Absorption of circular polarized light in tilted Type-I and II Weyl semimetals

We calculate the A.C. optical response to circularly polarized light of a Weyl semimetal (WSM) with varying amounts of tilt of the Dirac cones. Both type-I and II (overtilted) WSM are considered in a continuum model with broken time reversal (TR) symmetry. The Weyl nodes appear in pairs of equal energies but of opposite momentum and chirality. For type-I the response of a particular node to right (RHP) and left (LHP) hand polarized light are distinct only in a limited range of photon energy $\Omega$, $\frac{2}{1+C_{2}/v}<\frac{\Omega}{\mu}<\frac{2}{1-C_{2}/v}$ with $\mu$ the chemical potential and $C_{2}$ the tilt associated with the positive chirality node assuming the two nodes are oppositely tilted. For the over tilted case (type-II) the same lower bound applies but there is no upper bound. If the tilt is reversed the RHP and LHP response are also reversed. We present corresponding results for the Hall angle.