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The interband optical response of a three-dimensional Dirac cone is linear inphoton energy ($\Omega$). Here, we study the evolution of the interbandresponse within a model Hamiltonian which contains Dirac, Weyl and gappedsemimetal phases. In the pure Dirac case, a single linear dependence isobserved, while in the Weyl phase, we find two quasilinear regions withdifferent slopes. These regions are also distinct from the large-$\Omega$dependence. As the boundary between the Weyl (WSM) and gapped phases isapproached, the slope of the low-$\Omega$ response increases, while thephoton-energy range over which it applies decreases. At the phase boundary, asquare root behaviour is obtained which is followed by a gapped response in thegapped semimetal phase. The density of states parallels these behaviours withthe linear law replaced by quadratic behaviour in the WSM phase and the squareroot dependence at the phase boundary changed to $|\omega|^{3/2}$. The opticalspectral weight under the intraband (Drude) response at low temperature ($T$)and/or small chemical potential ($\mu$) is found to change from $T^2$ ($\mu^2$)in the WSM phase to $T^{3/2}$ ($|\mu|^{3/2}$) at the phase boundary.

Optical Conductivity of Weyl Semimetals and Signatures of the Gapped Semimetal Phase Transition