Abstract
Holographic strange metals are known to have a power law resistivity rising with temperature, which is reminiscent of the strange metal phases in condensed matter systems. In some holographic models, however, the exponent of the power law in the resistivity can be negative. In this case one encounters phases with diverging resistivity at zero temperature: holographic strange insulators.
These states arise as a result of translational symmetry breaking in the system, which can either be strong explicit and relevant in the IR, or spontaneous, but pinned by a small explicit source. In some regards, one can associate these two classes to the normal band insulators due to the strong ionic potential, and Mott insulator due to the commensurate lock in of the charge density wave.
We study different features of these classes on the explicit example of a holographic helical model with homogeneous Bianchy VII type translational symmetry breaking, and uncover the main mechanisms underlying transport in these two cases. We find that while transport in the explicit relevant case is governed by the incoherent conductivity, in the pinned spontaneous case the leading contribution comes from the coherent part.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
T. Andrade, A. Krikun, K. Schalm and J. Zaanen, Doping the holographic Mott insulator, Nature Phys. 14 (2018) 1049 [arXiv:1710.05791] [INSPIRE].
L.V. Delacrétaz, B. Goutéraux, S.A. Hartnoll and A. Karlsson, Bad Metals from Fluctuating Density Waves, SciPost Phys. 3 (2017) 025 [arXiv:1612.04381] [INSPIRE].
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].
S. Grozdanov, A. Lucas, S. Sachdev and K. Schalm, Absence of disorder-driven metal-insulator transitions in simple holographic models, Phys. Rev. Lett. 115 (2015) 221601 [arXiv:1507.00003] [INSPIRE].
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].
J. Zaanen, Y.-W. Sun, Y. Liu and K. Schalm, Holographic Duality in Condensed Matter Physics, Cambridge University Press, (2015).
A. Donos and S.A. Hartnoll, Interaction-driven localization in holography, Nature Phys. 9 (2013) 649 [arXiv:1212.2998] [INSPIRE].
A. Donos and J.P. Gauntlett, Novel metals and insulators from holography, JHEP 06 (2014) 007 [arXiv:1401.5077] [INSPIRE].
M. Rangamani, M. Rozali and D. Smyth, Spatial Modulation and Conductivities in Effective Holographic Theories, JHEP 07 (2015) 024 [arXiv:1505.05171] [INSPIRE].
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].
N. Jokela, M. Jarvinen and M. Lippert, Pinning of holographic sliding stripes, Phys. Rev. D 96 (2017) 106017 [arXiv:1708.07837] [INSPIRE].
A. Donos and J.P. Gauntlett, Thermoelectric DC conductivities from black hole horizons, JHEP 11 (2014) 081 [arXiv:1406.4742] [INSPIRE].
R.A. Davison and B. Goutéraux, Dissecting holographic conductivities, JHEP 09 (2015) 090 [arXiv:1505.05092] [INSPIRE].
R.A. Davison, B. Goutéraux and S.A. Hartnoll, Incoherent transport in clean quantum critical metals, JHEP 10 (2015) 112 [arXiv:1507.07137] [INSPIRE].
Y. Ando, G.S. Boebinger, A. Passner, T. Kimura and K. Kishio, Logarithmic Divergence of both In-Plane and Out-of-Plane Normal-State Resistivities of Superconducting La-2-xSrxCu O-4 in the Zero-Temperature Limit, Phys. Rev. Lett. 75 (1995) 4662 [INSPIRE].
A. Krikun, A. Romero-Bermúdez, K. Schalm and J. Zaanen, The anomalous attenuation of plasmons in strange metals and holography, arXiv:1812.03968 [INSPIRE].
S. Nakamura, H. Ooguri and C.-S. Park, Gravity Dual of Spatially Modulated Phase, Phys. Rev. D 81 (2010) 044018 [arXiv:0911.0679] [INSPIRE].
H. Ooguri and C.-S. Park, Holographic End-Point of Spatially Modulated Phase Transition, Phys. Rev. D 82 (2010) 126001 [arXiv:1007.3737] [INSPIRE].
A. Donos and J.P. Gauntlett, Black holes dual to helical current phases, Phys. Rev. D 86 (2012) 064010 [arXiv:1204.1734] [INSPIRE].
A. Donos, B. Goutéraux and E. Kiritsis, Holographic Metals and Insulators with Helical Symmetry, JHEP 09 (2014) 038 [arXiv:1406.6351] [INSPIRE].
T. Andrade and B. Withers, A simple holographic model of momentum relaxation, JHEP 05 (2014) 101 [arXiv:1311.5157] [INSPIRE].
M. Baggioli, B. Goutéraux, E. Kiritsis and W.-J. Li, Higher derivative corrections to incoherent metallic transport in holography, JHEP 03 (2017) 170 [arXiv:1612.05500] [INSPIRE].
A. Donos and J.P. Gauntlett, Holographic Q-lattices, JHEP 04 (2014) 040 [arXiv:1311.3292] [INSPIRE].
L. Alberte, M. Ammon, A. Jiménez-Alba, M. Baggioli and O. Pujolàs, Holographic Phonons, Phys. Rev. Lett. 120 (2018) 171602 [arXiv:1711.03100] [INSPIRE].
