Unbalanced Stückelberg holographic superconductors with backreaction

  • Ahmad Jamali Hafshejani
  • Seyed Ali Hosseini MansooriEmail author
Open Access
Regular Article - Theoretical Physics


We numerically investigate some properties of unbalanced Stückelberg holographic superconductors, by considering backreaction effects of fields on the background geometry. More precisely, we study the impacts of the chemical potential mismatch and Stückelberg mechanism on the condensation and conductivity types (electrical, spin, mixed, thermo-electric, thermo-spin and thermal conductivity). Our results show that the Stückelberg’s model parameters Cα and α not only have significant impacts on the phase transition, but also affect the conductivity pseudo-gap and the strength of conductivity fluctuations. Moreover, the effects of these parameters on a system will be gradually reduced as the imbalance grows. We also find that the influence of α on the amplitude of conductivity fluctuations depends on the magnitude of the both Cα and δμ/μ in the electric and thermal conductivity cases. This results in that increasing α can damp the conductivity fluctuations of an unbalanced system in contrast to balanced ones.


Holography and condensed matter physics (AdS/CMT) AdS-CFT Correspondence Black Holes Gauge-gravity correspondence 


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.


  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].MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Building a Holographic Superconductor, Phys. Rev. Lett. 101 (2008) 031601 [arXiv:0803.3295] [INSPIRE].
  3. [3]
    S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Holographic Superconductors, JHEP 12 (2008) 015 [arXiv:0810.1563] [INSPIRE].
  4. [4]
    C.P. Herzog, Lectures on Holographic Superfluidity and Superconductivity, J. Phys. A 42 (2009) 343001 [arXiv:0904.1975] [INSPIRE].
  5. [5]
    S.S. Gubser, C.P. Herzog, S.S. Pufu and T. Tesileanu, Superconductors from Superstrings, Phys. Rev. Lett. 103 (2009) 141601 [arXiv:0907.3510] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  6. [6]
    J. Bardeen, L.N. Cooper and J.R. Schrieffer, Microscopic theory of superconductivity, Phys. Rev. 106 (1957) 162 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    J. Bardeen, L.N. Cooper and J.R. Schrieffer, Theory of superconductivity, Phys. Rev. 108 (1957) 1175 [INSPIRE].
  8. [8]
    S.S. Gubser and A. Nellore, Low-temperature behavior of the Abelian Higgs model in anti-de Sitter space, JHEP 04 (2009) 008 [arXiv:0810.4554] [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    S.S. Gubser, Breaking an Abelian gauge symmetry near a black hole horizon, Phys. Rev. D 78 (2008) 065034 [arXiv:0801.2977] [INSPIRE].
  10. [10]
    C.P. Herzog, An Analytic Holographic Superconductor, Phys. Rev. D 81 (2010) 126009 [arXiv:1003.3278] [INSPIRE].
  11. [11]
    Q. Pan, B. Wang, E. Papantonopoulos, J. Oliveira and A.B. Pavan, Holographic Superconductors with various condensates in Einstein-Gauss-Bonnet gravity, Phys. Rev. D 81 (2010) 106007 [arXiv:0912.2475] [INSPIRE].
  12. [12]
    R.-G. Cai, Z.-Y. Nie and H.-Q. Zhang, Holographic p-wave superconductors from Gauss-Bonnet gravity, Phys. Rev. D 82 (2010) 066007 [arXiv:1007.3321] [INSPIRE].
  13. [13]
