The holographic model for a two-dimensional superconductor has been investigated, by considering the three-dimensional gravity in the bulk. To find the critical temperature we used the Sturm–Liouville variational method. Where as the same method is applied for calculating the condensation of the dual operators on the boundary.We included the back reactions on the metric by a combination of the perturbation method of the fields with respect to the small parameter and then applying the variational integrals on the resulting equations of the motion. The critical temperature has been successfully obtained on the backreaction effects, and we showed that it dropped with a rise in the backreaction of the fields, and it makes the condensation harder. We can use our analytical results to support the numerical data which was reported previously.
