  In arXiv:0803.3295 [hep-th] a holographic black hole solution is discussed
which exhibits a superconductor like transition. In the superconducting phase
the black holes show infinite DC conductivity. This gives rise to the
possibility of deforming the solutions by turning on a time independent current
(supercurrent), without any electric field. This type of deformation does not
exist for normal (non-superconducting) black holes, due to the no-hair
theorems. In this paper we have studied such a supercurrent solution and the
associated phase diagram. Interestingly, we have found a "special point"
(critical point) in the phase diagram where the second order superconducting
phase transition becomes first order. Supercurrent in superconducting materials
is a well studied phenomenon in condensed matter systems. We have found some
qualitative agreement with known results.
