Thermoelectric DC conductivities with momentum dissipation from higher derivative gravity

Open Access
Regular Article - Theoretical Physics

Abstract

We present a mechanism of momentum relaxation in higher derivative gravity by adding linear scalar fields to the Gauss-Bonnet theory. We analytically computed all of the DC thermoelectric conductivities in this theory by adopting the method given by Donos and Gauntlett in [arXiv:1406.4742]. The results show that the DC electric conductivity is not a monotonic function of the effective impurity parameter β: in the small β limit, the DC conductivity is dominated by the coherent phase, while for larger β, pair creation contribution to the conductivity becomes dominant, signaling an incoherent phase. In addition, the DC heat conductivity is found independent of the Gauss-Bonnet coupling constant.

Keywords

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

Notes

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.

References

  1. [1]
    S.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav. 26 (2009) 224002 [arXiv:0903.3246] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  2. [2]
    J. McGreevy, Holographic duality with a view toward many-body physics, Adv. High Energy Phys. 2010 (2010) 723105 [arXiv:0909.0518] [INSPIRE].CrossRefMATHGoogle Scholar
  3. [3]
    C.P. Herzog, Lectures on Holographic Superfluidity and Superconductivity, J. Phys. A 42 (2009) 343001 [arXiv:0904.1975] [INSPIRE].MathSciNetMATHGoogle Scholar
  4. [4]
    G.T. Horowitz, J.E. Santos and D. Tong, Optical conductivity with holographic lattices, JHEP 07 (2012) 168 [arXiv:1204.0519] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  5. [5]
    G.T. Horowitz, J.E. Santos and D. Tong, Further evidence for lattice-induced scaling, JHEP 11 (2012) 102 [arXiv:1209.1098] [INSPIRE].ADSCrossRefGoogle Scholar
  6. [6]
    G.T. Horowitz and J.E. Santos, General relativity and the cuprates, JHEP 06 (2013) 087 [arXiv:1302.6586] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  7. [7]
    A. Donos and S.A. Hartnoll, Interaction-driven localization in holography, Nature Phys. 9 (2013) 649 [arXiv:1212.2998] [INSPIRE].ADSCrossRefGoogle Scholar
  8. [8]
    J. Erdmenger, X.-H. Ge and D.-W. Pang, Striped phases in the holographic insulator/superconductor transition, JHEP 11 (2013) 027 [arXiv:1307.4609] [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    Y. Ling, C. Niu, J.-P. Wu and Z.-Y. Xian, Holographic lattice in Einstein-Maxwell-Dilaton gravity, JHEP 11 (2013) 006 [arXiv:1309.4580] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    Y. Ling, C. Niu, J. Wu, Z. Xian and H.-b. Zhang, Metal-insulator Transition by Holographic Charge Density Waves, Phys. Rev. Lett. 113 (2014) 091602 [arXiv:1404.0777] [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]
    Y. Ling, P. Liu, C. Niu, J.-P. Wu and Z.-Y. Xian, Holographic superconductor on Q-lattice, JHEP 02 (2015) 059 [arXiv:1410.6761] [INSPIRE].ADSCrossRefGoogle Scholar
  13. [13]
    D. Vegh, Holography without translational symmetry, arXiv:1301.0537 [INSPIRE].
  14. [14]
    B. Goutéraux, Charge transport in holography with momentum dissipation, JHEP 04 (2014) 181 [arXiv:1401.5436] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    R.A. Davison, Momentum relaxation in holographic massive gravity, Phys. Rev. D 88 (2013) 086003 [arXiv:1306.5792] [INSPIRE].ADSGoogle Scholar
  16. [16]
    M. Blake and D. Tong, Universal Resistivity from Holographic Massive Gravity, Phys. Rev. D 88 (2013) 106004 [arXiv:1308.4970] [INSPIRE].ADSGoogle Scholar
  17. [17]
    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
  18. [18]
    H.B. Zeng and J.-P. Wu, Holographic superconductors from the massive gravity, Phys. Rev. D 90 (2014) 046001 [arXiv:1404.5321] [INSPIRE].ADSGoogle Scholar
