Optical properties of anisotropic Dirac semimetals

The current-dipole conductivity formula for doped three-dimensional Dirac semimetals is derived by using a modified gauge-invariant tight-binding approach. In a heavily doped regime, the effective number of charge carriers $n_{\alpha \alpha}^{\rm eff}$ in the Drude contribution is found to be by a factor of 4 larger than the nominal electron concentration $n$. However, its structure is the same as in standard Fermi liquid theory. In a lightly doped regime, on the other hand, the ratio $n_{\alpha \alpha}^{\rm eff}/n$ is much larger, with much more complex structure of $n_{\alpha \alpha}^{\rm eff}$. It is shown that the dc resistivity and reflectivity date measured in two TlBiSSe samples can be easily understood, even in the relaxation-time approximation, provided that finite quasiparticle lifetime effects in the momentum distribution functions are properly taken into account.