L. Alberte, M. Ammon, M. Baggioli, A. Jiménez and O. Pujolàs, Black hole elasticity and gapped transverse phonons in holography, JHEP 01 (2018) 129 [arXiv:1708.08477] [INSPIRE].
T. Andrade and A. Krikun, Commensurability effects in holographic homogeneous lattices, JHEP 05 (2016) 039 [arXiv:1512.02465] [INSPIRE].
D. Musso, Simplest phonons and pseudo-phonons in field theory, arXiv:1810.01799 [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].
A. Adam, S. Kitchen and T. Wiseman, A numerical approach to finding general stationary vacuum black holes, Class. Quant. Grav. 29 (2012) 165002 [arXiv:1105.6347] [INSPIRE].
T. Wiseman, Numerical construction of static and stationary black holes, arXiv:1107.5513 [INSPIRE].
M. Henningson and K. Skenderis, The holographic Weyl anomaly, JHEP 07 (1998) 023 [hep-th/9806087] [INSPIRE].
S. de Haro, S.N. Solodukhin and K. Skenderis, Holographic reconstruction of space-time and renormalization in the AdS/CFT correspondence, Commun. Math. Phys. 217 (2001) 595 [hep-th/0002230] [INSPIRE].
S.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav. 26 (2009) 224002 [arXiv:0903.3246] [INSPIRE].
A. Donos, J.P. Gauntlett, T. Griffin and L. Melgar, DC Conductivity of Magnetised Holographic Matter, JHEP 01 (2016) 113 [arXiv:1511.00713] [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].
M. Blake and D. Tong, Universal Resistivity from Holographic Massive Gravity, Phys. Rev. D 88 (2013) 106004 [arXiv:1308.4970] [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].
B. Goutéraux, N. Jokela and A. Pönni, Incoherent conductivity of holographic charge density waves, JHEP 07 (2018) 004 [arXiv:1803.03089] [INSPIRE].
A. Amoretti, D. Areán, B. Goutéraux and D. Musso, DC resistivity of quantum critical, charge density wave states from gauge-gravity duality, Phys. Rev. Lett. 120 (2018) 171603 [arXiv:1712.07994] [INSPIRE].
A. Amoretti, D. Areán, B. Goutéraux and D. Musso, Effective holographic theory of charge density waves, Phys. Rev. D 97 (2018) 086017 [arXiv:1711.06610] [INSPIRE].
A. Donos, J.P. Gauntlett, T. Griffin and V. Ziogas, Incoherent transport for phases that spontaneously break translations, JHEP 04 (2018) 053 [arXiv:1801.09084] [INSPIRE].
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].
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].
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].
G. Policastro, D.T. Son and A.O. Starinets, From AdS/CFT correspondence to hydrodynamics, JHEP 09 (2002) 043 [hep-th/0205052] [INSPIRE].
P. Kovtun, D.T. Son and A.O. Starinets, Viscosity in strongly interacting quantum field theories from black hole physics, Phys. Rev. Lett. 94 (2005) 111601 [hep-th/0405231] [INSPIRE].
V. Cardoso and J.P.S. Lemos, Quasinormal modes of Schwarzschild anti-de Sitter black holes: Electromagnetic and gravitational perturbations, Phys. Rev. D 64 (2001) 084017 [gr-qc/0105103] [INSPIRE].
E. Berti and K.D. Kokkotas, Quasinormal modes of Reissner-Nordström-anti-de Sitter black holes: Scalar, electromagnetic and gravitational perturbations, Phys. Rev. D 67 (2003) 064020 [gr-qc/0301052] [INSPIRE].
G. Michalogiorgakis and S.S. Pufu, Low-lying gravitational modes in the scalar sector of the global AdS 4 black hole, JHEP 02 (2007) 023 [hep-th/0612065] [INSPIRE].
A. Balatsky, S.B. Gudnason, Y. Kedem, A. Krikun, L. Thorlacius and K. Zarembo, Classical and quantum temperature fluctuations via holography, JHEP 01 (2015) 011 [arXiv:1405.4829] [INSPIRE].
A. Amoretti, D. Areán, B. Goutéraux and D. Musso, A holographic strange metal with slowly fluctuating translational order, arXiv:1812.08118 [INSPIRE].
A. Krikun, Holographic discommensurations, JHEP 12 (2018) 030 [arXiv:1710.05801] [INSPIRE].
J. Erdmenger, B. Herwerth, S. Klug, R. Meyer and K. Schalm, S-Wave Superconductivity in Anisotropic Holographic Insulators, JHEP 05 (2015) 094 [arXiv:1501.07615] [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: 1812.08132
On leave from Institute for Theoretical and Experimental Physics (ITEP), B. Cheryomushkinskaya 25, 117218 Moscow, Russia (Alexander Krikun)
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, 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 licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Andrade, T., Krikun, A. Coherent vs incoherent transport in holographic strange insulators. J. High Energ. Phys. 2019, 119 (2019). https://doi.org/10.1007/JHEP05(2019)119
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2019)119