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We investigate the properties of the backreacting holographic superconductorsfrom the coupling of a scalar field to the Einstein tensor in the background ofa d-dimensional AdS black hole. Imposing the Dirichlet boundary condition ofthe trial function without the Neumann boundary conditions, we improve theanalytical Sturm-Liouville method with an iterative procedure to explore thepure effect of the Einstein tensor on the holographic superconductors and findthat the Einstein tensor hinders the condensate of the scalar field but doesnot affect the critical phenomena. Our analytical findings are in very goodagreement with the numerical results from the "marginally stable modes" method,which implies that the Sturm-Liouville method is still powerful to study theholographic superconductors from the coupling of a scalar field to the Einsteintensor even if we consider the backreactions.

Backreacting holographic superconductors from the coupling of a scalar field to the Einstein tensor