Conductivity of the holographic p-wave superconductors with higher order corrections

Abstract

We investigate the holographic p-wave superconductors in the presence of the higher order corrections on the gravity as well as on the gauge field side. On the gravity side, we add the Gauss-Bonnet curvature correction terms, while on the gauge field side we take the nonlinear Lagrangian in the form F + bF 2 , where F is the Maxwell Lagrangian and b indicates the strength of nonlinearity. We employ the shooting method for the numerical calculations in order to obtain the ratio of the critical temperature Tc over ρ 1/(d−2) . We observe that by increasing the values of the mass and the nonlinear parameters the critical temperature decreases and thus the condensation becomes harder to form. In addition, the stronger Gauss-Bonnet parameter α hinders the superconducting phase in Gauss-Bonnet gravity. Furthermore, we calculate the electrical conductivity based on the holographic setup. The real and imaginary parts are related to each other by Kramers-Kronig relation which indicates a delta function and pole in low frequency regime, respectively. However, at enough large frequencies the trend of real part can be interpreted by Re[σ] = ω (d−4) . Moreover, in holographic model the ratio ωg/Tc is always much larger than the BCS value 3.5 due to the strong coupling of holographic superconductors. In both gravity kinds, decreasing the temperature or increasing the effect of nonlinearity shifts the gap frequency toward larger values. Besides, the gap frequency is occurred at larger values by enlarging the Gauss-Bonnet parameter. In general, the behavior of conductivity depends on the choice of the mass, the nonlinear and the Gauss-Bonnet parameters.

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

“…[55,61] and agree with the ones for the case of b = 0 and d = 4 in Ref. [63]. Meanwhile, we find that the effect of the C 2 F 2 correction on the superconductor phase transition is similar to the one of the Weyl correction(C F 2 ) on the superconductor model in Ref.…”

“…It should be noted that the current Drude-like peak is produced by the promoting conductivity near zero frequency, which is different from the one formed in the BTZ black hole in Ref. [63]. Meanwhile, for the case of γ = 1 50 , we can obtain an obviously pronounced peak at the intermediate frequency.…”

“…In particular, as γ = 0, i.e., the standard AdS case, we have T ca = 0.1006 √ ρ which is consistent with the result in Refs. [50,53,63].…”

“…However, the order of the phase transition is always 1 2 in the threedimensional BTZ (Bandos-Teitelboim-Zanelli) black hole although the increasing backreaction makes the condensate harder to form [60]. Meanwhile, 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 F 2 correction [65,66]. Concretely, the authors in Ref.…”

“…Concretely, the authors in Ref. [63] built an one-dimensional holographic p-wave superconductors by coupling Born-Infeld (BI) electrodynamics in the BTZ black hole and reproduced the interesting Drude-like peak in the real part of conductivity. Thereafter, by considering the general nonlinear electrodynamics with high order correction, Ref.…”