  19. [19]
    R.A. Davison, K. Schalm and J. Zaanen, Holographic duality and the resistivity of strange metals, Phys. Rev. B 89 (2014) 245116 [arXiv:1311.2451] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    M. Blake and A. Donos, Quantum Critical Transport and the Hall Angle, Phys. Rev. Lett. 114 (2015) 021601 [arXiv:1406.1659] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    T. Andrade and B. Withers, A simple holographic model of momentum relaxation, JHEP 05 (2014) 101 [arXiv:1311.5157] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    K.-Y. Kim, K.K. Kim, Y. Seo and S.-J. Sin, Coherent/incoherent metal transition in a holographic model, JHEP 12 (2014) 170 [arXiv:1409.8346] [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    A. Donos, B. Goutéraux and E. Kiritsis, Holographic Metals and Insulators with Helical Symmetry, JHEP 09 (2014) 038 [arXiv:1406.6351] [INSPIRE].ADSCrossRefGoogle Scholar
  24. [24]
    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
  25. [25]
    X.-H. Ge, Y. Ling, C. Niu and S.-J. Sin, Holographic transports and stability in anisotropic linear axion model, arXiv:1412.8346 [INSPIRE].
  26. [26]
    S. Nakamura, H. Ooguri and C.-S. Park, Gravity Dual of Spatially Modulated Phase, Phys. Rev. D 81 (2010) 044018 [arXiv:0911.0679] [INSPIRE].ADSGoogle Scholar
  27. [27]
    A. Donos and J.P. Gauntlett, Holographic striped phases, JHEP 08 (2011) 140 [arXiv:1106.2004] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  28. [28]
    A. Donos and J.P. Gauntlett, Novel metals and insulators from holography, JHEP 06 (2014) 007 [arXiv:1401.5077] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    A. Donos and J.P. Gauntlett, Thermoelectric DC conductivities from black hole horizons, JHEP 11 (2014) 081 [arXiv:1406.4742] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    A. Amoretti, A. Braggio, N. Maggiore, N. Magnoli and D. Musso, Analytic DC thermo-electric conductivities in holography with massive gravitons, Phys. Rev. D 91 (2015) 025002 [arXiv:1407.0306].ADSGoogle Scholar
  31. [31]
    A. Donos and J.P. Gauntlett, The thermoelectric properties of inhomogeneous holographic lattices, JHEP 01 (2015) 035 [arXiv:1409.6875] [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    R.-G. Cai, Gauss-Bonnet black holes in AdS spaces, Phys. Rev. D 65 (2002) 084014 [hep-th/0109133] [INSPIRE].ADSMathSciNetGoogle Scholar
  33. [33]
    M. Cvetič, S. Nojiri and S.D. Odintsov, Black hole thermodynamics and negative entropy in de Sitter and anti-de Sitter Einstein-Gauss-Bonnet gravity, Nucl. Phys. B 628 (2002) 295 [hep-th/0112045] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  34. [34]
    R.-G. Cai, Z.-Y. Nie and H.-Q. Zhang, Holographic p-wave superconductors from Gauss-Bonnet gravity, Phys. Rev. D 82 (2010) 066007 [arXiv:1007.3321] [INSPIRE].ADSGoogle Scholar
  35. [35]
    L. Barclay, R. Gregory, S. Kanno and P. Sutcliffe, Gauss-Bonnet holographic superconductors, JHEP 12 (2010) 029 [arXiv:1009.1991] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  36. [36]
    J. Jing, L. Wang, Q. Pan and S. Chen, Holographic Superconductors in Gauss-Bonnet gravity with Born-Infeld electrodynamics, Phys. Rev. D 83 (2011) 066010 [arXiv:1012.0644] [INSPIRE].ADSGoogle Scholar
  37. [37]
    Q. Pan, J. Jing and B. Wang, Analytical investigation of the phase transition between holographic insulator and superconductor in Gauss-Bonnet gravity, JHEP 11 (2011) 088 [arXiv:1105.6153] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  38. [38]
    D. Mateos and D. Trancanelli, Thermodynamics and instabilities of a strongly coupled anisotropic plasma, JHEP 07 (2011) 054 [arXiv:1106.1637] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  39. [39]
