Skip to main content

p-wave holographic superconductors from Born-Infeld black holes

A preprint version of the article is available at arXiv.

Abstract

We obtain (2+1) dimensional p-wave holographic superconductors from charged Born-Infeld black holes in the presence of massive charged vector fields in a bulk AdS4 Einstein-Born-Infeld theory through the AdS4-CF T3 correspondence. Below a certain critical transition temperature the charged black hole develops vector hair that corresponds to charged vector condensate in the strongly coupled (2+1) dimensional boundary field theory that breaks both the U(1) symmetry as well as the rotational invariance. The holographic free energy is computed for the boundary field theory which shows that the vector order parameter exhibits a rich phase structure involving zeroth order, first order, second order and retrograde phase transitions for different values of the backreaction and the Born-Infeld parameters. We numerically compute the ac conductivity for the p-wave superconducting phase of the strongly coupled (2+1) dimensional boundary field theory which also depends on the relative values of the parameters in the theory.

References

  1. J.M. Maldacena, The Large-N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].

    MathSciNet  Article  MATH  Google Scholar 

  2. 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].

    ADS  Article  MATH  Google Scholar 

  3. E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  4. 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].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  5. E. Witten, Anti-de Sitter space, thermal phase transition and confinement in gauge theories, Adv. Theor. Math. Phys. 2 (1998) 505 [hep-th/9803131] [INSPIRE].

    MathSciNet  Article  MATH  Google Scholar 

  6. S.S. Gubser, Breaking an Abelian gauge symmetry near a black hole horizon, Phys. Rev. D 78 (2008) 065034 [arXiv:0801.2977] [INSPIRE].

    ADS  Google Scholar 

  7. S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Building a Holographic Superconductor, Phys. Rev. Lett. 101 (2008) 031601 [arXiv:0803.3295] [INSPIRE].

    ADS  Article  Google Scholar 

  8. S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Holographic Superconductors, JHEP 12 (2008) 015 [arXiv:0810.1563] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  9. C.P. Herzog, Lectures on Holographic Superfluidity and Superconductivity, J. Phys. A 42 (2009) 343001 [arXiv:0904.1975] [INSPIRE].

    MathSciNet  MATH  Google Scholar 

  10. G.T. Horowitz, Introduction to Holographic Superconductors, Lect. Notes Phys. 828 (2011) 313 [arXiv:1002.1722] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  11. C.P. Herzog, An Analytic Holographic Superconductor, Phys. Rev. D 81 (2010) 126009 [arXiv:1003.3278] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  12. S. Sachdev, Condensed Matter and AdS/CFT, Lect. Notes Phys. 828 (2011) 273 [arXiv:1002.2947] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  13. M.M. Roberts and S.A. Hartnoll, Pseudogap and time reversal breaking in a holographic superconductor, JHEP 08 (2008) 035 [arXiv:0805.3898] [INSPIRE].

    ADS  Article  Google Scholar 

  14. G.T. Horowitz and M.M. Roberts, Zero Temperature Limit of Holographic Superconductors, JHEP 11 (2009) 015 [arXiv:0908.3677] [INSPIRE].

    ADS  Article  Google Scholar 

  15. K.-Y. Kim and M. Taylor, Holographic d-wave superconductors, JHEP 08 (2013) 112 [arXiv:1304.6729] [INSPIRE].

    ADS  Article  Google Scholar 

  16. 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].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  17. 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].

    ADS  Google Scholar 

  18. S.S. Gubser and S.S. Pufu, The Gravity dual of a p-wave superconductor, JHEP 11 (2008) 033 [arXiv:0805.2960] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  19. M. Ammon, J. Erdmenger, V. Grass, P. Kerner and A. O’Bannon, On Holographic p-wave Superfluids with Back-reaction, Phys. Lett. B 686 (2010) 192 [arXiv:0912.3515] [INSPIRE].

    ADS  Article  Google Scholar 

  20. H.-B. Zeng, W.-M. Sun and H.-S. Zong, Supercurrent in p-wave Holographic Superconductor, Phys. Rev. D 83 (2011) 046010 [arXiv:1010.5039] [INSPIRE].

    ADS  Google Scholar 

  21. 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].

    ADS  Google Scholar 

  22. F. Aprile, D. Rodriguez-Gomez and J.G. Russo, p-wave Holographic Superconductors and five-dimensional gauged Supergravity, JHEP 01 (2011) 056 [arXiv:1011.2172] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  23. L.A. Pando Zayas and D. Reichmann, A Holographic Chiral p x + ip y Superconductor, Phys. Rev. D 85 (2012) 106012 [arXiv:1108.4022] [INSPIRE].

