Abstract
In a recent paper, Kiritsis and Li presented a holographic model to study the competition between different orders at finite doping in holographic superconductors. In the present work, we introduce fermions into such model and study the fermionic spectral functions in the normal phase at zero and finite temperatures. Combining analytic and numerical methods, we found that there is a crossover from a strange metal with short lived excitations at small doping, into a Fermi liquid with well defined quasiparticles at large doping. The critical doping at which excitations becomes long lived increases with temperature. The emerging phase diagram is qualitatively similar to that of High Temperature Superconductors.
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References
J.G. Bednorz and K.A. Müller, Possible high Tc superconductivity in the Ba-La-Cu-O system, Z. Phys. B 64 (1986) 189 [INSPIRE].
J. Bardeen, L.N. Cooper and J.R. Schrieffer, Microscopic theory of superconductivity, Phys. Rev. 106 (1957) 162 [INSPIRE].
B. Keimer, S. Kivelson, M. Norman, S. Uchida and J. Zaanen, From quantum matter to high-temperature superconductivity in copper oxides, Nature 518 (2015) 179.
E. Fradkin, S.A. Kivelson and J.M. Tranquada, Colloquium: Theory of intertwined orders in high temperature superconductors, Rev. Mod. Phys. 87 (2015) 457.
U. Chatterjee, D. Ai, J. Zhao, S. Rosenkranz, A. Kaminski, H. Raffy et al., Electronic phase diagram of high-temperature copper oxide superconductors, Proc. Nat. Acad. Sci. 108 (2011) 9346.
J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
O. Aharony, S.S. Gubser, J.M. Maldacena, H. Ooguri and Y. Oz, Large N field theories, string theory and gravity, Phys. Rept. 323 (2000) 183 [hep-th/9905111] [INSPIRE].
S.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav. 26 (2009) 224002 [arXiv:0903.3246] [INSPIRE].
J. McGreevy, Holographic duality with a view toward many-body physics, Adv. High Energy Phys. 2010 (2010) 723105 [arXiv:0909.0518] [INSPIRE].
J. Zaanen, Y. Liu, Y.-W. Sun and K. Schalm, Holographic Duality in Condensed Matter Physics, Cambridge University Press, (2015).
S.A. Hartnoll, A. Lucas and S. Sachdev, Holographic quantum matter, MIT press, (2018).
M. Rangamani, Gravity and Hydrodynamics: Lectures on the fluid-gravity correspondence, Class. Quant. Grav. 26 (2009) 224003 [arXiv:0905.4352] [INSPIRE].
P. Kovtun, Lectures on hydrodynamic fluctuations in relativistic theories, J. Phys. A 45 (2012) 473001 [arXiv:1205.5040] [INSPIRE].
P. Kovtun, D.T. Son and A.O. Starinets, Holography and hydrodynamics: Diffusion on stretched horizons, JHEP 10 (2003) 064 [hep-th/0309213] [INSPIRE].
S.S. Gubser, Breaking an Abelian gauge symmetry near a black hole horizon, Phys. Rev. D 78 (2008) 065034 [arXiv:0801.2977] [INSPIRE].
B. de Wit and H. Samtleben, The end of the p-form hierarchy, JHEP 08 (2008) 015 [arXiv:0805.4767] [INSPIRE].
C.P. Herzog, Lectures on Holographic Superfluidity and Superconductivity, J. Phys. A 42 (2009) 343001 [arXiv:0904.1975] [INSPIRE].
S. Ryu and T. Takayanagi, Holographic derivation of entanglement entropy from AdS/CFT, Phys. Rev. Lett. 96 (2006) 181602 [hep-th/0603001] [INSPIRE].
G. Bertoldi, T.J. Hollowood and J.L. Miramontes, Double scaling limits in gauge theories and matrix models, JHEP 06 (2006) 045 [hep-th/0603122] [INSPIRE].
H. Casini, M. Huerta and R.C. Myers, Towards a derivation of holographic entanglement entropy, JHEP 05 (2011) 036 [arXiv:1102.0440] [INSPIRE].
A. Lewkowycz and J. Maldacena, Generalized gravitational entropy, JHEP 08 (2013) 090 [arXiv:1304.4926] [INSPIRE].
H. Liu, J. McGreevy and D. Vegh, Non-Fermi liquids from holography, Phys. Rev. D 83 (2011) 065029 [arXiv:0903.2477] [INSPIRE].
T. Faulkner, N. Iqbal, H. Liu, J. McGreevy and D. Vegh, Strange metal transport realized by gauge/gravity duality, Science 329 (2010) 1043 [INSPIRE].
T. Faulkner, N. Iqbal, H. Liu, J. McGreevy and D. Vegh, Holographic non-Fermi-liquid fixed points, Phil. Trans. Roy. Soc. Lond. A 369 (2011) 1640.
M. Čubrović, J. Zaanen and K. Schalm, String Theory, Quantum Phase Transitions and the Emergent Fermi-Liquid, Science 325 (2009) 439 [arXiv:0904.1993] [INSPIRE].
S.-S. Lee, A Non-Fermi Liquid from a Charged Black Hole: A Critical Fermi Ball, Phys. Rev. D 79 (2009) 086006 [arXiv:0809.3402] [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].
E. Kiritsis and L. Li, Holographic Competition of Phases and Superconductivity, JHEP 01 (2016) 147 [arXiv:1510.00020] [INSPIRE].
M. Baggioli and M. Goykhman, Under The Dome: Doped holographic superconductors with broken translational symmetry, JHEP 01 (2016) 011 [arXiv:1510.06363] [INSPIRE].
T. Faulkner, H. Liu, J. McGreevy and D. Vegh, Emergent quantum criticality, Fermi surfaces and AdS 2, Phys. Rev. D 83 (2011) 125002 [arXiv:0907.2694] [INSPIRE].
C. Cosnier-Horeau and S.S. Gubser, Holographic Fermi surfaces at finite temperature in top-down constructions, Phys. Rev. D 91 (2015) 066002 [arXiv:1411.5384] [INSPIRE].
G. Baym and C. Pethick, Landau Fermi-liquid theory: concepts and applications, John Wiley & Sons, (2008).
B. Pioline and J. Troost, Schwinger pair production in AdS 2, JHEP 03 (2005) 043 [hep-th/0501169] [INSPIRE].
S.A. Hartnoll and A. Tavanfar, Electron stars for holographic metallic criticality, Phys. Rev. D 83 (2011) 046003 [arXiv:1008.2828] [INSPIRE].
M. Henningson and K. Sfetsos, Spinors and the AdS/CFT correspondence, Phys. Lett. B 431 (1998) 63 [hep-th/9803251] [INSPIRE].
I.S. Gradshteyn and I.M. Ryshik, Table of Integrals, Series, and Products, 4th edition, Academic Press, London, (1965).
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Giordano, G., Grandi, N., Lugo, A. et al. Strange metal crossover in the doped holographic superconductor. J. High Energ. Phys. 2018, 68 (2018). https://doi.org/10.1007/JHEP10(2018)068
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DOI: https://doi.org/10.1007/JHEP10(2018)068