Analytical study of holographic superconductor in Born–Infeld electrodynamics with backreaction

We extend the analytical studies on the properties of s-wave holographic superconductors in the presence of Born–Infeld nonlinear electrodynamics by taking the backreaction into account. We find that even in the case of nonlinear electrodynamics, one can still employ the analytical method when the backreaction is turned on. In our calculations, we use the variational method which is based on the Sturm–Liouville eigenvalue problem. For this system, we obtain the relation between the critical temperature and the charge density. We find that both backreaction and Born–Infeld parameters decrease the critical temperature of the superconductor and make the condensation harder. Finally, we compute the critical exponent associated with the condensation near the critical temperature and find that it equals 1/2 which is the universal value in the mean field theory.