Holographic entanglement entropy with Born–Infeld electrodynamics in higher dimensional AdS black hole spacetime

We examine the entanglement entropy in higher dimensional holographic metal/superconductor model with Born–Infeld (BI) electrodynamics. We note that the entanglement entropy is still a powerful tool to probe the critical phase transition point and the order of the phase transition in higher dimensional AdS spacetime. Due to the presence of the BI electromagnetic field, the formation of the scalar condensation becomes harder. For both operators ⟨O+⟩\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle \mathcal {O}_{+}\rangle $$\end{document} and ⟨O-⟩\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle \mathcal {O}_{-}\rangle $$\end{document}, we show that the entanglement entropy in the metal phase decreases as the BI factor increases, but in condensation phase the entanglement entropy increases monotonically for stronger nonlinearity of BI electromagnetic field. Furthermore, we also study the influence of the width of the subsystem on the holographic entanglement entropy and observe that with the increase of the width the entanglement entropy increases.