Holographic Superconductors From The Coupling Of A Scalar Field To The Einstein Tensor

The gauge/gravity duality,which connects the strongly coupled gauge theory with the weakly coupled classical gravity system,provides a new effective way to study the strong coupling properties of the quantum chromodynamics(QCD)and some difficult problems in the condensed matter physics,such as the high temperature superconductivity,superfluid and Bose-Einstein condensation(BEC),and motivates many new research directions.In this thesis,we constructed the backreacting holographic superconductor model from the coupling of a scalar field to the Einstein tensor in the background of a d-dimensional AdS black hole by using the gauge/gravity duality,and tried to provide a possible solution to understand the effect of impurities on the hightemperature superconductor systems.Imposing the Dirichlet boundary condition of the trial function without the Neumann boundary conditions,we improved the analytical Sturm-Liouville method with an iterative procedure to explore the pure effect of the Einstein tensor on the holographic superconductors and found that the critical temperature decreases with the increase of the coupling parameter of the Einstein tensor,which indicates that the Einstein tensor hinders the condensate of the scalar field.Our analytical findings are in very good agreement with the numerical results from the “marginally stable modes” method,which implies that the Sturm-Liouville method is still powerful to study the holographic superconductors from the coupling of a scalar field to the Einstein tensor even if we consider the backreactions.Moreover,we interestingly noted that the Einstein tensor,backreaction and spacetime dimension cannot modify the critical phenomena,i.e.,this holographic superconductor phase transition belongs to the second order and the critical exponent of the system always takes the mean-field value.