Numerical study of the properties of a holographic superconductor from an anti-de Sitter-Einstein-Born-Infeld black hole with backreaction

We study numerically an s -wave holographic superconductor arising from an anti-de Sitter-Einstein-Born-Infeld black hole with backreaction within the framework of the anti-de Sitter/conformal field theory (AdS/CFT) correspondence, exploring how superconducting properties can be tuned through the nonlinearity of electrodynamics and gravitational backreaction. By introducing a parameter G to control the strength of the backreaction, we investigate non-perturbatively how the properties of the superconductor evolve as backreaction increases. We find that for small values of G , increasing the nonlinearity of the Born–Infeld electrodynamics makes the formation of the condensate harder—consistent with previous results in the literature—whereas for values of G close to unity the opposite behavior emerges, with nonlinearity slightly facilitating condensate formation. This qualitative switch between weak and strong backreaction regimes is also reflected in the electrical conductivity, the holographic entanglement entropy in the superconducting phase, and the superconducting gap ratio ω g / T c , which exhibits significant deviations from its so-called universal value as backreaction strengthens. Moreover, we perform a detailed analysis of the superfluid density and the penetration depth associated with the Meissner effect, finding that nonlinear electrodynamics can induce effects analogous to those observed experimentally in the doping of conventional superconductors.