Abstract
We study the competition between the p-wave and the p+ip superfluid solutions in a holographic model with applied magnetic field intensity H. We find that when H is turned on, both the grand potential and the critical temperature of the p+ip solution are shifted, while the p-wave solution is only slightly affected. Combining the effect of H and back reaction parameter b, we build H − T phase diagrams with a slit region of p+ip phase. The zero (or finite) value of H at the starting point of the slit region is related to second (or first) order of the p-wave phase transition at zero magnetic intensity, which should be universal in systems with degenerate critical points (spinodal points) at zero magnetic field.
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References
J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys. 2 (1998) 231 [hep-th/9711200] [INSPIRE].
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 and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
S.S. Gubser, Breaking an Abelian gauge symmetry near a black hole horizon, Phys. Rev. D 78 (2008) 065034 [arXiv:0801.2977] [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].
C.P. Herzog, P.K. Kovtun and D.T. Son, Holographic model of superfluidity, Phys. Rev. D 79 (2009) 066002 [arXiv:0809.4870] [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.S. Gubser and S.S. Pufu, The Gravity dual of a p-wave superconductor, JHEP 11 (2008) 033 [arXiv:0805.2960] [INSPIRE].
R.-G. Cai, L. Li and L.-F. Li, A Holographic P-wave Superconductor Model, JHEP 01 (2014) 032 [arXiv:1309.4877] [INSPIRE].
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].
L.-F. Li, R.-G. Cai, L. Li and C. Shen, Entanglement entropy in a holographic p-wave superconductor model, Nucl. Phys. B 894 (2015) 15 [arXiv:1310.6239] [INSPIRE].
Y.-B. Wu, J.-W. Lu, W.-X. Zhang, C.-Y. Zhang, J.-B. Lu and F. Yu, Holographic p-wave superfluid, Phys. Rev. D 90 (2014) 126006 [arXiv:1410.5243] [INSPIRE].
M. Rogatko and K.I. Wysokinski, P-wave holographic superconductor/insulator phase transitions affected by dark matter sector, JHEP 03 (2016) 215 [arXiv:1508.02869] [INSPIRE].
Q. Pan and S.-J. Zhang, Revisiting holographic superconductors with hyperscaling violation, Eur. Phys. J. C 76 (2016) 126 [arXiv:1510.09199] [INSPIRE].
C. Lai, Q. Pan, J. Jing and Y. Wang, Analytical study on holographic superfluid in AdS soliton background, Phys. Lett. B 757 (2016) 65 [arXiv:1601.00134] [INSPIRE].
Z.-Y. Nie, Q. Pan, H.-B. Zeng and H. Zeng, Split degenerate states and stable p + i p phases from holography, Eur. Phys. J. C 77 (2017) 69 [arXiv:1611.07278] [INSPIRE].
J.-W. Lu, Y.-B. Wu, B.-P. Dong and H. Liao, Holographic p-wave superconductor in Lifshitz gravity with RF2 correction, Phys. Lett. B 785 (2018) 517 [INSPIRE].
Y. Huang, Q. Pan, W.L. Qian, J. Jing and S. Wang, Holographic p-wave superfluid with Weyl corrections, Sci. China Phys. Mech. Astron. 63 (2020) 230411.
J.-W. Lu, Y.-B. Wu, B.-P. Dong and Y. Zhang, Holographic p-wave superconductor with C2F2 correction, Eur. Phys. J. C 80 (2020) 114 [INSPIRE].
Y. Lv, X. Qiao, M. Wang, Q. Pan, W.-L. Qian and J. Jing, Holographic p-wave superfluid in the AdS soliton background with RF 2 corrections, Phys. Lett. B 802 (2020) 135216 [arXiv:2001.08364] [INSPIRE].
Z.-Y. Nie, Y.-P. Hu and H. Zeng, The holographic p + ip solution failed to win the competition in dRGT massive gravity, Eur. Phys. J. C 80 (2020) 1015 [arXiv:2003.12989] [INSPIRE].
X. Qiao, L. OuYang, D. Wang, Q. Pan and J. Jing, Holographic superconductors in 4D Einstein-Gauss-Bonnet gravity, JHEP 12 (2020) 192 [arXiv:2005.01007] [INSPIRE].
