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

ZrSiS exhibits a frequency-independent interband conductivity $\sigma (\omega )=\text{const}(\omega )\equiv {\sigma }_{\mathrm{flat}}$ in a broad range from 250 to $2500{\mathrm{cm}}^{-1}$ (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, ${\sigma }_{\mathrm{flat}}$ 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 $\mathrm{\Delta }$, for which we determine an upper bound $\max (\mathrm{\Delta })=30\mathrm{meV}$ 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.

Figure 1

Frequency-dependent reflectivity of ZrSiS at 10 and 300 K. For intermediate temperatures the reflectivity curves lie in between, and are not shown for clarity. No temperature dependence is seen above $\sim 8000{\mathrm{cm}}^{-1}$. The sketches show the position of the low-energy nodal line (red dashed line) in BZ and the Dirac bands near the Fermi level.

Figure 2

Real part of the optical conductivity of ZrSiS as a function of frequency.

Figure 3

Examples of the optical conductivity fits for ZrSiS at low frequencies. Thick solid lines are experimental data; thin solid lines are total fits; dashed lines represent fit contributions of the Drude (red), Pauli-edge (black), and Lorentzian (olive, shown only for $T=10\mathrm{K}$) terms. Thin dotted (blue) lines represent attempts to fit the 300 K data without the Lorentzians.

Figure 4

Main frame: imaginary part of the optical conductivity in ZrSiS. Arrow indicates the position of the Pauli edge at 10 K. Inset: real part of the dielectric constant near the plasma frequency.