    S.A. Hosseini Mansoori, B. Mirza, A. Mokhtari, F.L. Dezaki and Z. Sherkatghanad, Weyl holographic superconductor in the Lifshitz black hole background, JHEP 07 (2016) 111 [arXiv:1602.07245] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  14. [14]
    S. Mahapatra, P. Phukon and T. Sarkar, Generalized Superconductors and Holographic Optics, JHEP 01 (2014) 135 [arXiv:1305.6273] [INSPIRE].ADSCrossRefGoogle Scholar
  15. [15]
    Z. Fan, Holographic superconductors with hyperscaling violation, JHEP 09 (2013) 048 [arXiv:1305.2000] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    Z. Sherkatghanad, B. Mirza and F. Lalehgani Dezaki, Exponential nonlinear electrodynamics and backreaction effects on holographic superconductor in the lifshitz black hole background, Int. J. Mod. Phys. D 27 (2017) 1750175 [arXiv:1708.04289] [INSPIRE].
  17. [17]
    J. Jing and S. Chen, Holographic superconductors in the Born-Infeld electrodynamics, Phys. Lett. B 686 (2010) 68 [arXiv:1001.4227] [INSPIRE].
  18. [18]
    Q. Pan, J. Jing, B. Wang and S. Chen, Analytical study on holographic superconductors with backreactions, JHEP 06 (2012) 087 [arXiv:1205.3543] [INSPIRE].ADSCrossRefGoogle Scholar
  19. [19]
    S.H. Hendi, Asymptotic charged BTZ black hole solutions, JHEP 03 (2012) 065 [arXiv:1405.4941] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  20. [20]
    K.K. Gomes, A.N. Pasupathy, A. Pushp, S. Ono, Y. Ando and A. Yazdani, isualizing pair formation on the atomic scale in the high-T c superconductor Bi 2 Sr 2 CaCu 2 O 8+δ , Nature 447 (2007) 569 [arXiv:0706.0214].
  21. [21]
    S. Franco, A. Garcia-Garcia and D. Rodriguez-Gomez, A General class of holographic superconductors, JHEP 04 (2010) 092 [arXiv:0906.1214] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  22. [22]
    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] [INSPIRE].
  23. [23]
    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].ADSCrossRefzbMATHGoogle Scholar
  24. [24]
    Q. Pan and B. Wang, General holographic superconductor models with Gauss-Bonnet corrections, Phys. Lett. B 693 (2010) 159 [arXiv:1005.4743] [INSPIRE].
  25. [25]
    Q. Pan and B. Wang, General holographic superconductor models with backreactions, arXiv:1101.0222 [INSPIRE].
  26. [26]
    D. Momeni, M.R. Setare and R. Myrzakulov, Condensation of the scalar field with Stuckelberg and Weyl Corrections in the background of a planar AdS-Schwarzschild black hole, Int. J. Mod. Phys. A 27 (2012) 1250128 [arXiv:1209.3104] [INSPIRE].
  27. [27]
    D.-Z. Ma, Y. Cao and J.-P. Wu, The Stückelberg holographic superconductors with Weyl corrections, Phys. Lett. B 704 (2011) 604 [arXiv:1201.2486] [INSPIRE].
  28. [28]
    G.T. Horowitz and M.M. Roberts, Holographic Superconductors with Various Condensates, Phys. Rev. D 78 (2008) 126008 [arXiv:0810.1077] [INSPIRE].
  29. [29]
    F. Bigazzi, A.L. Cotrone, D. Musso, N. Pinzani Fokeeva and D. Seminara, Unbalanced Holographic Superconductors and Spintronics, JHEP 02 (2012) 078 [arXiv:1111.6601] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  30. [30]
    D. Musso, Minimal Model for an Unbalanced Holographic Superconductor, PoS(Corfu2012)124 (2013) [arXiv:1304.6118] [INSPIRE].
  31. [31]
    S. Sachdev and B. Keimer, Quantum Criticality, Phys. Today 64N2 (2011) 29 [arXiv:1102.4628] [INSPIRE].
  32. [32]
    R. Casalbuoni and G. Nardulli, Inhomogeneous superconductivity in condensed matter and QCD, Rev. Mod. Phys. 76 (2004) 263 [hep-ph/0305069] [INSPIRE].
  33. [33]
