A General Holographic Superconductor Model with Non-Negative Scalar Mass

We study a general holographic superconductor model in four dimensional AdS back hole background. We explore the properties of the phase transitions in the scalar condensation and conclude the correspondence of a lower critical temperature with a deeper condensation gap holds with various scalar field mass above zero. We also examine the effects of the model parameters on the phase transition and find that this model allows first order phase transitions to occur with non-negative scalar mass when the model parameter is above a threshold value. Finally, we study the effects of the backreaction and scalar mass on the threshold model parameters.