Abstract
The theory of superconductivity can be divided into two groups depending on whether it has multi-kink solutions. For example, the BCS theory and the Gross-Neveu model have metastable multi-kink solutions whereas the conventional Ginzburg-Landau theory without higher-derivative interactions does not have any multi-kink solutions. In this paper, we systematically examine the solutions of the holographic superconductor model to find out which group the model falls into. We show that the holographic superconductor model has metastable multi-kink solutions. In this sense, we find that the holographic superconductor model falls into the category of the BCS theory and the Gross- Neveu model. We also find that the holographic superconductor model has kink crystalline condensates which are well-fitted by the Jacobi elliptic functions.
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References
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].
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].
J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys.38 (1999) 1113 [hep-th/9711200] [INSPIRE].
M. Ammon and J. Erdmenger, Gauge/gravity duality: foundations and applications, Cambridge University Press, Cambridge U.K. (2015).
M. Natsuume, AdS/CFT duality user guide, Lect. Notes Phys.903 (2015) pp.1 [arXiv:1409.3575] [INSPIRE].
J. Zaanen, Y.W. Sun, Y. Liu and K. Schalm, Holographic duality in condensed matter physics, Cambridge University Press, Cambridge U.K. (2015).
S.A. Hartnoll, A. Lucas and S. Sachdev, Holographic quantum matter, arXiv:1612.07324 [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].
S.A. Hartnoll, C.P. Herzog and G.T. Horowitz, Holographic superconductors, JHEP12 (2008) 015 [arXiv:0810.1563] [INSPIRE].
S.S. Gubser, Breaking an Abelian gauge symmetry near a black hole horizon, Phys. Rev.D 78 (2008) 065034 [arXiv:0801.2977] [INSPIRE].
E. Nakano and W.-Y. Wen, Critical magnetic field in a holographic superconductor, Phys. Rev.D 78 (2008) 046004 [arXiv:0804.3180] [INSPIRE].
T. Albash and C.V. Johnson, A holographic superconductor in an external magnetic field, JHEP09 (2008) 121 [arXiv:0804.3466] [INSPIRE].
P. Basu, A. Mukherjee and H.-H. Shieh, Supercurrent: vector hair for an AdS black hole, Phys. Rev.D 79 (2009) 045010 [arXiv:0809.4494] [INSPIRE].
D. Arean, M. Bertolini, J. Evslin and T. Prochazka, On holographic superconductors with DC current, JHEP07 (2010) 060 [arXiv:1003.5661] [INSPIRE].
C.P. Herzog, P.K. Kovtun and D.T. Son, Holographic model of superfluidity, Phys. Rev.D 79 (2009) 066002 [arXiv:0809.4870] [INSPIRE].
V. Keranen, E. Keski-Vakkuri, S. Nowling and K.P. Yogendran, Dark solitons in holographic superfluids, Phys. Rev.D 80 (2009) 121901 [arXiv:0906.5217] [INSPIRE].
V. Keranen, E. Keski-Vakkuri, S. Nowling and K.P. Yogendran, Inhomogeneous structures in holographic superfluids: I. Dark solitons, Phys. Rev.D 81 (2010) 126011 [arXiv:0911.1866] [INSPIRE].
V. Keranen, E. Keski-Vakkuri, S. Nowling and K.P. Yogendran, Inhomogeneous structures in holographic superfluids: II. Vortices, Phys. Rev.D 81 (2010) 126012 [arXiv:0912.4280] [INSPIRE].
S. Lan, W. Liu and Y. Tian, Static structures of the BCS-like holographic superfluid in AdS4spacetime, Phys. Rev.D 95 (2017) 066013 [arXiv:1701.02921] [INSPIRE].
R. Flauger, E. Pajer and S. Papanikolaou, A striped holographic superconductor, Phys. Rev.D 83 (2011) 064009 [arXiv:1010.1775] [INSPIRE].
S. Cremonini, L. Li and J. Ren, Holographic pair and charge density waves, Phys. Rev.D 95 (2017) 041901 [arXiv:1612.04385] [INSPIRE].
A.I. Larkin and Y.N. Ovchinnikov, Nonuniform state of superconductors, Zh. Eksp. Teor. Fiz.47 (1964) 1136 [Sov. Phys. JETP20 (1965) 762] [INSPIRE].
P. Fulde and R.A. Ferrell, Superconductivity in a strong spin-exchange field, Phys. Rev.135 (1964) A550 [INSPIRE].
U. Klein, Two-dimensional superconductor in a tilted magnetic field: states with finite Cooper-pair momentum, Phys. Rev.B 69 (2004) 134518.
A.A. Zyuzin and A.Y. Zyuzin, Anomalous transition temperature oscillations in the Larkin-Ovchinnikov-Fulde-Ferrell state, Phys. Rev.B 79 (2009) 174514.
K. Aoyama, R. Beaird, D. E. Sheehy, and I. Vekhter, Inhomogeneous Superconducting States of Mesoscopic Thin-Walled Cylinders in External Magnetic Fields, Phys. Rev. Lett.110 (2013) 177004.
H.T. Quan and J.-X. Zhu, Interplay between the Fulde-Ferrell-like phase and Larkin-Ovchinnikov phase in the superconducting ring pierced by an Aharonov-Bohm flux, Phys. Rev.B 81 (2010) 014518.