    N. Iqbal, H. Liu, M. Mezei and Q. Si, Quantum phase transitions in holographic models of magnetism and superconductors, Phys. Rev. D 82 (2010) 045002 [arXiv:1003.0010] [INSPIRE].
  34. [34]
    N.F. Mott and R.H. Fowler, The electrical Conductivity of Transition Metals, Proc. Roy. Soc. Lond. A 153 (1936) 699.Google Scholar
  35. [35]
    N.F. Mott, The Resistance and Thermoelectric Properties of the Transition Metals, Proc. Roy. Soc. Lond. A 156 (1936) 368.Google Scholar
  36. [36]
    A.I. larkin and Y.N. Ovchinnikov, Nonuniform state of superconductors, Zh. Eksp. Teor. Fiz. 47 (1964) 1136 [INSPIRE].
  37. [37]
    P. Fulde and R.A. Ferrell, Superconductivity in a Strong Spin-Exchange Field, Phys. Rev. 135 (1964) A550 [INSPIRE].ADSCrossRefGoogle Scholar
  38. [38]
    J.P. Gauntlett, J. Sonner and T. Wiseman, Quantum Criticality and Holographic Superconductors in M-theory, JHEP 02 (2010) 060 [arXiv:0912.0512] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  39. [39]
    N. Bobev, A. Kundu, K. Pilch and N.P. Warner, Minimal Holographic Superconductors from Maximal Supergravity, JHEP 03 (2012) 064 [arXiv:1110.3454] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  40. [40]
    P. Breitenlohner and D.Z. Freedman, Stability in Gauged Extended Supergravity, Annals Phys. 144 (1982) 249 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  41. [41]
    L. Rosa, P. Vitale and C. Wetterich, Critical exponents of the Gross-Neveu model from the effective average action, Phys. Rev. Lett. 86 (2001) 958 [hep-th/0007093] [INSPIRE].ADSCrossRefGoogle Scholar
  42. [42]
    B. Rosenstein, H.-L. Yu and A. Kovner, Critical exponents of new universality classes, Phys. Lett. B 314 (1993) 381 [INSPIRE].
  43. [43]
    M.B. Silva Neto and N.F. Svatier, Nontrivial critical exponents for finite temperature chiral transitions at fixed total fermion number, Phys. Lett. B 441 (1998) 339 [hep-th/9802040] [INSPIRE].
  44. [44]
    P.C. van Son, H. van Kempen and P. Wyder, Boundary Resistance of the Ferromagnetic-Nonferromagnetic Metal Interface, Phys. Rev. Lett. 58 (1987) 2271.ADSCrossRefGoogle Scholar
  45. [45]
    M. Johnson and R.H. Silsbee, Thermodynamic analysis of interfacial transport and of the thermomagnetoelectric system, Phys. Rev. B 35 (1987) 4959.Google Scholar
  46. [46]
    B. Bellazzini, M. Burrello, M. Mintchev and P. Sorba, Quantum Field Theory on Star Graphs, Proc. Symp. Pure Math. 77 (2008) 639 [arXiv:0801.2852] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  47. [47]
    J. Polchinski and M.J. Strassler, Deep inelastic scattering and gauge/string duality, JHEP 05 (2003) 012 [hep-th/0209211] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  48. [48]
    B.S. Chandrasekhar, A note on the maximum critical field of high field superconductors, Appl. Phys. Lett. 1 (1962) 7.ADSCrossRefGoogle Scholar
  49. [49]
    A.M. Clogston, Upper Limit for the Critical Field in Hard Superconductors, Phys. Rev. Lett. 9 (1962) 266 [INSPIRE].
  50. [50]
    A. Amoretti and D. Musso, Magneto-transport from momentum dissipating holography, JHEP 09 (2015) 094 [arXiv:1502.02631] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  • Ahmad Jamali Hafshejani
    • 1
  • Seyed Ali Hosseini Mansoori
    • 2
    Email author
  1. 1.Physics DepartmentYazd UniversityYazdIran
  2. 2.Faculty of PhysicsShahrood University of TechnologyShahroodIran

Personalised recommendations