Effect of chiral anomaly on the circular dichroism and Hall angle in doped and tilted Weyl semimetals

From the Kubo formula for transport in a tilted Weyl semimetal we calculate the absorptive part of the dynamic conductivity for both right and left handed circular polarized light. These depend on the real part of the longitudinal conductivity and the imaginary part of the transverse (Hall) conductivity. We include the effect of the chiral anomaly which pumps charge from negative to positive chirality node when the ususal ${\boldsymbol E}\cdot{\boldsymbol B}$ term is included in the electrodynamics and obtain analytic expressions. To calculate the Hall angle we further provide expressions for the imaginary part of longitudinal and real part of the transverse conductivity and compare results with and without the pumping term. We also consider the case of a non centro symmetric Weyl semimetal in which the chiral nodes are displaced in energy by an amount $\pm \mathcal{Q}_0$. This leads to modification in dichroism and Hall angle which parallel the pumping case.