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In the fully back reacted geometry we develop a supercurrent solution whichcorresponds to a deformation of superconducting black holes by the spatialcomponent of gauge fields with a non- trivial radial dependence. We investigatethe influence of the backreaction on the condensation and the phase structurein the AdS black hole spacetime. Different from that observed in the probelimit, we find that two operators cannot give consistent information on thephase diagram. We argue that only one of these two operators can reflect thereal property of the condensation and phase structure in the holographicsuperconductor. We also generalize our study to the associated phase diagram inthe AdS soliton background.

Phase transition in the holographic model of superfluidity with backreactions