Transport properties in the Horndeski holographic two-currents model

The transport features of the holographic two-currents model are investigated in the Horndeski gravity framework. This system displays metallic or insulating characteristics depending on whether the Horndeski coupling parameter $\gamma$ is negative or positive, but is unaffected by other system parameters such as the strength of the momentum dissipation $\hat{k}$, the doping $\chi$ and the coupling between two gauge fields $\theta$. Secondly, we demonstrate that the thermal conductivities are affected not only by the inherent properties of the black hole, but also by the model parameters. Furthermore, we are particularly interested in the Lorentz ratios' properties. As expected, the Wiedemann-Franz (WF) law is violated, as it is in the majority of holographic systems. Particularly intriguing is the fact that several Lorentz ratio bounds reported in the typical axions model still remain true in our current theories. We would like to highlight out, however, that the lower bound for $\hat{\bar{L}}_A$ is affected by the system parameters $\chi$, $\theta$ and $\gamma$, which differs from the case of the typical axions model.