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

TL;DR

ZrSiS exhibits a broad, frequency-independent optical conductivity due to transitions in two-dimensional Dirac bands, with properties linked to the nodal line length and a small spin-orbit gap, supported by experimental and theoretical agreement.

Contribution

This study identifies the origin of flat optical conductivity in ZrSiS as transitions in quasi-2D Dirac bands and relates it to the nodal line length, providing a model that aligns with experimental data.

Findings

Flat optical conductivity spans 250-2500 cm$^{-1}$ in ZrSiS.

The conductivity is linked to the nodal line length in reciprocal space.

A small spin-orbit gap of up to 30 meV is estimated.

Abstract

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, $\sigma_{\rm{flat}}$ is not supposed to be universal but related to the length of the nodal line in the reciprocal space, $k_{0}$. When $\sigma_{\rm{flat}}$ 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 $\Delta$, for which we determine an upper bound max($\Delta$) = 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.