Abstract
Via numerical and analytical method, we construct the holographic p-wave conductor/superconductor model with C^2F^2 correction (where C^2F^2=C_{mu nu }^{alpha beta }C_{ alpha beta }^{mu nu }F_{rho sigma }F^{rho sigma }, and C_{mu nu }^{alpha beta } and F_{rho sigma } denotes the Weyl tensor and gauge field strength, respectively.)in the four-dimensional Schwarzschild-AdS black hole, and mainly study the effects of C^2F^2 correction parameter denoted by gamma on the properties of superconductors. The results show that for all values of the C^2F^2 parameter, there always exists a critical temperature below which the vector hair appears. Meanwhile, the critical temperature increases with the improving C^2F^2 parameter gamma , which suggests that the improving C^2F^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^2F^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^2F^2 parameter, which is consistent with the effect of the C^2F^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.
Highlights
Considering the Weyl term C F2 composed of the coupling of the Weyl tensor Cμρσν and the Maxwell field strength Fαβ, which was firstly introduced to realize the breakdown of the electromagnetic self-duality from a holographic perspective [41], Refs. [42,43] studied the effects of the 1 λ corrections on the s-wave superconductor model, and found that the increasing Weyl correction enhances the condensate and decreases the ratio of the energy gap to the critical temperature
To study systemically the effects of the C2 F2 correction on the superconductor phase transition, we plot the critical temperature with respect to the C2 F2 parameter γ in the right panel of Fig. 1 and list the related results in Table 1, from which we find that the critical temperature calculated from the numerical method increases with the increasing C2 F2 parameter γ, which means that the increasing C2 F2 correction makes the superconductor phase transition easier
We mainly studied the influences of the C2 F2 parameter γ in the range
Summary
L) method [19,20,21], the backreaction from the matter field to the gravitational background [22], the effects of external magnetic field [23,24] as well as the lattice effects [25,26,27,28,29], see, for example, Refs. [30,31,32] for reviews. [42,43] studied the effects of 1 λ corrections on the s-wave superconductor model, and found that the increasing Weyl correction enhances the condensate and decreases the ratio of the energy gap to the critical temperature. In order to investigate the 1 λ effects, the MCV p-wave superconductor model was constructed in Lifshitz gravity [61], by including nonlinear electrodynamics [62,63,64] and the R F2 correction [65,66]. 2, we construct the MCV p-wave superconductor model and mainly study the effects of the 6 derivative on the critical temperature and the condensate as well as the conductivity. The final section is devoted to the conclusions and discussions
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