Flat Optical Conductivity in ZrSiS due to Two-Dimensional Dirac Bands

ZrSiS exhibits a frequency-independent interband conductivity σ(ω)=const(ω)≡σ_{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, σ_{flat} is not universal but related to the length of the nodal line in the reciprocal space, k_{0}. Because of spin-orbit coupling, the discussed Dirac bands in ZrSiS possess a small gap Δ, for which we determine an upper bound max(Δ)=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.