Abstract
We analyze a class of bottom-up holographic models for low energy thermo-electric transport. The models we focus on belong to a family of Einstein-Maxwell-dilaton theories parameterized by two scalar functions, characterizing the dilaton self-interaction and the gauge coupling function. We impose spatially inhomogeneous lattice boundary conditions for the dilaton on the AdS boundary and study the resulting phase structure attained at low energies. We find that as we dial the scalar functions at our disposal (changing thus the theory under consideration), we obtain either (i) coherent metallic, or (ii) insulating, or (iii) incoherent metallic phases. We chart out the domain where the incoherent metals appear in a restricted parameter space of theories. We also analyze the optical conductivity, noting that non-trivial scaling behaviour at intermediate frequencies appears to only be possible for very narrow regions of parameter space.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav. 26 (2009) 224002 [arXiv:0903.3246] [INSPIRE].
C.P. Herzog, Lectures on Holographic Superfluidity and Superconductivity, J. Phys. A 42 (2009) 343001 [arXiv:0904.1975] [INSPIRE].
N. Iqbal, H. Liu and M. Mezei, Lectures on holographic non-Fermi liquids and quantum phase transitions, arXiv:1110.3814 [INSPIRE].
D.N. Basov, R.D. Averitt, D. van der Marel, M. Dressel and K. Haule, Electrodynamics of correlated electron materials, Reviews of Modern Physics 83 (2011) 471 [arXiv:1106.2309].
S.A. Hartnoll, Physics without momentum, talk given at Eurostrings 2015, Cambridge, U.K., 23-27 March 2015.
G.T. Horowitz, J.E. Santos and D. Tong, Optical conductivity with holographic lattices, JHEP 07 (2012) 168 [arXiv:1204.0519] [INSPIRE].
G.T. Horowitz, J.E. Santos and D. Tong, Further Evidence for Lattice-Induced Scaling, JHEP 11 (2012) 102 [arXiv:1209.1098] [INSPIRE].
D. van der Marel, F. Carbone, A.B. Kuzmenko and E. Giannini, Scaling properties of the optical conductivity of Bi-based cuprates, Annals Phys. 321 (2006) 1716 [cond-mat/0604037].
A. Donos and S.A. Hartnoll, Interaction-driven localization in holography, Nature Phys. 9 (2013) 649 [arXiv:1212.2998] [INSPIRE].
R.A. Davison and B. Goutéraux, Momentum dissipation and effective theories of coherent and incoherent transport, JHEP 01 (2015) 039 [arXiv:1411.1062] [INSPIRE].
D. Vegh, Holography without translational symmetry, arXiv:1301.0537 [INSPIRE].
M. Blake and D. Tong, Universal Resistivity from Holographic Massive Gravity, Phys. Rev. D 88 (2013) 106004 [arXiv:1308.4970] [INSPIRE].
R.A. Davison, Momentum relaxation in holographic massive gravity, Phys. Rev. D 88 (2013) 086003 [arXiv:1306.5792] [INSPIRE].
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].
A. Amoretti, A. Braggio, N. Maggiore, N. Magnoli and D. Musso, Thermo-electric transport in gauge/gravity models with momentum dissipation, JHEP 09 (2014) 160 [arXiv:1406.4134] [INSPIRE].
T. Andrade and B. Withers, A simple holographic model of momentum relaxation, JHEP 05 (2014) 101 [arXiv:1311.5157] [INSPIRE].
A. Donos and J.P. Gauntlett, Holographic Q-lattices, JHEP 04 (2014) 040 [arXiv:1311.3292] [INSPIRE].
B. Goutéraux, Charge transport in holography with momentum dissipation, JHEP 04 (2014) 181 [arXiv:1401.5436] [INSPIRE].
A. Donos and J.P. Gauntlett, Novel metals and insulators from holography, JHEP 06 (2014) 007 [arXiv:1401.5077] [INSPIRE].
A. Donos and J.P. Gauntlett, Thermoelectric DC conductivities from black hole horizons, JHEP 11 (2014) 081 [arXiv:1406.4742] [INSPIRE].
A. Donos, B. Goutéraux and E. Kiritsis, Holographic metals and insulators with helical symmetry, JHEP 09 (2014) 038 [arXiv:1406.6351] [INSPIRE].
A. Lucas and S. Sachdev, Memory matrix theory of magnetotransport in strange metals, Phys. Rev. B 91 (2015) 195122 [arXiv:1502.04704] [INSPIRE].
A. Lucas, Conductivity of a strange metal: from holography to memory functions, JHEP 03 (2015) 071 [arXiv:1501.05656] [INSPIRE].
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].
A. Donos and J.P. Gauntlett, The thermoelectric properties of inhomogeneous holographic lattices, JHEP 01 (2015) 035 [arXiv:1409.6875] [INSPIRE].
C. Charmousis, B. Gouteraux, B.S. Kim, E. Kiritsis and R. Meyer, Effective Holographic Theories for low-temperature condensed matter systems, JHEP 11 (2010) 151 [arXiv:1005.4690] [INSPIRE].
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].
D. Arean, A. Farahi, L.A. Pando Zayas, I.S. Landea and A. Scardicchio, Holographic superconductor with disorder, Phys. Rev. D 89 (2014) 106003 [arXiv:1308.1920] [INSPIRE].
S.A. Hartnoll and J.E. Santos, Disordered horizons: holography of randomly disordered fixed points, Phys. Rev. Lett. 112 (2014) 231601 [arXiv:1402.0872] [INSPIRE].
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].
S.A. Hartnoll and C.P. Herzog, Ohm’s Law at strong coupling: S duality and the cyclotron resonance, Phys. Rev. D 76 (2007) 106012 [arXiv:0706.3228] [INSPIRE].
L.N. Trefethen, Spectral Methods in MATLAB, SIAM Philadelphia (2000).
J.P. Boyd, Chebyshev and Fourier Spectral Methods, second edition, Dover Publications (2000).
S.A. Hartnoll, Theory of universal incoherent metallic transport, Nature Phys. 11 (2015) 54 [arXiv:1405.3651] [INSPIRE].
S.A. Hartnoll and D.M. Hofman, Locally Critical Resistivities from Umklapp Scattering, Phys. Rev. Lett. 108 (2012) 241601 [arXiv:1201.3917] [INSPIRE].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1505.05171
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Rangamani, M., Rozali, M. & Smyth, D. Spatial modulation and conductivities in effective holographic theories. J. High Energ. Phys. 2015, 24 (2015). https://doi.org/10.1007/JHEP07(2015)024
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP07(2015)024