In the paper using matching method in the probe limit, we investigate some properties of holographic superconductor in Gauss-Bonnet gravity with Born-Infeld electrodynamics . We discuss the effects of the Gauss-Bonnet coupling α and Born-Infeld parameter b on the critical temperature and condensate. We find that both of α and b make the critical temperature decrease, which implies the condensate harder to form. Moreover we study the magnetic effect on holographic superconductor and obtain that the ratio between the critical magnetic field and the square of the critical temperature increases from zero as the temperature is lowered below the critical value Tc, which agrees well with the former results. We also find the critical magnetic field is indeed affected by Gauss-Bonnet coupling, but not by Born-Infeld parameter.

We study the holographic superconductors in f (R) gravity, and show how the critical temperature and condensate of the dual operators depend on the modifications of f (R) to Einstein gravity. A nontrivial planar black hole which is asymptotic to AdS spacetime is investigated for a specific f (R). The corrections to the thermal quantities of the black hole, the critical temperature and the condensate of the dual operator are all obtained in a perturbative approach explicitly. Some comments are given on the affections of such modifications to the holographic superconductors.

We consider a holographic model constructed from the intersecting brane configuration D4-D4=D4 in noncritical string theory. We study the chiral phase diagram of this holographic QCD-like model with a finite baryon chemical potential through the supergravity dual approximation.