More on Superconductors via Gauge/Gravity Duality with Nonlinear Maxwell Field

We have developed the recent investigations on the second-order phase transition in the holographic superconductor using the probe limit for a nonlinear Maxwell field strength coupled to a massless scalar field. By analytic methods, based on the variational Sturm- Liouville minimization technique, we study the effects of the space-time dimension and the non-linearity parameter on the critical temperature and the scalar condensation of the dual operators on the boundary. Further, as a motivated result, we analytically deduce the DC conductivity in the low and zero temperatures regime. Especially in the zero temperature limit and in two dimensional toy model, we thoroughly compute the conductivity analytically. Our work clarifies more features of the holographic superconductors both in different space dimensions and on the effect of the non-linearity in Maxwell's strength field.