Abstract
We discuss exotic properties of charged hydrodynamical systems, in the broken superconducting phase, probed by electromagnetic waves. Motivated by general arguments from hydrodynamics, we observe that negative refraction, namely the propagation in opposite directions of the phase velocities and of the energy flux, is expected for low enough frequencies. We corroborate this general idea by analyzing a holographic superconductor in the AdS/CFT correspondence, where the response functions can be explicitly computed. We study the dual gravitational theory both in the probe and in the backreacted case. We find that, while in the first case the refractive index is positive at every frequency, in the second case there is negative refraction at low enough frequencies. This is in agreement with hydrodynamic considerations.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J.B. Pendry, A.J. Holden, W.J. Stewart and I. Youngs, Extremely low frequency plasmons in metallic mesostructures, Phys. Rev. Lett. 76 (1996) 4773.
J.B. Pendry, A.J. Holden, D.J. Robbins and W.J. Stewart, Magnetism from conductors and enhanced nonlinear phenomena, IEEE Trans. Microwave Theory Tech. 47 (1999) 2075.
V.G. Veselago, The electrodynamics of substances with simultaneously negative values of ϵ and μ, Sov. Phys. Usp. 10 (1968) 509.
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.
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].
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].
F. Bigazzi, A.L. Cotrone, D. Mayerson, A. Paredes and J. Tarrio, Holographic Flavored quark-gluon Plasmas, PoS(FACESQCD)005 [arXiv:1101.3841] [ inSPIRE].
A. Amariti, D. Forcella and A. Mariotti, Negative Refractive Index in Hydrodynamical Systems, arXiv:1107.1240 [ inSPIRE].
S.M. Anlage, The physics and applications of superconducting metamaterials, J. Optics 13 (2011) 024001 [arXiv:1004.3226].
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.A. Hartnoll, Lectures on holographic methods for condensed matter physics, Class. Quant. Grav. 26 (2009) 224002 [arXiv:0903.3246] [ inSPIRE].
C.P. Herzog, Lectures on Holographic Superfluidity and Superconductivity, J. Phys. A A 42 (2009) 343001 [arXiv:0904.1975] [ inSPIRE].
G.T. Horowitz, Introduction to Holographic Superconductors, arXiv:1002.1722 [ inSPIRE].
X. Gao and H. Zhang, Refractive index in holographic superconductors, JHEP 08 (2010) 075 [arXiv:1008.0720] [ inSPIRE].
L.D. Landau and E.M. Lifshitz, Electrodynamics of continous media, Pergamon Press, Oxford U.K. (1984).
V.M. Agranovich and Y.N. Gartstein, Spatial dispersion and negative refraction of light, Phys. Usp. 49 (2006) 1029.
V.M. Agranovich, Y.R. Shen, R.H. Baughman and A.A. Zakhidov, Optical bulk and surface waves with negative refraction, Phys. Rev. B 69 (2004) 165112.
V.M. Agranovich and Y.N. Gartstein, Electrodynamics of metamaterials and the Landau-Lifshitz approach to the magnetic permeability, Metamaterials 3 (2009) 1.
R.A. Depine and A. Lakhtakia, A new condition to identify isotropic dielectric-magnetic materials displaying negative phase velocity, Microwave Opt. Technol. Lett. 41 (2004) 315.
D. Foster, Hydrodynamic Fluctuations, Broken Symmetries and Correlation Functions, Benjamin/Cummings Pub. Co., Reading U.S.A. (1975).
L.P. Kadanoff and P.C. Martin, Hydrodynamics Equations and Correlation Functions, Ann. Phys. 24 (1963) 419.
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].
C.P. Herzog, N. Lisker, P. Surowka and A. Yarom, Transport in holographic superfluids, JHEP 08 (2011) 052 [arXiv:1101.3330] [ inSPIRE].
L. Barclay, R. Gregory, S. Kanno and P. Sutcliffe, Gauss-Bonnet Holographic Superconductors, JHEP 12 (2010) 029 [arXiv:1009.1991] [ inSPIRE].
I.R. Klebanov and E. Witten, AdS/CFT correspondence and symmetry breaking, Nucl. Phys. B 556 (1999) 89 [hep-th/9905104] [ inSPIRE].
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].
C.P. Herzog, An Analytic Holographic Superconductor, Phys. Rev. D 81 (2010) 126009 [arXiv:1003.3278] [ inSPIRE].
G. Policastro, D.T. Son and A.O. Starinets, From AdS/CFT correspondence to hydrodynamics, JHEP 09 (2002) 043 [hep-th/0205052] [ inSPIRE].
G.T. Horowitz and M.M. Roberts, Holographic Superconductors with Various Condensates, Phys. Rev. D 78 (2008) 126008 [arXiv:0810.1077] [ inSPIRE].
G.T. Horowitz, J.E. Santos and B. Way, A Holographic Josephson Junction, Phys. Rev. Lett. 106 (2011) 221601 [arXiv:1101.3326] [ inSPIRE].
M. Siani, Holographic Superconductors and Higher Curvature Corrections, JHEP 12 (2010) 035 [arXiv:1010.0700] [ inSPIRE].
S.I. Pekar, The theory of electromagnetic waves in a crystal in which excitons are produced, Zh. Eksp. Teor. Fiz. 33 (1957) 1022 [Sov. Phys. JETP 6 (1958) 785].
S.I. Pekar, Dispersion of light in the exciton absorption region of crystals, Zh. Eksp. Teor. Fiz. 34 (1958) 1176 [Sov. Phys. JETP 7 (1958) 813].
S.I. Pekar, Crystal optics and additional light waves, Benjamin/Cummings Pub. Co., Menlo Park U.S.A. (1983).
A. Amariti, D. Forcella and A. Mariotti, Additional Light Waves in Hydrodynamics and Holography, arXiv:1010.1297 [ inSPIRE].
V.A. Golick, D.V. Kadygrob, V.A. Yampolskii, A.L. Rakhmanov, B.A. Ivanov and F. Nori, Surface Josephson PlasmaWaves in Layered Superconductors above the Plasma Frequency:Evidence for a Negative Index of Refraction, Phys. Rev. Lett. 104 (2010) 187003.
Y.-Q. Wang, Y.-X. Liu and Z.-H. Zhao, Holographic Josephson Junction in 3 + 1 dimensions, arXiv:1104.4303 [ inSPIRE].
M. Siani, On inhomogeneous holographic superconductors, arXiv:1104.4463 [ inSPIRE].
E. Kiritsis and V. Niarchos, Josephson Junctions and AdS/CFT Networks, JHEP 07 (2011) 112 [arXiv:1105.6100] [ inSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1107.1242
Rights and permissions
About this article
Cite this article
Amariti, A., Forcella, D., Mariotti, A. et al. Negative refraction and superconductivity. J. High Energ. Phys. 2011, 104 (2011). https://doi.org/10.1007/JHEP10(2011)104
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2011)104