Influence Of Electrodynamics And Space-time On Holographic Superconductors

We study the application of AdS/CFT on holographic superconductors. We present analysis on the holographic superconductor of Born-Infeld electrodynam-ics, Gauss-Bonnet holographic superconductors and Hofava-Lifshitz holographic superconductors and achieve the following results.We extend the study of the holographic superconductor to Born-Infeld electro-dynamics by replacing Maxwell electrodynamics with Born-Infeld electrodynamics, and obtain the superconductor phase and the relation between the conduction and frequency. We find that the larger Born-Infeld parameter makes the condensation of scalar charge harder to form and the gap frequency of the conductivity becomes smaller. By the numerical calculation, we find that, on the background of Gauss-Bonnet spacetime, the higher order curvature correction makes the condensation harder to form and the ratio of the gap frequency in conductivity to the criti-cal temperature larger. And the increase of the dimensionality of AdS spacetime makes condensation of scalar operator easier to form.We then study the model of general holographic superconductors with the first phase transition on Born-Infeld electrodynamics. We find that for the model F(ψ)=ψ2+c4ψ4, the existance of the Born-Infeld coupling parameter b makes the phase transition from the second order to the first order more easily. For the general mode F(ψ)=ψ2+cγψγ+c4ψ4, the critical exponents near the second-order phase transition point is only determined by the model parameter γ and is independent of Born-Infeld coupling parameter b. The ratio of the gap frequency in conductivity to the critical temperature is connected with the model parameters cγ and γ and the Born-Infeld coupling parameter b. When we use Born-Infeld electrodynamics and Gauss-Bonnet gravity, we find that for the simple model F(ψ)=ψ2+c4ψ4, at the transition point of phase transition from the second order to the first one the relation of the Gauss-Bonnet constant α, the model parameter c4and the critical Born-Infeld coupling parameter bc and the critical temperature Tc is:both bc and Tc decrease as a increases for fixed c4, and bc decreases but Tc increases as c4increases for fixed a. For general model F(ψ)=ψ2+cγψγ+c4ψ4, if we fix the model parameters (cγ,γ,c4), we note that the critical temperature becomes smaller as the Born-Infeld coupling parameter b increases for two types of phase transitions. However, if we fix the Born-Infeld coupling parameter b, for the cases of second phase transition, the formation of the scalar hair is not affected by model parameters (cγ,γ,c4). But for the case of first phase transition, the scalar hair is formed easier for the larger model parameter (cγ,γ, c4). And the ratio of the gap frequency in conductivity to the critical temperature depends on the Gauss-Bonnet constant α, model parameters (cγ,γ,c4) and the Born-Infeld coupling parameter b.We also construct the model for Hofava-Lifshitz holographic superconductors without the condition of the detailed balance. With the fixed mass of the scalar field, as the parameter of the detailed balance ε increases, the scalar hair forms easier, and it is harder for the scalar hair to form as the mass of the scalar field becomes larger for the same ε. The ratio of the gap frequency in conductivity to the critical temperature almost linear decreases with the increase of the balance constant. For ε=0, the ratio reduces to the situations of Horava-Lifshitz black holes with the condition of the detailed balance, while for ε=1, it tends to the situations obtained in AdS Schwarzschild black holes.