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

Mahya Mohammadi,Ahmad Sheykhi

doi:10.1140/epjc/s10052-019-7250-1

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 {mathcal {F}}+b {mathcal {F}}^{2}, where {mathcal {F}} is the Maxwell Lagrangian and b indicates the strength of the nonlinearity. We employ the shooting method for the numerical calculations in order to obtain the ratio of the critical temperature T_{c} over rho ^{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 alpha 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 by the Kramers–Kronig relation, which indicates a delta function and a pole in low frequency regime, respectively. However, at enough large frequencies the trend of the real part can be interpreted by Re[sigma ]=omega ^{(d-4)}. Moreover, in holographic model the ratio omega _{g}/T_{c} is always much larger than the BCS value 3.5 due to the strong coupling of holographic superconductors. In both kinds of gravity, decreasing the temperature or increasing the effect of nonlinearity shifts the gap frequency toward larger values. Besides, the gap frequency occurred at larger values by enlarging the Gauss–Bonnet parameter. In general, the behavior of the conductivity depends on the choice of the mass, the nonlinear and the Gauss–Bonnet parameters.

Highlights

In recent years, the gauge/gravity duality, which connects a weak gravitational system in (d + 1) dimensions to the strong coupling conformal field theory in d dimensions, has attracted a lot of attention because it provides a powerful theoretical method to study strong interacting systems such as high temperature superconductors [1,2,3,4,5,6]
By applying the AdS/CFT correspondence in higher dimensional spacetime, we have analyzed the behavior of a holographic p-wave superconductor by considering the higher order corrections on the gravity as well as the gauge field side
We studied the condensation of the vector field in the presence of a nonlinear correction to the electrodynamics as given in Eq (3)

Summary

Introduction

The gauge/gravity duality, which connects a weak gravitational system in (d + 1) dimensions to the strong coupling conformal field theory in d dimensions, has attracted a lot of attention because it provides a powerful theoretical method to study strong interacting systems such as high temperature superconductors [1,2,3,4,5,6]. The idea of a holographic superconductor was proposed in 2008 [2] by applying the AdS4/CFT3 correspondence on the probe limit in Einstein gravity Based on this theory in order to describe a superconductor on the boundary, we need a transition from hairy black hole to a no-hair black hole in the bulk for temperatures below and above the critical value, respectively [7]. We consider the electrical conductivity for a holographic p-wave superconductor in Gauss–Bonnet gravity with higher order corrections. The global trends are seen in this case In this gravity, the gap frequency depends on the mass, nonlinearity and the Gauss–Bonnet parameters and the ratio of ωg/Tc deviates from the universal value 8 by increasing the effect of α, too.

The holographic model and condensation of the vector field

Holographic p-wave superconductor in Gauss–Bonnet gravity

Conductivity

Summary and conclusion