Holographic p -wave superconductor with $$C^2F^2$$C2F2 correction
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Regular Article - Theoretical Physics
Holographic p-wave superconductor with C 2 F 2 correction Jun-Wang Lu1,a , Ya-Bo Wu2,b , Bao-Ping Dong1, Yu Zhang3 1
School of Physics and Electronics, Qiannan Normal University for Nationalities, Duyun 558000, People’s Republic of China Department of Physics, Liaoning Normal University, Dalian 116029, People’s Republic of China 3 Faculty of Science, Kunming University of Science and Technology, Kunming 650500, People’s Republic of China
2
Received: 21 October 2019 / Accepted: 10 January 2020 © The Author(s) 2020
Abstract Via numerical and analytical method, we construct the holographic p-wave conductor/superconductor αβ μν model with C 2 F 2 correction (where C 2 F 2 = Cμν Cαβ Fρσ αβ
F ρσ , and Cμν and Fρσ denotes the Weyl tensor and gauge field strength, respectively.)in the four-dimensional Schwarzschild-AdS black hole, and mainly study the effects of C 2 F 2 correction parameter denoted by γ on the properties of superconductors. The results show that for all values of the C 2 F 2 parameter, there always exists a critical temperature below which the vector hair appears. Meanwhile, the critical temperature increases with the improving C 2 F 2 parameter γ , which suggests that the improving C 2 F 2 parameter enhances the superconductor phase transition. Furthermore, at the critical temperature, the real part of conductivity reproduces respectively a Drude-like peak and an obviously pronounced peak for some value of nonvanishing C 2 F 2 parameter. At the low temperature, a clear energy gap can be observed at the intermediate frequency and the ratio of the energy gap to the critical temperature decreases with the increasing C 2 F 2 parameter, which is consistent with the effect of the C 2 F 2 parameter on the critical temperature. In addition, the analytical results agree well with the numerical results, which means that the analytical Sturm–Liouville method is still reliable in the grand canonical ensemble.
1 Introduction The AdS/CFT correspondence relates the weak gravitational theory in the anti-de Sitter spacetime to the strong quantum field theory lived on its conformal boundary, and thus provides us a new theoretical framework to study the strongly coupled systems [1,2]. Over the past years, the AdS/CFT correspondence(or its generalized version, the gauge/gravity a e-mail:
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duality) has been intensively applied in many aspects in condensed systems [3–9], especially the high Tc superconductor (s-wave), which was realized successfully via an Einstein–Maxwell theory coupled to a complex scalar field in the Schwarzschild-AdS black hole in the probe limit [10,11]. After that, the holographic superconductor model was extended to the SU (2) p-wave superconductor model [12], d-wave superconductor model [13], the insulator/superconductor model [14], the competition and coexistence of two order parameters [15–18], Sturm–Liouville (S– L) method [19–21], the backreaction from the matter field to the gravi
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