Abstract
The linear-T resistivity is one of the hallmarks of various strange metals regardless of their microscopic details. Towards understanding this universal property, the holographic method or gauge/gravity duality has made much progress. Most holographic models have focused on the low temperature limit, where the linear-T resistivity has been explained by the infrared geometry. We extend this analysis to high temperature and identify the conditions for a robust linear-T resistivity up to high temperature. This extension is important because, in experiment, the linear-T resistivity is observed in a large range of temperatures, up to room temperature. In the axion-dilaton theories we find that, to have a robust linear-T resistivity, the strong momentum relaxation is a necessary condition, which agrees with the previous results for the Guber-Rocha model. However, it is not sufficient in the sense that, among large range of parameters giving a linear-T resistivity in low temperature limit, only very limited parameters can support the linear-T resistivity up to high temperature even in strong momentum relaxation. We also show that the incoherent term in the general holographic conductivity formula or the coupling between the dilaton and Maxwell term is responsible for a robust linear-T resistivity up to high temperature.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S.A. Hartnoll, A. Lucas and S. Sachdev, Holographic quantum matter, arXiv:1612.07324 [INSPIRE].
M. Blake and A. Donos, Quantum critical transport and the Hall angle, Phys. Rev. Lett.114 (2015) 021601 [arXiv:1406.1659] [INSPIRE].
Z. Zhou, J.-P. Wu and Y. Ling, DC and Hall conductivity in holographic massive Einstein-Maxwell-dilaton gravity, JHEP08 (2015) 067 [arXiv:1504.00535] [INSPIRE].
K.-Y. Kim, K.K. Kim, Y. Seo and S.-J. Sin, Thermoelectric conductivities at finite magnetic field and the Nernst effect, JHEP07 (2015) 027 [arXiv:1502.05386] [INSPIRE].
Z.-N. Chen, X.-H. Ge, S.-Y. Wu, G.-H. Yang and H.-S. Zhang, Magnetothermoelectric DC conductivities from holography models with hyperscaling factor in Lifshitz spacetime, Nucl. Phys.B 924 (2017) 387 [arXiv:1709.08428] [INSPIRE].
E. Blauvelt, S. Cremonini, A. Hoover, L. Li and S. Waskie, Holographic model for the anomalous scalings of the cuprates, Phys. Rev.D 97 (2018) 061901 [arXiv:1710.01326] [INSPIRE].
B.S. Kim, E. Kiritsis and C. Panagopoulos, Holographic quantum criticality and strange metal transport, New J. Phys.14 (2012) 043045 [arXiv:1012.3464] [INSPIRE].
C.C. Homes et al., Universal scaling relation in high-temperature superconductors, Nature430 (2004) 539 [cond-mat/0404216] [INSPIRE].
J. Zaanen, Superconductivity: why the temperature is high, Nature430 (2004) 512.
J. Erdmenger, B. Herwerth, S. Klug, R. Meyer and K. Schalm, S-wave superconductivity in anisotropic holographic insulators, JHEP05 (2015) 094 [arXiv:1501.07615] [INSPIRE].
K.-Y. Kim, K.K. Kim and M. Park, A simple holographic superconductor with momentum relaxation, JHEP04 (2015) 152 [arXiv:1501.00446] [INSPIRE].
K.K. Kim, M. Park and K.-Y. Kim, Ward identity and Homes’ law in a holographic superconductor with momentum relaxation, JHEP10 (2016) 041 [arXiv:1604.06205] [INSPIRE].
K.-Y. Kim and C. Niu, Homes’ law in holographic superconductor with Q-lattices, JHEP10 (2016) 144 [arXiv:1608.04653] [INSPIRE].
J. Zaanen, Y. Liu, Y.-W. Sun and K. Schalm, Holographic duality in condensed matter physics, Cambridge University Press, Cambridge, U.K. (2015).
M. Ammon and J. Erdmenger, Gauge/gravity duality, Cambridge University Press, Cambridge, U.K. (2015).
C. Charmousis, B. Gouteraux, B.S. Kim, E. Kiritsis and R. Meyer, Effective holographic theories for low-temperature condensed matter systems, JHEP11 (2010) 151 [arXiv:1005.4690] [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].
B. Goutéraux, Charge transport in holography with momentum dissipation, JHEP04 (2014) 181 [arXiv:1401.5436] [INSPIRE].
X.-H. Ge, Y. Tian, S.-Y. Wu, S.-F. Wu and S.-F. Wu, Linear and quadratic in temperature resistivity from holography, JHEP11 (2016) 128 [arXiv:1606.07905] [INSPIRE].