    L. Cheng, X.-H. Ge and S.-J. Sin, Anisotropic plasma with a chemical potential and scheme-independent instabilities, Phys. Lett. B 734 (2014) 116 [arXiv:1404.1994] [INSPIRE].ADSCrossRefGoogle Scholar
  40. [40]
    L. Cheng, X.-H. Ge and S.-J. Sin, Anisotropic plasma at finite U(1) chemical potential, JHEP 07 (2014) 083 [arXiv:1404.5027] [INSPIRE].ADSCrossRefGoogle Scholar
  41. [41]
    V. Jahnke, A.S. Misobuchi and D. Trancanelli, Holographic renormalization and anisotropic black branes in higher curvature gravity, JHEP 01 (2015) 122 [arXiv:1411.5964] [INSPIRE].ADSCrossRefGoogle Scholar
  42. [42]
    L.Q. Fang, X.-H. Ge, J.-P. Wu and H.-Q. Leng, Anisotropic Fermi surface from holography, arXiv:1409.6062 [INSPIRE].
  43. [43]
    S. Carroll, Spacetime and Geometry, Addision-Wesley, Reading U.S.A. (2004).MATHGoogle Scholar
  44. [44]
    X.-H. Ge, Y. Ling, Y. Tian and X.-N. Wu, Holographic RG flows and transport coefficients in Einstein-Gauss-Bonnet-Maxwell theory, JHEP 01 (2012) 117 [arXiv:1112.0627] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  45. [45]
    D. Tong, Lectures on holographic conductivity, talk presented at Cracow school of theoretical Physics, Cracow Poland (2013), http://www.damtp.cam.ac.uk/user/tong/talks/zakopane.pdf.
  46. [46]
    M. Brigante, H. Liu, R.C. Myers, S. Shenker and S. Yaida, Viscosity Bound Violation in Higher Derivative Gravity, Phys. Rev. D 77 (2008) 126006 [arXiv:0712.0805] [INSPIRE].ADSGoogle Scholar
  47. [47]
    X.-H. Ge and S.-J. Sin, Shear viscosity, instability and the upper bound of the Gauss-Bonnet coupling constant, JHEP 05 (2009) 051 [arXiv:0903.2527] [INSPIRE].ADSCrossRefGoogle Scholar
  48. [48]
    R.-G. Cai, Z.-Y. Nie and Y.-W. Sun, Shear Viscosity from Effective Couplings of Gravitons, Phys. Rev. D 78 (2008) 126007 [arXiv:0811.1665] [INSPIRE].ADSGoogle Scholar
  49. [49]
    X.-H. Ge, S.-J. Sin, S.-F. Wu and G.-H. Yang, Shear viscosity and instability from third order Lovelock gravity, Phys. Rev. D 80 (2009) 104019 [arXiv:0905.2675] [INSPIRE].ADSGoogle Scholar
  50. [50]
    R.C. Myers, M.F. Paulos and A. Sinha, Holographic hydrodynamics with a chemical potential, JHEP 06 (2009) 006 [arXiv:0903.2834] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  51. [51]
    X.-H. Ge, Y. Matsuo, F.-W. Shu, S.-J. Sin and T. Tsukioka, Viscosity bound, causality violation and instability with stringy correction and charge, JHEP 10 (2008) 009 [arXiv:0808.2354] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  52. [52]
    A. Bhattacharyya and D. Roychowdhury, Viscosity bound for anisotropic superfluids in higher derivative gravity, JHEP 03 (2015) 063 [arXiv:1410.3222] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  53. [53]
    L.K. Joshi and P. Ramadevi, Backreaction effects due to matter coupled higher derivative gravity, arXiv:1409.8019 [INSPIRE].
  54. [54]
    V. Balasubramanian and P. Kraus, A stress tensor for Anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  55. [55]
    Y. Brihaye and E. Radu, Black objects in the Einstein-Gauss-Bonnet theory with negative cosmological constant and the boundary counterterm method, JHEP 09 (2008) 006 [arXiv:0806.1396] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  56. [56]
    J.T. Liu and W.A. Sabra, Hamilton-Jacobi Counterterms for Einstein-Gauss-Bonnet Gravity, Class. Quant. Grav. 27 (2010) 175014 [arXiv:0807.1256] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar

Copyright information

© The Author(s) 2015

Authors and Affiliations

  1. 1.Institute of Theoretical Physics and Shanghai Key Laboratory of High Temperature Superconductors, Department of PhysicsShanghai UniversityShanghaiChina
  2. 2.College of Arts and SciencesShanghai Maritime UniversityShanghaiChina

Personalised recommendations