    ADS  Google Scholar 

  24. D. Momeni, N. Majd and R. Myrzakulov, p-wave holographic superconductors with Weyl corrections, Europhys. Lett. 97 (2012) 61001 [arXiv:1204.1246] [INSPIRE].

    ADS  Article  Google Scholar 

  25. D. Roychowdhury, Holographic droplets in p-wave insulator/superconductor transition, JHEP 05 (2013) 162 [arXiv:1304.6171] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  26. R.-G. Cai, L. Li, L.-F. Li and R.-K. Su, Entanglement Entropy in Holographic P-Wave Superconductor/Insulator Model, JHEP 06 (2013) 063 [arXiv:1303.4828] [INSPIRE].

    ADS  Article  Google Scholar 

  27. R.-G. Cai, S. He, L. Li and L.-F. Li, A Holographic Study on Vector Condensate Induced by a Magnetic Field, JHEP 12 (2013) 036 [arXiv:1309.2098] [INSPIRE].

    ADS  Article  Google Scholar 

  28. R.-G. Cai, L. Li and L.-F. Li, A Holographic P-wave Superconductor Model, JHEP 01 (2014) 032 [arXiv:1309.4877] [INSPIRE].

    ADS  Article  Google Scholar 

  29. V.P. Maslov, Zeroth-order phase transitions, Math. Notes 76 (2004) 697.

    MathSciNet  Article  MATH  Google Scholar 

  30. T. Narayanan and A. Kumar, Reentrant phase transitions in multicomponent liquid mixtures, Phys. Rept. 249 (1994) 135.

    ADS  Article  Google Scholar 

  31. G.T. Horowitz and B. Way, Complete Phase Diagrams for a Holographic Superconductor/Insulator System, JHEP 11 (2010) 011 [arXiv:1007.3714] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  32. Y. Peng, Q. Pan and B. Wang, Various types of phase transitions in the AdS soliton background, Phys. Lett. B 699 (2011) 383 [arXiv:1104.2478] [INSPIRE].

    ADS  Article  Google Scholar 

  33. R.-G. Cai, S. He, L. Li and L.-F. Li, Entanglement Entropy and Wilson Loop in Stúckelberg Holographic Insulator/Superconductor Model, JHEP 10 (2012) 107 [arXiv:1209.1019] [INSPIRE].

    ADS  Article  Google Scholar 

  34. G.T. Horowitz and M.M. Roberts, Holographic Superconductors with Various Condensates, Phys. Rev. D 78 (2008) 126008 [arXiv:0810.1077] [INSPIRE].

    ADS  Google Scholar 

  35. M. Born and L. Infeld, Foundations of the new field theory, Proc. Roy. Soc. Lond. A 144 (1934) 425 [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  36. G.W. Gibbons and D.A. Rasheed, Electric-magnetic duality rotations in nonlinear electrodynamics, Nucl. Phys. B 454 (1995) 185 [hep-th/9506035] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  37. E.S. Fradkin and A.A. Tseytlin, Nonlinear Electrodynamics from Quantized Strings, Phys. Lett. B 163 (1985) 123 [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  38. T.K. Dey, Born-Infeld black holes in the presence of a cosmological constant, Phys. Lett. B 595 (2004) 484 [hep-th/0406169] [INSPIRE].

    ADS  MathSciNet  MATH  Google Scholar 

  39. R.-G. Cai, D.-W. Pang and A. Wang, Born-Infeld black holes in (A)dS spaces, Phys. Rev. D 70 (2004) 124034 [hep-th/0410158] [INSPIRE].

    ADS  MathSciNet  Google Scholar 

  40. J. Jing and S. Chen, Holographic superconductors in the Born-Infeld electrodynamics, Phys. Lett. B 686 (2010) 68 [arXiv:1001.4227] [INSPIRE].

    ADS  Article  Google Scholar 

  41. S. Gangopadhyay, Holographic superconductors in Born-Infeld electrodynamics and external magnetic field, Mod. Phys. Lett. A29 (2014) 1450088 [arXiv:1311.4416] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  42. J. Jing, Q. Pan and S. Chen, Holographic Superconductors with Power-Maxwell field, JHEP 11 (2011) 045 [arXiv:1106.5181] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  43. 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].

