Abstract
We study the d-wave holographic superconductors (the d-wave model proposed in [arXiv:1003.2991[hep-th]]) immersed in constant external magnetic fields by using the analytic matching method and numerical computation. In the probe limit, we calculate the spatially dependent condensate solution in the presence of the magnetism and find that the expression for the upper critical magnetic field satisfies the relation given in the Ginzburg- Landau theory. The result shows that the upper critical field gradually increases to its maximum value B c2 at absolute zero temperature T = 0, while vanishing at the critical temperature T = T c. Moving away from the probe limit, we investigate the effect of spacetime backreaction on the critical temperature and the upper critical magnetic field. The magnetic fields as well as the electric fields acting as gravitational sources reduce the critical temperature of the superconductor and actually result in a dyonic black hole solution to the leading order. We obtain the expression for the upper critical magnetic field up to O(κ2) order. The analytic result is consistent with the numerical findings.
Similar content being viewed by others
References
J.M. Maldacena, The large-N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [Int. J. Theor. Phys. 38 (1999) 1113] [hep-th/9711200] [INSPIRE].
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, Phase transitions near black hole horizons, Class. Quant. Grav. 22 (2005) 5121 [hep-th/0505189] [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].
J.-W. Chen, Y.-J. Kao, D. Maity, W.-Y. Wen and C.-P. Yeh, Towards a holographic model of d-wave superconductors, Phys. Rev. D 81 (2010) 106008 [arXiv:1003.2991] [INSPIRE].
F. Benini, C.P. Herzog, R. Rahman and A. Yarom, Gauge gravity duality for d-wave superconductors: prospects and challenges, JHEP 11 (2010) 137 [arXiv:1007.1981] [INSPIRE].
S. Kanno, A note on Gauss-bonnet holographic superconductors, Class. Quant. Grav. 28 (2011) 127001 [arXiv:1103.5022] [INSPIRE].
Y. Brihaye and B. Hartmann, Holographic superconductors in 3 + 1 dimensions away from the probe limit, Phys. Rev. D 81 (2010) 126008 [arXiv:1003.5130] [INSPIRE].
L. Barcaly, R. Gregory, S. Kanno and P. Sutcliffe, Gauss-Bonnet holographic superconductors, JHEP 12 (2010) 029 [arXiv:1009.1991] [INSPIRE].
M. Siani, Holographic superconductors and higher curvature corrections, JHEP 12 (2010) 035 [arXiv:1010.0700] [INSPIRE].
M. Ammon, J. Erdmenger, M. Kaminski and P. Kerner, Superconductivity from gauge/gravity duality with flavor, Phys. Lett. B 680 (2009) 516 [arXiv:0810.2316] [INSPIRE].
M. Ammon, J. Erdmenger, P. Kerner and M. Kaminski, Flavor superconductivity from gauge/gravity duality, JHEP 10 (2009) 067 [arXiv:0903.1864] [INSPIRE].
T. Konstandin, G. Nardini and M. Quirós, Gravitational backreaction effects on the holographic phase transition, Phys. Rev. D 82 (2010) 083513 [arXiv:1007.1468] [INSPIRE].
R.-G. Cai, Z.-Y. Nie and H.-Q. Zhang, Holographic phase transitions of p-wave superconductors in Gauss-Bonnet gravity with back-reaction, Phys. Rev. D 83 (2011) 066013 [arXiv:1012.5559] [INSPIRE].
Q. Pan and B. Wang, General holographic superconductor models with backreactions, arXiv:1101.0222 [INSPIRE].
Y. Liu, Q. Pan and B. Wang, Holographic superconductor developed in BTZ black hole background with backreactions, Phys. Lett. B 702 (2011) 94 [arXiv:1106.4353] [INSPIRE].
Y. Liu, Y. Peng and B. Wang, Gauss-Bonnet holographic superconductors in Born-Infeld electrodynamics with backreactions, arXiv:1202.3586 [INSPIRE].
Y. Peng, X.-M. Kuang, Y. Liu and B. Wang, Phase transition in the holographic model of superfluidity with backreactions, arXiv:1204.2853 [INSPIRE].
J. Jing, L. Wang, Q. Pan and S. Chen, Holographic superconductors in Gauss-Bonnet gravity with Born-Infeld electrodynamics, Phys. Rev. D 83 (2011) 066010 [arXiv:1012.0644] [INSPIRE].
S. Chen, Q. Pan and J. Jing, Holographic superconductor models in the non-minimal derivative coupling theory, Chin. Phys. B 21 (2012) 040403 [arXiv:1012.3820] [INSPIRE].
X.H. Ge, Analytical calculation on critical magnetic field in holographic superconductors with backreaction, [arXiv:1105.4333] [INSPIRE].
