Optical conductivity of Weyl semimetals and signatures of the gapped semimetal phase transition

The interband optical response of a three-dimensional Dirac cone is linear in\nphoton energy ($\\Omega$). Here, we study the evolution of the interband\nresponse within a model Hamiltonian which contains Dirac, Weyl and gapped\nsemimetal phases. In the pure Dirac case, a single linear dependence is\nobserved, while in the Weyl phase, we find two quasilinear regions with\ndifferent slopes. These regions are also distinct from the large-$\\Omega$\ndependence. As the boundary between the Weyl (WSM) and gapped phases is\napproached, the slope of the low-$\\Omega$ response increases, while the\nphoton-energy range over which it applies decreases. At the phase boundary, a\nsquare root behaviour is obtained which is followed by a gapped response in the\ngapped semimetal phase. The density of states parallels these behaviours with\nthe linear law replaced by quadratic behaviour in the WSM phase and the square\nroot dependence at the phase boundary changed to $|\\omega|^{3/2}$. The optical\nspectral weight under the intraband (Drude) response at low temperature ($T$)\nand/or small chemical potential ($\\mu$) is found to change from $T^2$ ($\\mu^2$)\nin the WSM phase to $T^{3/2}$ ($|\\mu|^{3/2}$) at the phase boundary.\n