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Holographic entanglement entropy in metal/superconductor phase transition with exponential nonlinear electrodynamics

We study the holographic entanglement entropy in metal/superconductor phase transition with exponential nonlinear electrodynamics (ENE) in four and five dimensional spacetimes. We find that the holographic entanglement entropy is powerful tool in studying the properties of the holographic phase transition. For the operator $\langle\mathcal{O}_{+}\rangle$, we observe that the entanglement entropy in 4-dimensional spacetime decreases in metal phase but changes non-monotonously in superconducting phase with the increase of the ENE parameter. Interestingly, the change of the entanglement entropy in 5-dimensional spacetime for both the phases is monotonous as the ENE factor alters. For the operator $\langle\mathcal{O}_{-}\rangle$, we show that the behavior of entanglement entropy in four and five dimensions changes monotonously for both phases as one tunes the strength of the ENE. Furthermore, for both the operators the entanglement entropy in four or five dimensional black hole increases with the increase of the width of the region.