The St\"{u}ckelberg Holographic Superconductors with Weyl corrections

In this letter we construct the St"{u}ckelberg holographic superconductor with Weyl corrections. Under such corrections, the Weyl coupling parameter $\gamma$ plays an important role in the order of phase transitions and the critical exponents of second order phase transitions. So do the model parameters $c_{\alpha }$, $\alpha$ and $c_4$. Moreover, we show that the Weyl coupling parameter $\gamma$ and the model parameters $c_{\alpha }$, $\alpha$, $c_4$ which together control the size and strength of the conductivity coherence peak and the ratio of gap frequency over critical temperature ${\omega }_g\mathrm{/}{T}_c$.