Advertisement

Incoherent transport for phases that spontaneously break translations

  • Aristomenis Donos
  • Jerome P. Gauntlett
  • Tom Griffin
  • Vaios Ziogas
Open Access
Regular Article - Theoretical Physics
  • 61 Downloads

Abstract

We consider phases of matter at finite charge density which spontaneously break spatial translations. Without taking a hydrodynamic limit we identify a boost invariant incoherent current operator. We also derive expressions for the small frequency behaviour of the thermoelectric conductivities generalising those that have been derived in a translationally invariant context. Within holographic constructions we show that the DC conductivity for the incoherent current can be obtained from a solution to a Stokes flow for an auxiliary fluid on the black hole horizon combined with specific thermodynamic quantities associated with the equilibrium black hole solutions.

Keywords

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

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]
    R.A. Davison, B. Goutéraux and S.A. Hartnoll, Incoherent transport in clean quantum critical metals, JHEP 10 (2015) 112 [arXiv:1507.07137] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  2. [2]
    R.A. Davison and B. Goutéraux, Dissecting holographic conductivities, JHEP 09 (2015) 090 [arXiv:1505.05092] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  3. [3]
    S.A. Hartnoll, P.K. Kovtun, M. Muller and S. Sachdev, Theory of the Nernst effect near quantum phase transitions in condensed matter and in dyonic black holes, Phys. Rev. B 76 (2007) 144502 [arXiv:0706.3215] [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    A. Donos and J.P. Gauntlett, Navier-Stokes Equations on Black Hole Horizons and DC Thermoelectric Conductivity, Phys. Rev. D 92 (2015) 121901 [arXiv:1506.01360] [INSPIRE].ADSGoogle Scholar
  5. [5]
    A. Donos and J.P. Gauntlett, On the thermodynamics of periodic AdS black branes, JHEP 10 (2013) 038 [arXiv:1306.4937] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    A. Donos and J.P. Gauntlett, Minimally packed phases in holography, JHEP 03 (2016) 148 [arXiv:1512.06861] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  7. [7]
    A. Amoretti, D. Areán, B. Goutéraux and D. Musso, Effective holographic theory of charge density waves, arXiv:1711.06610 [INSPIRE].
  8. [8]
    G. Gruner, The dynamics of charge-density waves, Rev. Mod. Phys. 60 (1988) 1129 [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    L.V. Delacrétaz, B. Goutéraux, S.A. Hartnoll and A. Karlsson, Theory of hydrodynamic transport in fluctuating electronic charge density wave states, Phys. Rev. B 96 (2017) 195128 [arXiv:1702.05104] [INSPIRE].ADSCrossRefGoogle Scholar
  10. [10]
    T. Andrade, M. Baggioli, A. Krikun and N. Poovuttikul, Pinning of longitudinal phonons in holographic spontaneous helices, JHEP 02 (2018) 085 [arXiv:1708.08306] [INSPIRE].ADSCrossRefGoogle Scholar
  11. [11]
    L. Alberte, M. Ammon, M. Baggioli, A. Jiménez-Alba and O. Pujolàs, Holographic Phonons, arXiv:1711.03100 [INSPIRE].
  12. [12]
    A. Amoretti, D. Areán, B. Goutéraux and D. Musso, DC resistivity of quantum critical, charge density wave states from gauge-gravity duality, arXiv:1712.07994 [INSPIRE].
  13. [13]
    N. Jokela, M. Jarvinen and M. Lippert, Holographic sliding stripes, Phys. Rev. D 95 (2017) 086006 [arXiv:1612.07323] [INSPIRE].ADSGoogle Scholar
  14. [14]
    N. Jokela, M. Jarvinen and M. Lippert, Pinning of holographic sliding stripes, Phys. Rev. D 96 (2017) 106017 [arXiv:1708.07837] [INSPIRE].ADSGoogle Scholar
  15. [15]
    M. Blake, Momentum relaxation from the fluid/gravity correspondence, JHEP 09 (2015) 010 [arXiv:1505.06992] [INSPIRE].MathSciNetCrossRefGoogle Scholar
  16. [16]
    C.P. Herzog, Lectures on Holographic Superfluidity and Superconductivity, J. Phys. A 42 (2009) 343001 [arXiv:0904.1975] [INSPIRE].MathSciNetzbMATHGoogle Scholar
  17. [17]
    A. Donos, J.P. Gauntlett and V. Ziogas, Diffusion in inhomogeneous media, Phys. Rev. D 96 (2017) 125003 [arXiv:1708.05412] [INSPIRE].ADSGoogle Scholar
  18. [18]
    A. Donos, J.P. Gauntlett, T. Griffin and L. Melgar, DC Conductivity of Magnetised Holographic Matter, JHEP 01 (2016) 113 [arXiv:1511.00713] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  19. [19]
    A. Donos, J.P. Gauntlett, T. Griffin, N. Lohitsiri and L. Melgar, Holographic DC conductivity and Onsager relations, JHEP 07 (2017) 006 [arXiv:1704.05141] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    E. Banks, A. Donos and J.P. Gauntlett, Thermoelectric DC conductivities and Stokes flows on black hole horizons, JHEP 10 (2015) 103 [arXiv:1507.00234] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© The Author(s) 2018

Authors and Affiliations

  1. 1.Centre for Particle Theory and Department of Mathematical SciencesDurham UniversityDurhamU.K.
  2. 2.Blackett Laboratory, Imperial CollegeLondonU.K.

Personalised recommendations