DC conductivities and Stokes flows in Dirac semimetals

TL;DR

This paper develops a holographic model for Dirac semimetals incorporating kinetic mixing, deriving exact Hamiltonian forms and Stokes equations to compute their DC conductivities through black brane responses.

Contribution

It introduces a novel holographic framework with kinetic mixing for Dirac semimetals and derives explicit formulas for their DC conductivities.

Findings

Derived exact Hamiltonian and equations of motion for the model.

Formulated Stokes equations for the dual fluid.

Calculated DC conductivities of holographic Dirac semimetals.

Abstract

In the holographic model of Dirac semimetals being the Einstein-Maxwell scalar gravity with the auxiliary $U(1)$-gauge field, coupled to the ordinary Maxwell one by {\it 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 considered phase space. Examination of the Hamiltonian constraints enables us, to the leading order expansion of the linearised perturbations at the black brane event horizon, to derive Stokes equations for incompressible doubly charged fluid. Solving the aforementioned equations, one arrives at the DC conductivities for the holographic Dirac semimetals.