Effects of massive gravity on s-wave holographic superconductor

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.