p-wave holographic superconductors from Born-Infeld black holes

Open Access
Regular Article - Theoretical Physics

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.

Keywords

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

Notes

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.

References

  1. [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].MathSciNetCrossRefMATHGoogle Scholar
  2. [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].ADSCrossRefMATHGoogle Scholar
  3. [3]
    E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  4. [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].ADSMathSciNetCrossRefMATHGoogle Scholar
  5. [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].MathSciNetCrossRefMATHGoogle Scholar
  6. [6]
    S.S. Gubser, Breaking an Abelian gauge symmetry near a black hole horizon, Phys. Rev. D 78 (2008) 065034 [arXiv:0801.2977] [INSPIRE].ADSGoogle Scholar
  7. [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].ADSCrossRefGoogle Scholar
  8. [8]
    S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Holographic Superconductors, JHEP 12 (2008) 015 [arXiv:0810.1563] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  9. [9]
    C.P. Herzog, Lectures on Holographic Superfluidity and Superconductivity, J. Phys. A 42 (2009) 343001 [arXiv:0904.1975] [INSPIRE].MathSciNetMATHGoogle Scholar
  10. [10]
    G.T. Horowitz, Introduction to Holographic Superconductors, Lect. Notes Phys. 828 (2011) 313 [arXiv:1002.1722] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  11. [11]
    C.P. Herzog, An Analytic Holographic Superconductor, Phys. Rev. D 81 (2010) 126009 [arXiv:1003.3278] [INSPIRE].ADSMathSciNetGoogle Scholar
  12. [12]
    S. Sachdev, Condensed Matter and AdS/CFT, Lect. Notes Phys. 828 (2011) 273 [arXiv:1002.2947] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  13. [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].ADSCrossRefGoogle Scholar
  14. [14]
    G.T. Horowitz and M.M. Roberts, Zero Temperature Limit of Holographic Superconductors, JHEP 11 (2009) 015 [arXiv:0908.3677] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    K.-Y. Kim and M. Taylor, Holographic d-wave superconductors, JHEP 08 (2013) 112 [arXiv:1304.6729] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [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].ADSMathSciNetCrossRefMATHGoogle Scholar
  17. [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].ADSGoogle Scholar
  18. [18]
    S.S. Gubser and S.S. Pufu, The Gravity dual of a p-wave superconductor, JHEP 11 (2008) 033 [arXiv:0805.2960] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  19. [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].ADSCrossRefGoogle Scholar
  20. [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].ADSGoogle Scholar
  21. [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].ADSGoogle Scholar
  22. [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].ADSMathSciNetCrossRefMATHGoogle Scholar
  23. [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].ADSGoogle Scholar
  24. [24]
    D. Momeni, N. Majd and R. Myrzakulov, p-wave holographic superconductors with Weyl corrections, Europhys. Lett. 97 (2012) 61001 [arXiv:1204.1246] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    D. Roychowdhury, Holographic droplets in p-wave insulator/superconductor transition, JHEP 05 (2013) 162 [arXiv:1304.6171] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  26. [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].ADSCrossRefGoogle Scholar
  27. [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].ADSCrossRefGoogle Scholar
  28. [28]
    R.-G. Cai, L. Li and L.-F. Li, A Holographic P-wave Superconductor Model, JHEP 01 (2014) 032 [arXiv:1309.4877] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    V.P. Maslov, Zeroth-order phase transitions, Math. Notes 76 (2004) 697.MathSciNetCrossRefMATHGoogle Scholar
  30. [30]
    T. Narayanan and A. Kumar, Reentrant phase transitions in multicomponent liquid mixtures, Phys. Rept. 249 (1994) 135.ADSCrossRefGoogle Scholar
  31. [31]
    G.T. Horowitz and B. Way, Complete Phase Diagrams for a Holographic Superconductor/Insulator System, JHEP 11 (2010) 011 [arXiv:1007.3714] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  32. [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].ADSCrossRefGoogle Scholar
