Holographic Insulator/Superconductor Phase Transition And Study On Non-equilibrium Holographic Superconductors

The correspondence between the gravity in a d-dimensional anti-de Sitter?AdS?spacetime and the conformal field theory?CFT?residing on the?d-1?-dimensional boundary of this space-time,known as the AdS/CFT correspondence,provides an established method for calculating correlation functions in a strongly interacting field theory using a dual classical gravity descrip-tion.In recent years the study of this duality has been extended and applied into many different aspects:strongly coupled dynamics of Quantum Color Dynamics,QCD and Quark Gluon Plas-ma?QGP?Physics,black hole physics and quantum gravity,fluid mechanics and Quantum Phase Transitions.Especially in condensed matter physics,people make full use of holographic principle to construct plenty of holographic superconductor or superfluid modes,such as s-wave,p-wave,d-wave and multi-band order parameters coexisting and competing superconductor.In these holographic models ones study quantum critical points,strange metal,holographic entan-glement entropy and superconductor/insulator phase transition and so on,having made fruitful results.In chapter two,our holographic s+p superconductor model is constructed by the scalar triplet under?2?gauge field coupling to Einstein theory.We study the holographic s+p insu-lator/superconductor phase transition at zero temperature,in this model,besides the insulator phase,s-wave condensate phase,p-wave condensate phase,the s+p coexisting condensate phase condensate phase is found numerically when operator dimension?is greater than a critical value.We also construct the complete phase in?-plane,which shows the s+p coexisting region is very narrow.Furthermore,we calculate the corresponding conductivities for different phases.In chapter three,we investigate the holographic superconductor model that is described by the Einstein-Maxwell theory with the self-interaction term of complex scalar field in asymptotic Anti-de Sitter?AdS?spacetime.Below critical temperature₍?8?,the planar Reissner-Nordstrom-AdS?RNAdS?black hole is unstable due to the near-horizon scalar condensation instability.We study the full nonlinear development of this instability by numerically solving the gravitational dynamics in the asymptotic AdS spacetime,and observe a dynamical process from the perturbed Reissner-Nordstrom-AdS black hole to a hairy black hole when the initial black hole temperature.At early times,small scalar perturbation grows as expected from linearized Quasinormal modes analysis.By the gauge/gravity duality,this dynamical process is then holographically dual to the dynamical superconducting phase transition process in the boundary theory.Furthermore,we also study the effect of the scalar self-interaction on time evolution of superconducting condensate operator,event and apparent horizon areas of the final hairy black hole.With the self-interaction coupling parameter is bigger and bigger,event and apparent horizon areas of the final hairy black hole decrease,and the horizons need shorter time to settle down to a constant value,which means that it needs less time to develop a stable hairy black hole.In chapter four,we give summary and outlook about this thesis.