R. Yoshii et al., Fulde-Ferrell-Larkin-Ovchinnikov states in a superconducting ring with magnetic fields: Phase diagram and the first-order phase transitions, Phys. Rev.B 92 (2015) 224512.
H.A. Radovan et al., Magnetic enhancement of superconductivity from electron spin domains, Nature425 (2003) 51.
S. Yonezawa et al., Anomalous In-Plane Anisotropy of the Onset of Superconductivity in (TMTSF)2Cl4 , Phys. Rev. Lett.100 (2008) 117002.
Y. Liao et al., Spin-imbalance in a one-dimensional Fermi gas, Nature467 (2010) 567.
S.A. Brazovskii, S.A. Gordynin and N.N. Kirova, Exact solution of the Peierls model with an arbitrary number of electrons in the unit cell, Pis. Zh. Eksp. Teor. Fiz.31 (1980) 486.
S.A. Brazovskii and N.N. Kirova, Excitons, polarons and bipolarons in conducting polymers, Pis. Zh. Eksp. Teor. Fiz.33 (1981) 6.
S.A. Brazovskii, N.N. Kirova and S.I. Matveenko, Peierls effect in conducting polymers, Zh. Eksp. Teor. Fiz.86 (1981) 743.
D.K. Campbell and A.R. Bishop, Soliton excitations in polyacetylene and relativistic field theory models, Nucl. Phys.B 200 (1982) 297 [INSPIRE].
A.J. Heeger, S. Kivelson, J.R. Schrieffer and W.P. Su, Solitons in conducting polymers, Rev. Mod. Phys.60 (1988) 781 [INSPIRE].
R. Jackiw and C. Rebbi, Solitons with Fermion number 1/2, Phys. Rev.D 13 (1976) 3398 [INSPIRE].
A.J. Niemi and G.W. Semenoff, Fermion number fractionization in quantum field theory, Phys. Rept.135 (1986) 99 [INSPIRE].
R. Casalbuoni and G. Nardulli, Inhomogeneous superconductivity in condensed matter and QCD, Rev. Mod. Phys.76 (2004) 263 [hep-ph/0305069] [INSPIRE].
M. Buballa and S. Carignano, Inhomogeneous chiral condensates, Prog. Part. Nucl. Phys.81 (2015) 39 [arXiv:1406.1367] [INSPIRE].
Y. Nambu and G. Jona-Lasinio, Dynamical model of elementary particles based on an analogy with superconductivity. 1., Phys. Rev.122 (1961) 345 [INSPIRE].
D.J. Gross and A. Neveu, Dynamical symmetry breaking in asymptotically free field theories, Phys. Rev.D 10 (1974) 3235 [INSPIRE].
G. Basar and G.V. Dunne, Self-consistent crystalline condensate in chiral Gross-Neveu and Bogoliubov-de Gennes systems, Phys. Rev. Lett.100 (2008) 200404 [arXiv:0803.1501] [INSPIRE].
G. Basar and G.V. Dunne, A twisted kink crystal in the chiral Gross-Neveu model, Phys. Rev.D 78 (2008) 065022 [arXiv:0806.2659] [INSPIRE].
G. Basar, G.V. Dunne and M. Thies, Inhomogeneous condensates in the thermodynamics of the chiral NJL(2) model, Phys. Rev.D 79 (2009) 105012 [arXiv:0903.1868] [INSPIRE].
R. Yoshii and M. Nitta, Nambu-Jona Lasinio and nonlinear sigma models in condensed matter systems, Symmetry11 (2019) 636.
D. Nickel, How many phases meet at the chiral critical point?, Phys. Rev. Lett.103 (2009) 072301 [arXiv:0902.1778] [INSPIRE].
D.A. Takahashi, S. Tsuchiya, R. Yoshii and M. Nitta, Fermionic solutions of chiral Gross-Neveu and Bogoliubov-de Gennes systems in nonlinear Schr´odinger hierarchy, Phys. Lett.B 718 (2012) 632 [arXiv:1205.3299] [INSPIRE].
G.T. Horowitz, Introduction to holographic superconductors, Lect. Notes Phys.828 (2011) 313 [arXiv:1002.1722] [INSPIRE].
P. Breitenlohner and D.Z. Freedman, Stability in gauged extended supergravity, Annals Phys.144 (1982) 249 [INSPIRE].
F. Correa, G.V. Dunne and M.S. Plyushchay, The Bogoliubov/de Gennes system, the AKNS hierarchy and nonlinear quantum mechanical supersymmetry, Annals Phys.324 (2009) 2522 [arXiv:0904.2768] [INSPIRE].
A.A. Zyuzin and A.Y. Zyuzin, Aharonov-Bohm effect in the superconducting LOFF state, JETP Lett.88 (2008) 136.
S. Nakamura, H. Ooguri and C.-S. Park, Gravity dual of spatially modulated phase, Phys. Rev.D 81 (2010) 044018 [arXiv:0911.0679] [INSPIRE].
A. Donos and J.P. Gauntlett, Holographic striped phases, JHEP08 (2011) 140 [arXiv:1106.2004] [INSPIRE].
Z. Xu et al., Holographic superfluid solitons with back-reaction, arXiv:1910.09253 [INSPIRE].
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Matsumoto, M., Nakamura, S. & Yoshii, R. Kink crystalline condensate and multi-kink solution in holographic superconductor. J. High Energ. Phys. 2020, 22 (2020). https://doi.org/10.1007/JHEP04(2020)022
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DOI: https://doi.org/10.1007/JHEP04(2020)022