Study On Holographic Superconductor In Massive Gravity And Its Spontaneous Symmetry Breaking

Holographic duality as one of the major achievements from string theory has been widely used in the study of strongly coupled systems,including holographic superconductor,ever since it had been proven to be capable of constructing a connection between weak gravity in(3+1)dimensional spacetime and strongly coupled field theory in one dimensional lower spacetime.With the study of s-wave,p-wave and d-wave holographic superconductors have been developing further in different gravity models with or without considering the backreaction,recently,the study of its excited states has become one of the major directions and has raised broad discussions.The ground state of holographic superconductor refers to the solution of matter field,used to model condensation of cooper pairs,that has no node along the black hole redius,while the n-excited states correspond to n nodes.These excited states indicate an excitation among quasi-particles in the modeled material that can form new bound states with their interactions.Now,the study toward the excited states is still at an initial stage.On the other hand,to btter remedy the holographic superconductor and real experiment,attentions also focus on how to break the translational invariance and to dissipate the momentum of modeled electrons.Current methods include introducing lattice to dissipate momentum,substituting the Einstein gravity for massive gravity model or to introduce axion model,etc.Our study focus exactly on the above topics.We generalized the excited states of s-wave holographic superconductor to the framework of massive gravity by using numerical method to study a ghost-free massive gravity model's impact on holographic superconductor's ground state and its excited states.We revealed relation between Tc of ground and excited states and parameters of massive gravity model,meanwhile,we found that the chemical potential also had a linear dependence on node number n.At last,we presented the impact of massive gravity acting on condensation and optical conductivity where by increasing the effect of massive gravity,condensation values would drop while peaks of optical conductivity would shift to lower frequencies.In addition,we also studied a two dimensional inhomogeneous holographic superconductor.This type of holographic superconductor with its matter field possessing periodicity on the two dimensional infinite boundary of black hole radius usually requires a periodic source in chemical potential or matter field that is used to model condensate to break the translational symmetry,and thus models lattice.In this paper,we show that without giving a source manually the translational symmetry can be broken spontaneously.Meanwhile,we also present the free energy of ground and excited states of such holographic superconductor,analysing their stabilities.