Abstract
Using linear response theory, we analyze the electromagnetic response functions of generalized holographic superconductors, in AdS-Schwarzschild and single R-charged black hole backgrounds in four dimensions. By introducing momentum dependent vector mode perturbations, the response functions for these systems are studied numerically, including the effects of backreaction. This complements and completes the probe limit analysis for these backgrounds initiated in our previous work (arXiv:1305.6273). Our numerical analysis indicates a negative Depine-Lakhtakia index for both the backgrounds studied, at low enough frequencies. The dependence of the response functions on the backreaction parameter and the model parameters are established and analyzed with respect to similar backgrounds in five dimensions.
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References
J.M. Maldacena, The Large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
S.S. Gubser, Breaking an Abelian gauge symmetry near a black hole horizon, Phys. Rev. D 78 (2008) 065034 [arXiv:0801.2977] [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].
S. Franco, A. Garcia-Garcia and D. Rodriguez-Gomez, A General class of holographic superconductors, JHEP 04 (2010) 092 [arXiv:0906.1214] [INSPIRE].
A. Bianchi, R. Movshovich, N. Oeschler, P. Gegenwart, F. Steglich et al., First order superconducting phase transition in CeCoIn(5), Phys. Rev. Lett. 89 (2002) 137002 [cond-mat/0203310] [INSPIRE].
D.R. Smith, W.J. Padilla, J. Willie, D.C. Vier, S.C. Nemat-Nasser and S. Schultz, Composite medium with simultaneously negative permeability and permittivity, Phys. Rev. Lett. 84 (2000) 4184.
J.B. Pendry, Negative Refraction Makes a Perfect Lens, Phys. Rev. Lett. 85 (2000) 3966.
R.A. Depine and A. Lakhtakia, A new condition to identify isotropic dielectric-magnetic materials displaying negative phase velocity, Micro. Opt. Tech. Lett. 41 (2004) 315.
V.M. Agranovich and Y.N. Gartstein, Spatial dispersion and negative refraction of light, Phys.-Usp. 49 (2006) 1029.
D. Forcella, J. Zaanen, D. Valentinis and D. van der Marel, Electromagnetic properties of viscous charged fluids, Phys. Rev. B 90 (2014) 035143 [arXiv:1406.1356] [INSPIRE].
A. Amariti, D. Forcella, A. Mariotti and G. Policastro, Holographic Optics and Negative Refractive Index, JHEP 04 (2011) 036 [arXiv:1006.5714] [INSPIRE].
X.-H. Ge, K. Jo and S.-J. Sin, Hydrodynamics of RN AdS 4 black hole and Holographic Optics, JHEP 03 (2011) 104 [arXiv:1012.2515] [INSPIRE].
P. Phukon and T. Sarkar, R-Charged Black Holes and Holographic Optics, JHEP 09 (2013) 102 [arXiv:1305.2745] [INSPIRE].
F. Bigazzi, A.L. Cotrone, J. Mas, D. Mayerson and J. Tarrio, D3-D7 quark-gluon Plasmas at Finite Baryon Density, JHEP 04 (2011) 060 [arXiv:1101.3560] [INSPIRE].
S.M. Anlage, The physics and applications of superconducting metamaterials, Journal of Optics 13 (2011) 024001 [arXiv:1004.3226].
X. Gao and H.-b. Zhang, Refractive index in holographic superconductors, JHEP 08 (2010) 075 [arXiv:1008.0720] [INSPIRE].
A. Amariti, D. Forcella, A. Mariotti and M. Siani, Negative Refraction and Superconductivity, JHEP 10 (2011) 104 [arXiv:1107.1242] [INSPIRE].
S. Mahapatra, P. Phukon and T. Sarkar, Generalized Superconductors and Holographic Optics, JHEP 01 (2014) 135 [arXiv:1305.6273] [INSPIRE].
A. Dey, S. Mahapatra and T. Sarkar, Generalized Holographic Superconductors with Higher Derivative Couplings, JHEP 06 (2014) 147 [arXiv:1404.2190] [INSPIRE].
A. Amariti, D. Forcella and A. Mariotti, Negative Refractive Index in Hydrodynamical Systems, JHEP 01 (2013) 105 [arXiv:1107.1240] [INSPIRE].
D. Forcella, A. Mezzalira and D. Musso, Electromagnetic response of strongly coupled plasmas, JHEP 11 (2014) 153 [arXiv:1404.4048] [INSPIRE].
L.D. Landau and E.M. Lifshitz, Electrodynamics of continous media, Pergamon press, Oxford U.K. (1984).
M. Dressel and G. Gruner, Electrodynamics of solids, Cambridge University Press (2002).
P. Breitenlohner and D.Z. Freedman, Stability in Gauged Extended Supergravity, Annals Phys. 144 (1982) 249 [INSPIRE].
D.T. Son and A.O. Starinets, Minkowski space correlators in AdS/CFT correspondence: Recipe and applications, JHEP 09 (2002) 042 [hep-th/0205051] [INSPIRE].
X.-H. Ge, Y. Matsuo, F.-W. Shu, S.-J. Sin and T. Tsukioka, Density Dependence of Transport Coefficients from Holographic Hydrodynamics, Prog. Theor. Phys. 120 (2008) 833 [arXiv:0806.4460] [INSPIRE].
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 and J.E. Santos, General Relativity and the Cuprates, JHEP 06 (2013) 087 [arXiv:1302.6586] [INSPIRE].
M.W. McCall, A. Lakhtakia and W.S. Weiglhofer, The negative index of refraction demystified, Eur. J. Phys. 23 (2002) 353 [physics/0204067].
M. Cvetič, M.J. Duff, P. Hoxha, J.T. Liu, H. Lü et al., Embedding AdS black holes in ten-dimensions and eleven-dimensions, Nucl. Phys. B 558 (1999) 96 [hep-th/9903214] [INSPIRE].
A. Dey, S. Mahapatra and T. Sarkar, Very General Holographic Superconductors and Entanglement Thermodynamics, JHEP 12 (2014) 135 [arXiv:1409.5309] [INSPIRE].
R. Flauger, E. Pajer and S. Papanikolaou, A Striped Holographic Superconductor, Phys. Rev. D 83 (2011) 064009 [arXiv:1010.1775] [INSPIRE].
K. Maeda, M. Natsuume and T. Okamura, Dynamic critical phenomena in the AdS/CFT duality, Phys. Rev. D 78 (2008) 106007 [arXiv:0809.4074] [INSPIRE].
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Mahapatra, S. Generalized superconductors and holographic optics. Part II. J. High Energ. Phys. 2015, 148 (2015). https://doi.org/10.1007/JHEP01(2015)148
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DOI: https://doi.org/10.1007/JHEP01(2015)148