A Study On Holographic Insulator/superconductor Phase Transitions With Excited States

Anti-de Sitter/conformal field theory(AdS/CFT)correspondence reveals the equivalence relation between the high-dimensional gravity theory and low-dimensional quantum field theory,which provides a new effective way to study the various properties of the strongly coupled quantum field theory.In recent years,the AdS/CFT correspondence has been used to investigate some difficult problems in the condensed matter physics,such as the high temperature superconductivity,superfluid and Bose-Einstein condensation(BEC),and has triggered a new research direction,i.e.,the Anti-de Sitter/condensed matter theory(AdS/CMT)duality.In this thesis,we apply the AdS/CFT correspondence to construct a family of solutions of the holographic insulator/superconductor phase transitions with the excited states in the AdS soliton background by using both the numerical and analytical methods.The interesting point is that the improved Sturm-Liouville method can not only analytically investigate the properties of the phase transition with the excited states,but also the distributions of the condensed fields in the vicinity of the critical point.We observe that,regardless of the type of the holographic model,the excited state has a higher critical chemical potential than the corresponding ground state,and the difference of the dimensionless critical chemical potential between the consecutive states is around 2.4,which is different from the finding of the metal/superconductor phase transition in the AdS black hole background.Furthermore,near the critical point,we find that the phase transition of the systems is of the second order and a linear relationship exists between the charge density and chemical potential for all the excited states in both s-wave and p-wave insulator/superconductor models.