We numerically investigate some properties of unbalanced Stückelberg holographic superconductors, by considering backreaction effects of fields on the background geometry. More precisely, we study the impacts of the chemical potential mismatch and Stückelberg mechanism on the condensation and conductivity types (electrical, spin, mixed, thermo-electric, thermo-spin and thermal conductivity). Our results show that the Stückelberg's model parameters C α and α 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 α on the amplitude of conductivity fluctuations depends on the magnitude of the both C α and δµ/µ in the electric and thermal conductivity cases. This results in that increasing α can damp the conductivity fluctuations of an unbalanced system in contrast to balanced ones.

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