Flat optical conductivity in ZrSiS due to two-dimensional Dirac bands

ZrSiS exhibits a frequency-independent interband conductivity $\sigma(\omega) = \rm{const}(\omega) \equiv \sigma_{\rm{flat}}$ in a broad range from 250 to 2500 cm${}^{-1}$ (30 - 300 meV). This makes ZrSiS similar to (quasi)two-dimensional Dirac electron systems, such as graphite and graphene. We assign the flat optical conductivity to the transitions between quasi-two-dimensional Dirac bands near the Fermi level. In contrast to graphene, ${\sigma }_{\mathrm{f}\mathrm{l}\mathrm{a}\mathrm{t}}$ is not supposed to be universal but related to the length of the nodal line in the reciprocal space, $k_0$. When ${\sigma }_{\mathrm{f}\mathrm{l}\mathrm{a}\mathrm{t}}$ and $k_0$ are connected by a simple model, we find good agreement between experiment and theory. Due to the spin-orbit coupling, the discussed Dirac bands in ZrSiS possess a small gap $\mathrm{\Delta }$, for which we determine an upper bound max($\mathrm{\Delta }$) = 30 meV from our optical measurements. At low temperatures the momentum-relaxation rate collapses, and the characteristic length scale of momentum relaxation is of the order of microns below 50 K.