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Analytical investigation of the properties of $s$-wave holographic superconductors in the background of a massive gravity theory in the probe limit has been carried out 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. Our findings show that as we increase the massive gravity couplings the critical temperature increases and the condensate decreases. More precisely we observe that the presence of massive graviton increases the critical temperature compared to the superconductors in Einstein gravity at some point if we keep on increasing the coupling constants. We also obtain 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., Comment: 17 pages

In this article we have analytically deduced the frequency dependent expression of conductivity and the band gap energy in $AdS_{4}$ Schwarzschild background for p-wave holographic superconductors considering Einstein-Yang-Mills theory. We also used the self consistent approach to obtain the expressions of conductivity for different frequency ranges at low temperature. We then compared the imaginary part of conductivity at low frequency region. The band gap energy obtained from these two methods seem to agree very well., Comment: 19 pages single column, 5 figures

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 ($\rho$) 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 $T_{c}^{2}$ increases with the increase in the back reaction parameter. However, the critical magnetic field $B_c$ decreases with increase in the back reaction parameter., Comment: 12 pages, 2 figures

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 $\theta$., Comment: 16 pages Latex, some minor corrections made