Holographic superconductor with momentum relaxation and Weyl correction

We construct a holographic model with Weyl corrections in five dimensional spacetime. In particular, we introduce a coupling term between the axion fields and the Maxwell field such that the momentum is relaxed even in the probe limit in this model. We investigate the Drude behavior of the optical conductivity in low frequency region. It is interesting to find that the incoherent part of the conductivity is suppressed with the increase of the axion parameter $k/T$, which is in contrast to other holographic axionic models at finite density. Furthermore, we study the superconductivity associated with the condensation of a complex scalar field and evaluate the critical temperature for condensation in both analytical and numerical manner. It turns out that the critical temperature decreases with $\tilde{k}$,indicating that the condensation becomes harder in the presence of the axions, while it increases with Weyl parameter $\gamma$. We also discuss the change of the gap in optical conductivity with coupling parameters. Finally, we evaluate the charge density of the superfluid in zero temperature limit, and find that it exhibits a linear relation with $\tilde{\sigma}_{DC}(\tilde{T_c})\tilde{T_c}$, such that a modified version of Homes' law is testified.