  In the fully back reacted geometry we develop a supercurrent solution which
corresponds to a deformation of superconducting black holes by the spatial
component of gauge fields with a non- trivial radial dependence. We investigate
the influence of the backreaction on the condensation and the phase structure
in the AdS black hole spacetime. Different from that observed in the probe
limit, we find that two operators cannot give consistent information on the
phase diagram. We argue that only one of these two operators can reflect the
real property of the condensation and phase structure in the holographic
superconductor. We also generalize our study to the associated phase diagram in
the AdS soliton background.
