Abstract
We consider holographic superconductors in a broad class of massive gravity backgrounds. These theories provide a holographic description of a superconductor with broken translational symmetry. Such models exhibit a rich phase structure: depending on the values of the temperature and the disorder strength the boundary system can be in superconducting, normal metallic or normal pseudo-insulating phases. Furthermore the system supports interesting collective excitation of the charge carriers, which appears in the normal phase, persists in the superconducting phase, but eventually gets destroyed by the superconducting condensate. We also show the possibility of building a phase diagram of a system with the superconducting phase occupying a dome-shaped region on the temperature-disorder plane.
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References
G.T. Horowitz and J.E. Santos, General Relativity and the Cuprates, JHEP 06 (2013) 087 [arXiv:1302.6586] [INSPIRE].
H.B. Zeng and J.-P. Wu, Holographic superconductors from the massive gravity, Phys. Rev. D 90 (2014) 046001 [arXiv:1404.5321] [INSPIRE].
D. Arean, A. Farahi, L.A. Pando Zayas, I.S. Landea and A. Scardicchio, Holographic p-wave Superconductor with Disorder, arXiv:1407.7526 [INSPIRE].
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].
T. Andrade and S.A. Gentle, Relaxed superconductors, arXiv:1412.6521 [INSPIRE].
K.-Y. Kim, K.K. Kim and M. Park, A Simple Holographic Superconductor with Momentum Relaxation, JHEP 04 (2015) 152 [arXiv:1501.00446] [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].
S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Building a Holographic Superconductor, Phys. Rev. Lett. 101 (2008) 031601 [arXiv:0803.3295] [INSPIRE].
S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Holographic Superconductors, JHEP 12 (2008) 015 [arXiv:0810.1563] [INSPIRE].
D. Vegh, Holography without translational symmetry, arXiv:1301.0537 [INSPIRE].
V.A. Rubakov and P.G. Tinyakov, Infrared-modified gravities and massive gravitons, Phys. Usp. 51 (2008) 759 [arXiv:0802.4379] [INSPIRE].
T. Andrade and B. Withers, A simple holographic model of momentum relaxation, JHEP 05 (2014) 101 [arXiv:1311.5157] [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].
M. Blake and D. Tong, Universal Resistivity from Holographic Massive Gravity, Phys. Rev. D 88 (2013) 106004 [arXiv:1308.4970] [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].
M. Baggioli and O. Pujolàs, Holographic Polarons, the Metal-Insulator Transition and Massive Gravity, arXiv:1411.1003 [INSPIRE].
M. Taylor and W. Woodhead, Inhomogeneity simplified, Eur. Phys. J. C 74 (2014) 3176 [arXiv:1406.4870] [INSPIRE].
S.N. Klimin and J.T. Devreese, Optical conductivity of a strong-coupling Frohlich polaron, Phys. Rev. B 89 (2014) 035201 [arXiv:1310.4413].
G.T. Horowitz and M.M. Roberts, Holographic Superconductors with Various Condensates, Phys. Rev. D 78 (2008) 126008 [arXiv:0810.1077] [INSPIRE].
P.A. Lee, N. Nagaosa and X.-G. Wen, Doping a Mott insulator: physics of high-temperature superconductivity, Rev. Mod. Phys. 78 (2006) 17 [INSPIRE].
A. Karch and A. O’Bannon, Metallic AdS/CFT, JHEP 09 (2007) 024 [arXiv:0705.3870] [INSPIRE].
B. Goutéraux, Charge transport in holography with momentum dissipation, JHEP 04 (2014) 181 [arXiv:1401.5436] [INSPIRE].
M. Baggioli and O. Pujolàs, to appear.
F. Denef and S.A. Hartnoll, Landscape of superconducting membranes, Phys. Rev. D 79 (2009) 126008 [arXiv:0901.1160] [INSPIRE].
I. Amado, M. Kaminski and K. Landsteiner, Hydrodynamics of Holographic Superconductors, JHEP 05 (2009) 021 [arXiv:0903.2209] [INSPIRE].
M. Kaminski, K. Landsteiner, J. Mas, J.P. Shock and J. Tarrio, Holographic Operator Mixing and Quasinormal Modes on the Brane, JHEP 02 (2010) 021 [arXiv:0911.3610] [INSPIRE].
M. Goykhman, A. Parnachev and J. Zaanen, Fluctuations in finite density holographic quantum liquids, JHEP 10 (2012) 045 [arXiv:1204.6232] [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].
A. Amoretti, A. Braggio, N. Magnoli and D. Musso, Bounds on charge and heat diffusivities in momentum dissipating holography, arXiv:1411.6631 [INSPIRE].
J.P. Gauntlett, J. Sonner and T. Wiseman, Quantum Criticality and Holographic Superconductors in M-theory, JHEP 02 (2010) 060 [arXiv:0912.0512] [INSPIRE].
S. Ganguli, J.A. Hutasoit and G. Siopsis, Superconducting Dome from Holography, Phys. Rev. D 87 (2013) 126003 [arXiv:1302.5426] [INSPIRE].
J. Erdmenger, P. Kerner and S. Muller, Towards a Holographic Realization of Homes’ Law, JHEP 10 (2012) 021 [arXiv:1206.5305] [INSPIRE].
V. Balasubramanian and P. Kraus, A stress tensor for Anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [INSPIRE].
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Baggioli, M., Goykhman, M. Phases of holographic superconductors with broken translational symmetry. J. High Energ. Phys. 2015, 35 (2015). https://doi.org/10.1007/JHEP07(2015)035
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DOI: https://doi.org/10.1007/JHEP07(2015)035