  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.
