Abstract
We study general models of holographic superconductivity parametrized by four arbitrary functions of a neutral scalar field of the bulk theory. The models can accommodate several features of real superconductors, like arbitrary critical temperatures and critical exponents in a certain range, and perhaps impurities or boundary or thickness effects. We find analytical expressions for the critical exponents of the general model and show that they satisfy the Rushbrooke identity. An important subclass of models exhibit second order phase transitions. A study of the specific heat shows that general models can also describe holographic superconductors undergoing first, second and third (or higher) order phase transitions. We discuss how small deformations of the HHH model can lead to the appearance of resonance peaks in the conductivity, which increase in number and become narrower as the temperature is gradually decreased, without the need for tuning mass of the scalar to be close to the Breitenlohner-Freedman bound. Finally, we investigate the inclusion of a generalized “theta term” producing Hall effect without magnetic field.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
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] [SPIRES].
S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from non-critical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [SPIRES].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [SPIRES].
S.S. Gubser, Breaking an Abelian gauge symmetry near a black hole horizon, Phys. Rev. D 78 (2008) 065034 [arXiv:0801.2977] [SPIRES].
S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Building a holographic superconductor, Phys. Rev. Lett. 101 (2008) 031601 [arXiv:0803.3295] [SPIRES].
S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Holographic superconductors, JHEP 12 (2008) 015 [arXiv:0810.1563] [SPIRES].
R.D.Parks, Superconductivity, Vol. I, II, R.D. Parks ed. M. Dekker, Inc., New York U.S.A. (1969).
S. Franco, A. Garcia-Garcia and D. Rodriguez-Gomez, A general class of holographic superconductors, JHEP 04 (2010) 092 [arXiv:0906.1214] [SPIRES].
S. Franco, A.M. Garcia-Garcia and D. Rodriguez-Gomez, A holographic approach to phase transitions, Phys. Rev. D 81 (2010) 041901 [arXiv:0911.1354] [SPIRES].
F. Aprile and J.G. Russo, Models of holographic superconductivity, Phys. Rev. D 81 (2010) 026009 [arXiv:0912.0480] [SPIRES].
P.G. de Gennes, Superconductivity of metals and alloys, P. Gilles de Gennes, Perseus (1966).
I.R. Klebanov and E. Witten, AdS/CFT correspondence and symmetry breaking, Nucl. Phys. B 556 (1999) 89 [hep-th/9905104] [SPIRES].
J.P. Gauntlett, J. Sonner and T. Wiseman, Quantum criticality and holographic superconductors in M-theory, JHEP 02 (2010) 060 [arXiv:0912.0512] [SPIRES].
S.S. Gubser, C.P. Herzog, S.S. Pufu and T. Tesileanu, Superconductors from superstrings, Phys. Rev. Lett. 103 (2009) 141601 [arXiv:0907.3510] [SPIRES].
J.P. Gauntlett, J. Sonner and T. Wiseman, Holographic superconductivity in M-theory, Phys. Rev. Lett. 103 (2009) 151601 [arXiv:0907.3796] [SPIRES].
G.T. Horowitz and M.M. Roberts, Holographic superconductors with various condensates, Phys. Rev. D 78 (2008) 126008 [arXiv:0810.1077] [SPIRES].
F. Denef and S.A. Hartnoll, Landscape of superconducting membranes, Phys. Rev. D 79 (2009) 126008 [arXiv:0901.1160] [SPIRES].
N. Iqbal, H. Liu, M. Mezei and Q. Si, Quantum phase transitions in holographic models of magnetism and superconductors, arXiv:1003.0010 [SPIRES].
R. Gregory, S. Kanno and J. Soda, Holographic superconductors with higher curvature corrections, JHEP 10 (2009) 010 [arXiv:0907.3203] [SPIRES].
K. Maeda, M. Natsuume and T. Okamura, Universality class of holographic superconductors, Phys. Rev. D 79 (2009) 126004 [arXiv:0904.1914] [SPIRES].
R. Werner, Low-temperature electronic properties of Sr 2 RuO 4 . II. Superconductivity, Phys. Rev. B 67 (2003) 014505.
T. Faulkner, H. Liu, J. McGreevy and D. Vegh, Emergent quantum criticality,Fermi surfaces and AdS2, arXiv:0907.2694 [SPIRES].
G.T. Horowitz and M.M. Roberts, Zero temperature limit of holographic superconductors, JHEP 11 (2009) 015 [arXiv:0908.3677] [SPIRES].
S.A. Hartnoll and P. Kovtun, Hall conductivity from dyonic black holes, Phys. Rev. D 76 (2007) 066001 [arXiv:0704.1160] [SPIRES].
M.M. Roberts and S.A. Hartnoll, Pseudogap and time reversal breaking in a holographic superconductor, JHEP 08 (2008) 035 [arXiv:0805.3898] [SPIRES].
G. Metalidis and P. Bruno, Topological hall effect studied in simple models, Phys. Rev. B 74 (2006) 045327.
R.M. Lutchyn, P. Nagornykh and Victor M. Yakovenko, Frequency and temperature dependence of the anomalous ac Hall conductivity in a chiral p x + ip y superconductor with impurities, Phys. Rev. B 80 (2009) 104508.
C.P. Herzog, An analytic holographic superconductor, arXiv:1003.3278 [SPIRES].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1003.4487
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Aprile, F., Franco, S., Rodríguez-Gómez, D. et al. Phenomenological models of holographic superconductors and hall currents. J. High Energ. Phys. 2010, 102 (2010). https://doi.org/10.1007/JHEP05(2010)102
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2010)102