Thermoelectric DC conductivities from black hole horizons

TL;DR

This paper derives analytic formulas for DC thermoelectric and thermal conductivities in holographic black holes, extending previous results for electrical conductivity, and applies these to various black hole models to analyze their insulating or metallic behavior.

Contribution

It generalizes existing holographic conductivity formulas to include thermoelectric and thermal conductivities, providing new tools for analyzing strongly coupled systems.

Findings

Certain holographic Q-lattice ground states are thermal insulators.

Derived formulas apply to both isotropic and anisotropic black holes.

Results include both four and five-dimensional bulk spacetime models.

Abstract

An analytic expression for the DC electrical conductivity in terms of black hole horizon data was recently obtained for a class of holographic black holes exhibiting momentum dissipation. We generalise this result to obtain analogous expressions for the DC thermoelectric and thermal conductivities. We illustrate our results using some holographic Q-lattice black holes as well as for some black holes with linear massless axions, in both $D=4$ and $D=5$ bulk spacetime dimensions, which include both spatially isotropic and anisotropic examples. We show that some recently constructed ground states of holographic Q-lattices, which can be either electrically insulating or metallic, are all thermal insulators.