Magnetothermoelectric Response from Holography

TL;DR

This paper uses holographic models to analyze how magnetic fields influence transport properties, deriving analytic expressions for conductivities by relating boundary currents to black hole horizon characteristics.

Contribution

It introduces a method to express DC transport currents in holography in terms of black hole horizon data, accounting for magnetisation currents and applicable to various symmetry-breaking models.

Findings

Derived analytic formulas for electrical, thermoelectric, and heat conductivities.

Established a framework for relating boundary transport to horizon properties in magnetic fields.

Applicable to isotropic, anisotropic, and axion-breaking holographic models.

Abstract

In this note we study the effects of a magnetic field on transport using holographic models with broken translational invariance. We show that, after carefully subtracting off non-trivial magnetisation currents, it is possible to express the DC transport currents of the boundary theory in terms of properties of a black hole horizon. This allows us to obtain simple analytic expressions for the electrical, thermoelectric and heat conductivity tensors. Our results apply to both isotropic and anisotropic models, including holographic Q-lattices and to certain theories where translational invariance is broken by linear sources for axions.