Higher dimensional holographic superconductors in Born–Infeld electrodynamics with back-reaction

Abstract

In this paper, we analytically investigate the properties of holographic superconductors in higher dimensions in the framework of Born–Infeld electrodynamics taking into account the back-reaction of the spacetime using the Sturm–Liouville eigenvalue method. In the background of pure Einstein and Gauss–Bonnet gravity, based on a perturbative approach, we obtain the relation between the critical temperature and the charge density. Higher values of the back-reaction and Born–Infeld parameters result in a harder condensation to form in both cases. The analytical results are found to agree with the existing numerical results. We also derive an expression for the condensation operator in d dimensions which yields a critical exponent of 1 / 2.