Holographic entanglement entropy in metal/superconductor phase transition with Born–Infeld electrodynamics

•We study holographic entanglement entropy in metal/superconductor phase transition for Born–Infeld electrodynamics with full backreaction.•For operator 〈O−〉〈O−〉, entanglement entropy decreases (or increases) with increase of parameter b in metal (or superconducting) phase.•For operator 〈O+〉〈O+〉, with increase of Born–Infeld parameter, the entanglement entropy in the metal phase decreases monotonously but entropy in superconducting phase first increases and forms a peak at some threshold bTbT, then decreases continuously as increase of b,•The value of bTbT becomes smaller as the width of the subsystem A decreases.

We investigate the holographic entanglement entropy in the metal/superconductor phase transition for the Born–Infeld electrodynamics with full backreaction and note that the entropy is a good probe to study the properties of the phase transition. For the operator 〈O−〉〈O−〉, we find that the entanglement entropy decreases (or increases) with the increase of the Born–Infeld parameter b   in the metal (or superconducting) phase. For the operator 〈O+〉〈O+〉, we observe that, with the increase of the Born–Infeld parameter, the entanglement entropy in the metal phase decreases monotonously but the entropy in the superconducting phase first increases and forms a peak at some threshold bTbT, then decreases continuously. Moreover, the value of bTbT becomes smaller as the width of the subsystem A decreases.