Holographic superconductors with Power-Maxwell field

With the Sturm-Lionville analytical and numerical methods, we investigate the behaviors of the holographic superconductors by introducing a complex charged scalar field coupled with a Power-Maxwell field in the background of d-dimensional Schwarzschild AdS black hole. We note that the Power-Maxwell field takes the special asymptotical solution near boundary which is different from all known cases. We find that the larger power parameter q for the Power-Maxwell field makes it harder for the scalar hair to be condensated. We also find that, for different q, the critical exponent of the system is still 1/2, which seems to be an universal property for various nonlinear electrodynamics if the scalar field takes the form of this paper.