The proposal that the physics of quantum critical phase transition in strongly coupledcondensed matter systems can be described by a gravitational theory within the framework of gauge/gravity correspondence is investigated more extensively for s-wave superconductors.We consider a gravitational theory with a black hole solution in anti de Sitterspacetime, coupled to an Abelian-Higgs system in (d + 1)-dimensions. A wide range ofnegative mass squared for the scalar field that satisfied the Brietenlohner-Freedman stabilitybound and the unitarity bound are considered in the probe limit. The...