Unbalanced St\"{u}ckelberg Holographic Superconductors with Backreaction

We numerically investigate some properties of unbalanced St\"{u}ckelberg holographic superconductors, by considering backreaction effects of fields on the background geometry. More precisely, we study the impacts of the chemical potential mismatch and St\"{u}ckelberg mechanism on the condensation and conductivity types (electrical, spin, mixed, thermo-electric, thermo-spin and thermal conductivity). Our results show that the St\"{u}ckelberg's model parameters $C_{\alpha}$ and $\alpha$ not only have significant impacts on the phase transition, but also affect the conductivity pseudo-gap and the strength of conductivity fluctuations. Moreover, the effects of these parameters on a system will be gradually reduced as the imbalance grows. We also find that the influence of $\alpha$ on the amplitude of conductivity fluctuations depends on the magnitude of the both $C_{\alpha}$ and $\delta\mu/\mu$ in the electric and thermal conductivity cases. This results in that increasing $\alpha$ can damp the conductivity fluctuations of an unbalanced system in contrast to balanced ones.