  From the viewpoint of holography, we study the behaviors of the entanglement
entropy in insulator/superconductor transition with exponential nonlinear
electrodynamics (ENE). We find that the entanglement entropy is a good probe to
the properties of the holographic phase transition. Both in the half space and
the belt space, the non-monotonic behavior of the entanglement entropy in
superconducting phase versus the chemical potential is general in this model.
Furthermore, the behavior of the entanglement entropy for the strip geometry
shows that the confinement/deconfinement phase transition appears in both
insulator and superconductor phases. And the critical width of the the
confinement/deconfinement phase transition depends on the chemical potential
and the exponential coupling term. More interestingly, the behaviors of the
entanglement entropy in their corresponding insulator phases are independent of
the exponential coupling factor but depends on the the width of the subsystem
$\mathcal{A}$.
