Conductivity of the one-dimensional holographic p-wave superconductors in the presence of nonlinear electrodynamics.

We investigate analytically as well as numerically effects of nonlinear Born-Infeld (BI) electrodynamics on the properties of (1+1)-dimensional holographic $p$-wave superconductor in the context of gauge/gravity duality. We consider the case in which the gauge and vector fields backreact on the background geometry. We apply the Sturm-Liouville eigenvalue problem for the analytical approach as well as the shooting method for the numerical calculations. In both methods, we find out the relation between critical temperature $T_{c}$ and chemical potential $\mu$ and show that both approaches are in good agreement with each other. We find that if one strengthen the effect of backreaction as well as nonlinearity, the critical temperature decreases which means that the condensation is harder to form. We also explore the conductivity of the one-dimensional holographic $p$-wave superconductor for different values of b and $T/T_{c}$. We find out that the real and imaginary parts of the conductivity have different behaviors in higher dimensions. The effects of different values of temperature is more apparent for larger values of nonlinearity parameter. In addition, for the fixed value of $T/T_{c}$ by increasing the effect of nonlinearity we observe larger values for Drude-like peak in real part of conductivity and deeper minimum for imaginary part.