Holographic p-wave superconductor with C${}^2$F${}^2$ correction

Via numerical and analytical method, we construct the holographic p-wave conductor/superconductor model with C${}^2$F${}^2$ correction (where C${}^2$F${}^2$=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${}^2$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.