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we find that when ρ > ρ$_{c}$ , the operator condensate will appear; this means when T < T$_{c}$ there will be an operator condensate, that is to say, the superconducting phase occurs. 

In what following we will present a detailed analysis of the condensation of the operator O + by numerical and analytical methods, respectively. 

## A. Numerical analysis of condensation 

The equations (3.4) and (3.5) can be solved numerically by doing integration from the horizon out to the infinity with the boundary conditions mentioned above . 

Changing the value of ϵ , we present in Fig. 1 the influence of the parameter of the bala nce on the condensation with fixed values m $^{2}$L2 AdS = 0, − 1 and − 2, and in Fig. 2 the critical temperature as a function of the balance parameter with fixed values m $^{2}$L2 AdS = 0, − 1 and − 2. We know from the figures that as the parameter of the detailed balance incr eases with fixed mass of the scalar field, the condensation gap becomes smaller, corresponding to larger the critical temperature, which means that the scalar hair can be formed easier for the larger ϵ . 

<img src='content_image/358273.jpg'>

Altering the value of m $^{2}$L2 $_{AdS}$, we show in Fig. 3 the influence of the mass on the condensationwith fixed values ϵ = 0 and 0 . 1. It is clear that for the same ϵ , the condensation gap becomes larger if m 2 becomes less negative, which means that the scalar hair can be formed more di ffi cult as m 2 becomes less negative. 

