Magnetothermoelectric Response from Holography

TL;DR

This work computes the DC magnetothermoelectric response of holographic models with broken translational invariance by subtracting magnetisation currents and expressing transport currents in terms of black hole horizon data. It derives explicit analytic expressions for the DC electrical, thermoelectric, and heat conductivities in terms of horizon quantities such as $Z(\phi)|_{r_+}$ and $\Phi(\phi)|_{r_+}$, applicable to isotropic, anisotropic, Q-lattice, and linear axion models. The horizon-based formulation reveals a two-parameter structure that parallels hydrodynamic expectations while remaining valid beyond perturbative momentum-dissipation regimes, and it enables robust study of magnetotransport under strong magnetic fields with potential relevance to strange metal phenomenology.

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.