C.P. Herzog, An analytic holographic superconductor, Phys. Rev. D 81 (2010) 126009 [arXiv:1003.3278] [INSPIRE].
G. Siopsis and J. Therrien, Analytic calculation of properties of holographic superconductors, JHEP 05 (2010) 013 [arXiv:1003.4275] [INSPIRE].
S. Gangopadhyay and D. Roychowdhury, Analytic study of properties of holographic superconductors in Born-Infeld electrodynamics, JHEP 05 (2012) 002 [arXiv:1201.6520] [INSPIRE].
R.-G. Cai, H.-F. Li and H.-Q. Zhang, Analytical studies on holographic insulator/superconductor phase transitions, Phys. Rev. D 83 (2011) 126007 [arXiv:1103.5568] [INSPIRE].
S.A. Hartnoll and P. Kovtun, Hall conductivity from dyonic black holes, Phys. Rev. D 76 (2007) 066001 [arXiv:0704.1160] [INSPIRE].
T. Albash and C.V. Johnson, A holographic superconductor in an external magnetic field, JHEP 09 (2008) 121 [arXiv:0804.3466] [INSPIRE].
E. Nakano and W.-Y. Wen, Critical magnetic field in a holographic superconductor, Phys. Rev. D 78 (2008) 046004 [arXiv:0804.3180] [INSPIRE].
W.-Y. Wen, Inhomogeneous magnetic field in AdS/CFT superconductor, arXiv:0805.1550 [INSPIRE].
T. Albash and C.V. Johnson, A holographic superconductor in an external magnetic field, JHEP 09 (2008) 121 [arXiv:0804.3466] [INSPIRE].
J.-P. Wu, The Stuckelberg holographic superconductors in constant external magnetic field, arXiv:1006.0456 [INSPIRE].
F. Preis, A. Rebhan and A. Schmitt, Holographic baryonic matter in a background magnetic field, J. Phys. G 39 (2012) 054006 [arXiv:1109.6904] [INSPIRE].
T. Albash and C.V. Johnson, Landau levels, magnetic fields and holographic Fermi liquids, J. Phys. A 43 (2010) 345404 [arXiv:1001.3700] [INSPIRE].
R.-G. Cai, L. Li, H.-Q. Zhang and Y.-L. Zhang, Magnetic field effect on the phase transition in AdS soliton spacetime, Phys. Rev. D 84 (2011) 126008 [arXiv:1109.5885] [INSPIRE].
E. Gubankova et al., Holographic fermions in external magnetic fields, Phys. Rev. D 84 (2011) 106003 [arXiv:1011.4051] [INSPIRE].
M. Montull, O. Pujolàs, A. Salvio and P.J. Silva, Magnetic response in the holographic insulator/superconductor transition, JHEP 04 (2012) 135 [arXiv:1202.0006] [INSPIRE].
H.-B. Zeng, Z.-Y. Fan and H.-S. Zong, d-wave holographic superconductor vortex lattice and non-abelian holographic superconductor droplet, Phys. Rev. D 82 (2010) 126008 [arXiv:1007.4151] [INSPIRE].
X.-H. Ge, B. Wang, S.-F. Wu and G.-H. Yang, Analytical study on holographic superconductors in external magnetic field, JHEP 08 (2010) 108 [arXiv:1002.4901] [INSPIRE].
R. Gregory, S. Kanno and J. Soda, Holographic superconductors with higher curvature corrections, JHEP 10 (2009) 010 [arXiv:0907.3203] [INSPIRE].
K. Maeda, M. Natsuume and T. Okamura, Vortex lattice for a holographic superconductor, Phys. Rev. D 81 (2010) 026002 [arXiv:0910.4475] [INSPIRE].
L. Romans, Supersymmetric, cold and lukewarm black holes in cosmological Einstein-Maxwell theory, Nucl. Phys. B 383 (1992) 395 [hep-th/9203018] [INSPIRE].
Y.M. Ma et al., Significantly enhanced critical current densities in MgB 2 tapes made by a scaleable nanocarbon addition route, Appl. Phys. Lett. 88 (2006) 072502 .
Y. Zhang et al., The effect of carbon doping on the upper critical field (H c2 ) and resistivity of MgB 2 by using sucrose (C 12 H 22 O 11 ) asthe carbon source, Supercond. Sci. Technol. 22 (2009) 015025 .
X.P. Zhang et al., Doping with a special carbohydrate, C 9 H 11 NO, to improve the J c -B properties of MgB 2 tapes, Supercond. Sci. Technol. 23 (2010) 025024.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1209.4272
Rights and permissions
About this article
Cite this article
Ge, XH., Tu, S.F. & Wang, B. d-wave holographic superconductors with backreaction in external magnetic fields. J. High Energ. Phys. 2012, 88 (2012). https://doi.org/10.1007/JHEP09(2012)088
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP09(2012)088