  We investigate the properties of the backreacting holographic superconductors
from the coupling of a scalar field to the Einstein tensor in the background of
a d-dimensional AdS black hole. Imposing the Dirichlet boundary condition of
the trial function without the Neumann boundary conditions, we improve the
analytical Sturm-Liouville method with an iterative procedure to explore the
pure effect of the Einstein tensor on the holographic superconductors and find
that the Einstein tensor hinders the condensate of the scalar field but does
not affect the critical phenomena. Our analytical findings are in very good
agreement with the numerical results from the "marginally stable modes" method,
which implies that the Sturm-Liouville method is still powerful to study the
holographic superconductors from the coupling of a scalar field to the Einstein
tensor even if we consider the backreactions.
