DC conductivities and Stokes flows in Dirac semimetals influenced by hidden sector

Abstract

Abstract In the holographic model of Dirac semimetals, the Einstein–Maxwell scalar gravity with the auxiliary U(1)-gauge field, coupled to the ordinary Maxwell one by a kinetic mixing term, the black brane response to the electric fields and temperature gradient has been elaborated. Using the foliation by hypersurfaces of constant radial coordinate we derive the exact form of the Hamiltonian and equations of motion in the phase space considered. Examination of the Hamiltonian constraints enables us, to the leading order expansion of the linearised perturbations at the black brane event horizon, to derive the Stokes equations for an incompressible doubly charged fluid. Solving the aforementioned equations, one arrives at the DC conductivities for the holographic Dirac semimetals.