Dynamic current-current susceptibility in 3D Dirac and Weyl semimetals

We study the linear response of doped three dimensional Dirac and Weyl semimetals to vector potentials, by calculating the wave-vector and frequency dependent current-current response function analytically. The longitudinal part of the dynamic current-current response function is then used to study the plasmon dispersion, and the optical conductivity. The transverse response in the static limit yields the orbital magnetic susceptibility. In a Weyl semimetal, along with the current-current response function, all these quantities are significantly impacted by the presence of parallel electric and magnetic fields (a finite ${\bf E}\cdot{\bf B}$ term), and can be used to experimentally explore the chiral anomaly.