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 $F+b{F}^2$, 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 $T_c$ 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 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 $Re[\sigma ]={\omega }^{(d-4)}$. 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 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.

26 pages

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• Investigating quantum criticality through charged scalar fields near the BTZ black hole horizon
• Gauss-Bonnet holographic superconductors in lower-dimensions
• Holographic entanglement entropy and subregion complexity for excited states of holographic superconductors
• An analytical approach to compute conductivity of p-wave holographic superconductors
• Probing quantum criticality near the BTZ black hole horizon: Insights from coupled fermion-antifermion pairs