Conductivity of higher dimensional holographic superconductors with nonlinear electrodynamics

We investigate analytically as well as numerically the properties of s-wave holographic superconductors in $d$-dimensional spacetime and in the presence of Logarithmic nonlinear electrodynamics. We study three aspects of these kind of superconductors. First, we obtain, by employing analytical Sturm-Liouville method as well as numerical shooting method, the relation between critical temperature and charge density, $\rho$, and disclose the effects of both nonlinear parameter $b$ and the dimensions of spacetime, $d$, on the critical temperature $T_c$. We find that in each dimension, $T_c/{\rho}^{1/(d-2)}$ decreases with increasing the nonlinear parameter $b$ while it increases with increasing the dimension of spacetime for a fixed value of $b$. Then, we calculate the condensation value and critical exponent of the system analytically and numerically and observe that in each dimension, the condensation get larger with increasing the nonlinear parameter $b$. Besides, for a fixed value of $b$, it increases with increasing the spacetime dimension. We confirm that the results obtained from our analytical method are in agreement with the results obtained from numerical shooting method. This fact may support the correctness of our analytical method. Finally, we explore the holographic conductivity of this system and find out that the superconducting gap increases with increasing either the nonlinear parameter or the spacetime dimension.