J.W. Lu, Y.B. Wu, H.F. Li, B.P. Dong, Y. Zheng and H. Liao, Holographic p-wave superconductors with momentum relaxation, Phys. Lett. B 819 (2021) 136448.
Z.-Y. Nie, R.-G. Cai, X. Gao and H. Zeng, Competition between the s-wave and p-wave superconductivity phases in a holographic model, JHEP 11 (2013) 087 [arXiv:1309.2204] [INSPIRE].
I. Amado, D. Arean, A. Jimenez-Alba, L. Melgar and I. Salazar Landea, Holographic s+p Superconductors, Phys. Rev. D 89 (2014) 026009 [arXiv:1309.5086] [INSPIRE].
D. Momeni, M. Raza and R. Myrzakulov, Analytical coexistence of s-, p-, (s + p)-phases of a holographic superconductor, Int. J. Geom. Meth. Mod. Phys. 12 (2015) 1550048 [arXiv:1310.1735] [INSPIRE].
Z.-Y. Nie, R.-G. Cai, X. Gao, L. Li and H. Zeng, Phase transitions in a holographic s + p model with back-reaction, Eur. Phys. J. C 75 (2015) 559 [arXiv:1501.00004] [INSPIRE].
S. Liu and Y.-Q. Wang, Holographic model of hybrid and coexisting s-wave and p-wave Josephson junction, Eur. Phys. J. C 75 (2015) 493 [arXiv:1504.06918] [INSPIRE].
Z.-Y. Nie and H. Zeng, P-T phase diagram of a holographic s + p model from Gauss-Bonnet gravity, JHEP 10 (2015) 047 [arXiv:1505.02289] [INSPIRE].
Y.-Q. Wang and S. Liu, Holographic s-wave and p-wave Josephson junction with backreaction, JHEP 11 (2016) 127 [arXiv:1608.06364] [INSPIRE].
R. Li, T. Zi and H. Zhang, Holographic s + p insulator/superconductor phase transition at zero temperature, Phys. Lett. B 766 (2017) 238 [INSPIRE].
D. Momeni, N. Majd, M. Mohammadzaheri, P. Channuie and M. Al Ajmi, Chaos in balanced and unbalanced holographic s+p superconductors, Results Phys. 14 (2019) 102449 [arXiv:1908.07994] [INSPIRE].
C.-Y. Xia, Z.-Y. Nie, H.-B. Zeng and Y. Zhang, Uniform quenching processes in a holographic s + p model with reentrance, Eur. Phys. J. C 81 (2021) 882 [arXiv:2102.01083] [INSPIRE].
M. Nishida, Phase Diagram of a Holographic Superconductor Model with s-wave and d-wave, JHEP 09 (2014) 154 [arXiv:1403.6070] [INSPIRE].
X. Li, Z.-Y. Nie and Y. Tian, Holographic boiling and generalized thermodynamic description beyond local equilibrium, JHEP 09 (2020) 063 [arXiv:2003.12987] [INSPIRE].
X.-K. Zhang, C.-Y. Xia, Z.-Y. Nie and H. Zeng, Holographic multicondensate with nonlinear terms, Phys. Rev. D 105 (2022) 046016 [arXiv:2105.14294] [INSPIRE].
D. Vollhardt and P. Wolfle, The superfluid phases of helium 3, Taylor and Francis Inc., Philadelphia, U.S.A. (1990).
L.J. Romans, Supersymmetric, cold and lukewarm black holes in cosmological Einstein-Maxwell theory, Nucl. Phys. B 383 (1992) 395 [hep-th/9203018] [INSPIRE].
E. Nakano and W.-Y. Wen, Critical magnetic field in a holographic superconductor, Phys. Rev. D 78 (2008) 046004 [arXiv:0804.3180] [INSPIRE].
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].
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Yang, YN., Xia, CY., Nie, ZY. et al. H − T phase diagrams of a holographic p-wave superfluid. J. High Energ. Phys. 2022, 13 (2022). https://doi.org/10.1007/JHEP04(2022)013
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DOI: https://doi.org/10.1007/JHEP04(2022)013