Holographic superconductor with nonlinear arcsin-electrodynamics

We investigate holographic s-wave superconductors with nonlinear arcsin-electrodynamics in the background of Schwarzschild anti-de Sitter black holes. The analytical Sturm-Liouville eigenvalue problem is explored and we assume that the scalar and electromagnetic fields do not influence on the background metric (the probe limit). The critical temperatures of phase transitions depending on the parameter of the model is obtained. We show that in our case the condensation formation becomes easier compared to Born-Infeld nonlinear electrodynamics. The critical exponent near the critical temperature is calculated which is 1/2. With the help of the matching method we derive analytic expressions for the condensation value and the critical temperature. The real and imaginary parts of the conductivity in our model, making use of an analytical method, are computed.