    ADS  Google Scholar 

  44. S. Gangopadhyay and D. Roychowdhury, Analytic study of properties of holographic superconductors in Born-Infeld electrodynamics, JHEP 05 (2012) 002 [arXiv:1201.6520] [INSPIRE].

    ADS  Article  Google Scholar 

  45. Y. Liu, Y. Peng and B. Wang, Gauss-Bonnet holographic superconductors in Born-Infeld electrodynamics with backreactions arXiv:1202.3586 [INSPIRE].

  46. D. Roychowdhury, Effect of external magnetic field on holographic superconductors in presence of nonlinear corrections, Phys. Rev. D 86 (2012) 106009 [arXiv:1211.0904] [INSPIRE].

    ADS  Google Scholar 

  47. Z. Zhao, Q. Pan, S. Chen and J. Jing, Notes on holographic superconductor models with the nonlinear electrodynamics, Nucl. Phys. B 871 (2013) 98 [arXiv:1212.6693] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  48. W. Yao and J. Jing, Analytical study on holographic superconductors for born-infeld electrodynamics in gauss-bonnet gravity with backreactions, JHEP 05 (2013) 101 [arXiv:1306.0064] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  49. G.W. Gibbons and S.W. Hawking, Action Integrals and Partition Functions in Quantum Gravity, Phys. Rev. D 15 (1977) 2752 [INSPIRE].

    ADS  Google Scholar 

  50. V. Balasubramanian and P. Kraus, A Stress tensor for Anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  51. F. Aprile, S. Franco, D. Rodriguez-Gomez and J.G. Russo, Phenomenological Models of Holographic Superconductors and Hall currents, JHEP 05 (2010) 102 [arXiv:1003.4487] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  52. T.H. Lin et al., Observation of a reentrant superconducting resistive transition in granular BaPb0.75Bi0.25O3 superconductor, Phys. Rev. B 29 (1984) 1493.

    ADS  Article  Google Scholar 

  53. Y. Zhao et al., Normal-state reentrant behavior in superconducting Bi2Sr2CaCu2O8 /Bi2Sr2Ca2Cu3O10 intergrowth single crystals, Phys. Rev. B 51 (1995) 3134.

    ADS  Article  Google Scholar 

  54. G.T. Horowitz, J.E. Santos and D. Tong, Optical Conductivity with Holographic Lattices, JHEP 07 (2012) 168 [arXiv:1204.0519] [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  55. G.T. Horowitz, J.E. Santos and D. Tong, Further Evidence for Lattice-Induced Scaling, JHEP 11 (2012) 102 [arXiv:1209.1098] [INSPIRE].

    ADS  Article  Google Scholar 

  56. T. Nishioka, S. Ryu and T. Takayanagi, Holographic Superconductor/Insulator Transition at Zero Temperature, JHEP 03 (2010) 131 [arXiv:0911.0962] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  57. N. Bai, Y.-H. Gao, B.-G. Qi and X.-B. Xu, Holographic insulator/superconductor phase transition in Born-Infeld electrodynamics arXiv:1212.2721 [INSPIRE].

  58. P. Chaturvedi and P. Basu, Holographic quantum phase transitions and interacting bulk scalars, Phys. Lett. B 739 (2014) 162 [arXiv:1409.4959] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

  59. S.R. Das, Holographic Quantum Quench, J. Phys. Conf. Ser. 343 (2012) 012027 [arXiv:1111.7275] [INSPIRE].

    Article  Google Scholar 

  60. P. Basu and S.R. Das, Quantum Quench across a Holographic Critical Point, JHEP 01 (2012) 103 [arXiv:1109.3909] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  61. P. Basu, D. Das, S.R. Das and T. Nishioka, Quantum Quench Across a Zero Temperature Holographic Superfluid Transition, JHEP 03 (2013) 146 [arXiv:1211.7076] [INSPIRE].

    ADS  MathSciNet  Article  MATH  Google Scholar 

Download references

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Pankaj Chaturvedi.

Additional information

ArXiv ePrint: 1501.06998

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Chaturvedi, P., Sengupta, G. p-wave holographic superconductors from Born-Infeld black holes. J. High Energ. Phys. 2015, 1 (2015). https://doi.org/10.1007/JHEP04(2015)001

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP04(2015)001

Keywords

  • Gauge-gravity correspondence
  • Holography and condensed matter physics (AdS/CMT)