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

Abstract

ZrSiS exhibits a frequency-independent interband conductivity $σ(ω) = \rm{const}(ω) \equiv σ_{\rm{flat}}$ 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, $σ_{\rm{flat}}$ is not supposed to be universal but related to the length of the nodal line in the reciprocal space, $k_{0}$. When $σ_{\rm{flat}}$ 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 $Δ$, 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.