Optical response in Weyl semimetal in model with gapped Dirac phase

We study the optical properties of Weyl semimetal (WSM) in a model which features, in addition to the usual term describing isolated Dirac cones proportional to the Fermi velocity v _F, a gap term m and a Zeeman spin-splitting term b with broken time reversal symmetry. Transport is treated within Kubo formalism and particular attention is payed to the modifications that result from a finite m and b. We consider how these modifications change when a finite residual scattering rate [Formula: see text] is included. For [Formula: see text] the A.C. conductivity as a function of photon energy [Formula: see text] continues to display the two quasilinear energy regions of the clean limit for [Formula: see text] below the onset of the second electronic band which is gapped at ([Formula: see text]). For [Formula: see text] of the order m little trace of two distinct linear energy scales remain and the optical response has evolved towards that for [Formula: see text]. Although some quantitative differences remain there are no qualitative differences. The magnitude of the D.C. conductivity [Formula: see text] at zero temperature ([Formula: see text]) and chemical potential ([Formula: see text]) is altered. While it remains proportional to [Formula: see text] it becomes inversely dependent on an effective Fermi velocity out of the Weyl nodes equal to [Formula: see text] which decreases strongly as the phase boundary between Weyl semimetal and gapped Dirac phase (GDSM) is approached at [Formula: see text]. The leading term in the approach to [Formula: see text] for finite [Formula: see text], [Formula: see text] and [Formula: see text] is found to be quadratic. The coefficient of these corrections tracks closely the [Formula: see text] dependence of the [Formula: see text] limit with differences largest near to the WSM-GDSM boundary.