DC Conductivity of Magnetised Holographic Matter

We consider general black hole solutions of Einstein-Maxwell-scalar theory that are holographically dual to conformal field theories at finite charge density with nonvanishing magnetic fields and local magnetisation currents, which generically break translation invariance explicitly. We show that the thermoelectric DC conductivity of the field theory can be obtained by solving a system of generalised Stokes equations on the black hole horizon. For various examples, including Q-lattices and one-dimensional lattices, we solve the Stokes equations explicitly and obtain expressions for the DC conductivity in terms of the solution at the black hole horizon.