholar
  10. [10]
    H. Liu, J. McGreevy and D. Vegh, Non-Fermi liquids from holography, Phys. Rev. D 83 (2011) 065029 [arXiv:0903.2477] [INSPIRE].ADSGoogle Scholar
  11. [11]
    T. Faulkner, H. Liu, J. McGreevy and D. Vegh, Emergent quantum criticality, Fermi surfaces and AdS 2, Phys. Rev. D 83 (2011) 125002 [arXiv:0907.2694] [INSPIRE].ADSGoogle Scholar
  12. [12]
    M. Cubrovic, J. Zaanen and K. Schalm, String theory, quantum phase transitions and the emergent Fermi-liquid, Science 325 (2009) 439 [arXiv:0904.1993] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  13. [13]
    F. Denef, S.A. Hartnoll and S. Sachdev, Quantum oscillations and black hole ringing, Phys. Rev. D 80 (2009) 126016 [arXiv:0908.1788] [INSPIRE].ADSGoogle Scholar
  14. [14]
    S.A. Hartnoll, J. Polchinski, E. Silverstein and D. Tong, Towards strange metallic holography, JHEP 04 (2010) 120 [arXiv:0912.1061] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    T. Faulkner and J. Polchinski, Semi-holographic Fermi liquids, JHEP 06 (2011) 012 [arXiv:1001.5049] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  16. [16]
    S. Sachdev, Holographic metals and the fractionalized Fermi liquid, Phys. Rev. Lett. 105 (2010) 151602 [arXiv:1006.3794] [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    S.A. Hartnoll and A. Tavanfar, Electron stars for holographic metallic criticality, Phys. Rev. D 83 (2011) 046003 [arXiv:1008.2828] [INSPIRE].ADSGoogle Scholar
  18. [18]
    M. Cubrovic, J. Zaanen and K. Schalm, Constructing the AdS dual of a Fermi liquid: AdS black holes with Dirac hair, JHEP 10 (2011) 017 [arXiv:1012.5681] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    S.A. Hartnoll, D.M. Hofman and A. Tavanfar, Holographically smeared Fermi surface: quantum oscillations and Luttinger count in electron stars, Europhys. Lett. 95 (2011) 31002 [arXiv:1011.2502] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    N. Iizuka, N. Kundu, P. Narayan and S.P. Trivedi, Holographic Fermi and non-Fermi liquids with transitions in dilaton gravity, arXiv:1105.1162 [INSPIRE].
  21. [21]
    S.A. Hartnoll, D.M. Hofman and D. Vegh, Stellar spectroscopy: fermions and holographic Lifshitz criticality, JHEP 08 (2011) 096 [arXiv:1105.3197] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    X. Arsiwalla, J. de Boer, K. Papadodimas and E. Verlinde, Degenerate stars and gravitational collapse in AdS/CFT, JHEP 01 (2011) 144 [arXiv:1010.5784] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    M. Cubrovic, Y. Liu, K. Schalm, Y.-W. Sun and J. Zaanen, Spectral probes of the holographic Fermi groundstate: dialing between the electron star and AdS Dirac hair, Phys. Rev. D 84 (2011) 086002 [arXiv:1106.1798] [INSPIRE].ADSGoogle Scholar
  24. [24]
    M. Edalati, K.W. Lo and P.W. Phillips, Neutral order parameters in metallic criticality in d = 2 + 1 from a hairy electron star, Phys. Rev. D 84 (2011) 066007 [arXiv:1106.3139] [INSPIRE].ADSGoogle Scholar
  25. [25]
    S. Sachdev, A model of a Fermi liquid using gauge-gravity duality, Phys. Rev. D 84 (2011) 066009 [arXiv:1107.5321] [INSPIRE].ADSGoogle Scholar
  26. [26]
    V.G.M. Puletti, S. Nowling, L. Thorlacius and T. Zingg, Holographic metals at finite temperature, JHEP 01 (2011) 117 [arXiv:1011.6261] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    S.A. Hartnoll and P. Petrov, Electron star birth: a continuous phase transition at nonzero density, Phys. Rev. Lett. 106 (2011) 121601 [arXiv:1011.6469] [INSPIRE].ADSCrossRefGoogle Scholar
  28. [28]
    M. Kulaxizi and A. Parnachev, Holographic responses of fermion matter, Nucl. Phys. B 815 (2009) 125 [arXiv:0811.2262] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  29. [29]
    S. Powell, S. Sachdev and H.P. Büchler, Depletion of the Bose-Einstein condensate in Bose-Fermi mixtures, Phys. Rev. B 72 (2005) 024534 [cond-mat/0502299].ADSGoogle Scholar
  30. [30]
    J.I. Kapusta and C. Gale, Finite-temperature field theory: principles and applications, Cambridge University Press, Cambridge U.K. (2006) [INSPIRE].zbMATHCrossRefGoogle Scholar
  31. [31]
    A.L. Fetter and J.D. Walecka, Quantum theory of many-particle systems, Dover Publications, New York U.S.A. (2003).Google Scholar
  32. [32]
    J. Erlich, E. Katz, D.T. Son and M.A. Stephanov, QCD and a holographic model of hadrons, Phys. Rev. Lett. 95 (2005) 261602 [hep-ph/0501128] [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    E. Witten, Anti-de Sitter space, thermal phase transition and confinement in gauge theories, Adv. Theor. Math. Phys. 2 (1998) 505 [hep-th/9803131] [INSPIRE].MathSciNetzbMATHGoogle Scholar
  34. [34]
    L. Huijse and S. Sachdev, Fermi surfaces and gauge-gravity duality, Phys. Rev. D 84 (2011) 026001 [arXiv:1104.5022] [INSPIRE].ADSGoogle Scholar
  35. [35]
    M. Edalati, J.I. Jottar and R.G. Leigh, Shear modes, criticality and extremal black holes, JHEP 04 (2010) 075 [arXiv:1001.0779] [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  36. [36]
    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
  37. [37]
    J.I. Kapusta and T. Toimela, Friedel oscillations in relativistic QED and QCD, Phys. Rev. D 37 (1988) 3731 [INSPIRE].ADSGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2012

Authors and Affiliations

  • V. Giangreco M. Puletti
    • 1
  • S. Nowling
    • 2
  • L. Thorlacius
    • 2
    • 3
  • T. Zingg
    • 2
    • 3
  1. 1.Department of Fundamental PhysicsChalmers University of TechnologyGöteborgSweden
  2. 2.NorditaStockholmSweden
  3. 3.Science InstituteUniversity of IcelandReykjavikIceland

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