  In this paper, we investigate a holographic model of superconductor with
hidden Fermi surfaces, which was defined by the logarithmic violation of area
law of entanglement entropy. We works in fully back-reacted background using
standard Einstein-Maxwell-Dilaton action with additional complex scalar filed
which was charged under the Maxwell field. Particularly, we analyze the
behavior of entanglement entropy during the phase transition. At the critical
point, the finite part of the entanglement entropy has a discontinuity of slope
and tends to a lower value in the superconducting phase all the way down to the
zero temperature limit, indicating the reorganization of degrees of freedom of
the system across the phase transition.