  33. [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].ADSCrossRefGoogle Scholar
  34. [34]
    G.T. Horowitz and M.M. Roberts, Holographic Superconductors with Various Condensates, Phys. Rev. D 78 (2008) 126008 [arXiv:0810.1077] [INSPIRE].ADSGoogle Scholar
  35. [35]
    M. Born and L. Infeld, Foundations of the new field theory, Proc. Roy. Soc. Lond. A 144 (1934) 425 [INSPIRE].ADSCrossRefMATHGoogle Scholar
  36. [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].ADSCrossRefMATHGoogle Scholar
  37. [37]
    E.S. Fradkin and A.A. Tseytlin, Nonlinear Electrodynamics from Quantized Strings, Phys. Lett. B 163 (1985) 123 [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  38. [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].ADSMathSciNetMATHGoogle Scholar
  39. [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].ADSMathSciNetGoogle Scholar
  40. [40]
    J. Jing and S. Chen, Holographic superconductors in the Born-Infeld electrodynamics, Phys. Lett. B 686 (2010) 68 [arXiv:1001.4227] [INSPIRE].ADSCrossRefGoogle Scholar
  41. [41]
    S. Gangopadhyay, Holographic superconductors in Born-Infeld electrodynamics and external magnetic field, Mod. Phys. Lett. A29 (2014) 1450088 [arXiv:1311.4416] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  42. [42]
    J. Jing, Q. Pan and S. Chen, Holographic Superconductors with Power-Maxwell field, JHEP 11 (2011) 045 [arXiv:1106.5181] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  43. [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].ADSGoogle Scholar
  44. [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].ADSCrossRefGoogle Scholar
  45. [45]
    Y. Liu, Y. Peng and B. Wang, Gauss-Bonnet holographic superconductors in Born-Infeld electrodynamics with backreactions arXiv:1202.3586 [INSPIRE].
  46. [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].ADSGoogle Scholar
  47. [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].ADSMathSciNetCrossRefMATHGoogle Scholar
  48. [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].ADSMathSciNetCrossRefMATHGoogle Scholar
  49. [49]
    G.W. Gibbons and S.W. Hawking, Action Integrals and Partition Functions in Quantum Gravity, Phys. Rev. D 15 (1977) 2752 [INSPIRE].ADSGoogle Scholar
  50. [50]
    V. Balasubramanian and P. Kraus, A Stress tensor for Anti-de Sitter gravity, Commun. Math. Phys. 208 (1999) 413 [hep-th/9902121] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  51. [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].ADSCrossRefMATHGoogle Scholar
  52. [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.ADSCrossRefGoogle Scholar
  53. [53]
    Y. Zhao et al., Normal-state reentrant behavior in superconducting Bi2Sr2CaCu2O8 /Bi2Sr2Ca2Cu3O10 intergrowth single crystals, Phys. Rev. B 51 (1995) 3134.ADSCrossRefGoogle Scholar
  54. [54]
    G.T. Horowitz, J.E. Santos and D. Tong, Optical Conductivity with Holographic Lattices, JHEP 07 (2012) 168 [arXiv:1204.0519] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  55. [55]
    G.T. Horowitz, J.E. Santos and D. Tong, Further Evidence for Lattice-Induced Scaling, JHEP 11 (2012) 102 [arXiv:1209.1098] [INSPIRE].ADSCrossRefGoogle Scholar
  56. [56]
    T. Nishioka, S. Ryu and T. Takayanagi, Holographic Superconductor/Insulator Transition at Zero Temperature, JHEP 03 (2010) 131 [arXiv:0911.0962] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  57. [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. [58]
    P. Chaturvedi and P. Basu, Holographic quantum phase transitions and interacting bulk scalars, Phys. Lett. B 739 (2014) 162 [arXiv:1409.4959] [INSPIRE].ADSMathSciNetCrossRefMATHGoogle Scholar
  59. [59]
    S.R. Das, Holographic Quantum Quench, J. Phys. Conf. Ser. 343 (2012) 012027 [arXiv:1111.7275] [INSPIRE].CrossRefGoogle Scholar
  60. [60]
    P. Basu and S.R. Das, Quantum Quench across a Holographic Critical Point, JHEP 01 (2012) 103 [arXiv:1109.3909] [INSPIRE].ADSCrossRefMATHGoogle Scholar
  61. [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].ADSMathSciNetCrossRefMATHGoogle Scholar

Copyright information

© The Author(s) 2015

Authors and Affiliations

  1. 1.Department of PhysicsIndian Institute of TechnologyKanpurIndia

Personalised recommendations