Coherence Length And Magnetic Penetration Depth Of Holographic Superconductor In Non-Relativistic Spacetime

With the development of the high-temperature superconductor,more and more people con-centrate on it in recent years.But people hardly investigate the microscopic source of the high-temperature superconductor because of its strongly coupled system.Fortunately,holographic duality bring hope to us.The duality match the weak interaction gravitational system with the lower dimensional strong interaction system on the boundary.With the help of the theory to construct the model of superconductor in the gravitational spacetime is called holographic superconductor.Firstly,we introduce the background knowledge of the holographic superconductor in this thesis.Secondly,we introduce the the s-wave holographic superconductor model in Schwartz-schild spacetime.It is very useful to investigate coherence length and magnetic penetration depth because they are important parameters of holographic superconductor.So,we calculate the coherence length of superconductor by using analytical method to study the perturbation of the system near the critical temperature in the probe limit in Lifshitz spacetime and IR modified Horava-Lifshitz spacetime,separately.Then,we obtain the magnetic penetration depth of the superconductor by adding a external homogeneous magnetic field.And the results correspond to the Ginzburg-Landau theory.