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 photon energy (Omega). Here, we study the evolution of the interband response within a model Hamiltonian which contains Dirac, Weyl, and gapped semimetal phases. In the pure Dirac case, a single linear dependence is observed, while in the Weyl phase, we find two quasilinear regions with different slopes. These regions are also distinct from the large-Omega dependence. As the boundary between the Weyl (WSM) and gapped phases is approached, the slope of the low-Omega response increases, while the photon-energy range over which it applies decreases. At the phase boundary, a square root behavior is obtained which is followed by a gapped response in the gapped semimetal phase. The density of states parallels these behaviors with the linear law replaced by quadratic behavior in the WSM phase and the square root dependence at the phase boundary changed to vertical bar omega vertical bar(3/2). The optical spectral 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 (vertical bar mu vertical bar(3/2)) at the phase boundary.