The matching method is employed to analytically investigate the properties of holographic superconductors in higher dimensions in the framework of power Maxwell electrodynamics taking into account the effects of spacetime noncommutativity. The relationship between the critical temperature and the charge density and the value of the condensation operator is obtained first. The Meissner like effect is then studied. The analysis indicate that larger values of the noncommutative parameter and the parameter q appearing in the power Maxwell theory makes the condensate difficult to form. The critical magnetic field however increases with increase in the noncommutative parameter θ. *

In this article we employ the matching method to analytically investigate the properties of holographic superconductors in the framework of Maxwell electrodynamics taking into account the effects of back reaction on spacetime. The relationship between the critical temperature (T c ) and the charge density (ρ) has been obtained first. The influence of back reaction on Meissner like effect in this holographic superconductor is then studied. The results for the critical temperature indicate that the condensation gets harder to form when we include the effect of back reaction. The expression for the critical magnetic field (B c ) above which the superconducting phase vanishes is next obtained. It is observed from our investigation that the ratio of B c and T 2 c increases with the increase in the back reaction parameter. However, the critical magnetic field B c decreases with increase in the back reaction parameter. *

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In this paper, analytical investigation of the properties of [Formula: see text]-wave holographic superconductors in the background of a massive gravity theory in the probe limit has been carried out by employing the Sturm–Liouville eigenvalue method. We obtain the analytical expression for the relation between the critical temperature and the charge density. We also obtain the expression for the condensation operator and value of the critical exponent. We observe that as we increase the massive gravity couplings, the critical temperature increases and the condensate decreases. Then we compute the frequency dependence of conductivity by solving analytically the wave equation for electromagnetic perturbations. From the real part of the conductivity, we finally estimate the energy band gap. Our results show that as one keeps on increasing the coupling parameters of the massive gravity background, the band gap energy increases compared to the holographic superconductors constructed in the Einstein gravity background. The results indicate that massive background is more favorable than Einstein gravity background for constructing a gravity dual of the strongly coupled high [Formula: see text] superconductor as it enhances the value of the critical temperature.