A Study of Holographic: Superconductors

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 dependenceof the some of the physical quantities on the scaling dimensions of the dual condensateswere thoroughly investigated. We observe that the holographic superconductors can beconsistently classified into two, based on the scaling dimensions and the charge of thedual condensates. Holographic superconductors of dimension ¸? exhibit features of typeII superconductors while those of dimension ¸+ show features of type I.