S. Cremonini, H.-S. Liu, H. Lü and C.N. Pope, DC conductivities from non-relativistic scaling geometries with momentum dissipation, JHEP04 (2017) 009 [arXiv:1608.04394] [INSPIRE].
H.-S. Jeong, Y. Ahn, D. Ahn, C. Niu, W.-J. Li and K.-Y. Kim, Thermal diffusivity and butterfly velocity in anisotropic Q-lattice models, JHEP01 (2018) 140 [arXiv:1708.08822] [INSPIRE].
A. Salvio, Transitions in dilaton holography with global or local symmetries, JHEP03 (2013) 136 [arXiv:1302.4898] [INSPIRE].
A. Donos and J.P. Gauntlett, Thermoelectric DC conductivities from black hole horizons, JHEP11 (2014) 081 [arXiv:1406.4742] [INSPIRE].
K.-Y. Kim, K.K. Kim, Y. Seo and S.-J. Sin, Coherent/incoherent metal transition in a holographic model, JHEP12 (2014) 170 [arXiv:1409.8346] [INSPIRE].
K.-Y. Kim, K.K. Kim, Y. Seo and S.-J. Sin, Gauge invariance and holographic renormalization, Phys. Lett.B 749 (2015) 108 [arXiv:1502.02100] [INSPIRE].
H.-S. Jeong, K.-Y. Kim and C. Niu, Linear-T resistivity at high temperature, JHEP10 (2018) 191 [arXiv:1806.07739] [INSPIRE].
S.S. Gubser and F.D. Rocha, Peculiar properties of a charged dilatonic black hole in AdS5 , Phys. Rev.D 81 (2010) 046001 [arXiv:0911.2898] [INSPIRE].
Z. Zhou, Y. Ling and J.-P. Wu, Holographic incoherent transport in Einstein-Maxwell-dilaton gravity, Phys. Rev.D 94 (2016) 106015 [arXiv:1512.01434] [INSPIRE].
K.-Y. Kim and C. Niu, Diffusion and butterfly velocity at finite density, JHEP06 (2017) 030 [arXiv:1704.00947] [INSPIRE].
S.A. Hartnoll, Theory of universal incoherent metallic transport, Nature Phys.11 (2015) 54 [arXiv:1405.3651] [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].
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. 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].
R.A. Davison, S.A. Gentle and B. Goutéraux, Slow relaxation and diffusion in holographic quantum critical phases, Phys. Rev. Lett.123 (2019) 141601 [arXiv:1808.05659] [INSPIRE].
R.A. Davison, S.A. Gentle and B. Goutéraux, Impact of irrelevant deformations on thermodynamics and transport in holographic quantum critical states, Phys. Rev.D 100 (2019) 086020 [arXiv:1812.11060] [INSPIRE].
E. Kiritsis and J. Ren, On holographic insulators and supersolids, JHEP09 (2015) 168 [arXiv:1503.03481] [INSPIRE].
Y. Ling, Z. Xian and Z. Zhou, Power law of shear viscosity in Einstein-Maxwell-dilaton-axion model, Chin. Phys.C 41 (2017) 023104 [arXiv:1610.08823] [INSPIRE].
J. Bhattacharya, S. Cremonini and B. Goutéraux, Intermediate scalings in holographic RG flows and conductivities, JHEP02 (2015) 035 [arXiv:1409.4797] [INSPIRE].
Y. Ling, Z. Xian and Z. Zhou, Power law of shear viscosity in Einstein-Maxwell-dilaton-axion model, Chin. Phys.C 41 (2017) 023104 [arXiv:1610.08823] [INSPIRE].
R.A. Davison and B. Goutéraux, Dissecting holographic conductivities, JHEP09 (2015) 090 [arXiv:1505.05092] [INSPIRE].
B. Gouteraux and E. Kiritsis, Generalized holographic quantum criticality at finite density, JHEP12 (2011) 036 [arXiv:1107.2116] [INSPIRE].
R.A. Cooper et al., Anomalous criticality in the electrical resistivity of La2−xSrxCuO4, Science323 (2009) 603.
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: 1907.12168
Rights and permissions
This article is published under an open access license. Please check the 'Copyright Information' section either on this page or in the PDF for details of this license and what re-use is permitted. If your intended use exceeds what is permitted by the license or if you are unable to locate the licence and re-use information, please contact the Rights and Permissions team.
About this article
Cite this article
Ahn, Y., Jeong, HS., Ahn, D. et al. Linear-T resistivity from low to high temperature: axion-dilaton theories. J. High Energ. Phys. 2020, 153 (2020). https://doi.org/10.1007/JHEP04(2020)153
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2020)153