Transport properties in the Horndeski holographic two-currents model

TL;DR

This paper explores the transport properties of a holographic two-currents model within Horndeski gravity, revealing how system parameters influence metallic or insulating behavior, thermal conductivities, and Lorentz ratio bounds, with violations of the Wiedemann-Franz law.

Contribution

It introduces a detailed analysis of transport phenomena in a Horndeski holographic two-currents model, highlighting parameter effects on conductivity and Lorentz ratios, and extends understanding beyond typical axions models.

Findings

Transport behavior depends on the Horndeski coupling parameter 

Thermal conductivities are influenced by black hole properties and model parameters

Lorentz ratio bounds from axion models largely hold, but some bounds are parameter-dependent

Abstract

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.