Pressure-Induced Excitations in the Out-of-Plane Optical Response of the Nodal-Line Semimetal ZrSiS

The anisotropic optical response of the layered, nodal-line semimetal ZrSiS at ambient and high pressure is investigated by frequency-dependent reflectivity measurements for the polarization along and perpendicular to the layers. The highly anisotropic optical conductivity is in very good agreement with results from density-functional theory calculations and confirms the anisotropic character of ZrSiS. Whereas the in-plane optical conductivity shows only modest pressure-induced changes, we found strong effects on the out-of-plane optical conductivity spectrum of ZrSiS, with the appearance of two prominent excitations. These pronounced pressure-induced effects can neither be attributed to a structural phase transition according to our single-crystal x-ray diffraction measurements, nor can they be explained by electronic correlation and electron-hole pairing effects, as revealed by theoretical calculations. Our findings are discussed in the context of the recently proposed excitonic insulator phase in ZrSiS.

Figure 1

Optical response functions of ZrSiS at ambient conditions for polarization directions $\mathbf{E}\parallel ab$ and $\mathbf{E}\parallel c$: (a) reflectivity spectra and (b) real part of the optical conductivity ${\sigma }_1$. Inset of (a): loss function $-\mathrm{Im}(1/\widehat{\epsilon })$, where $\widehat{\epsilon }$ is the complex dielectric function. Inset of (b): crystal structure of ZrSiS with Si square nets parallel to the $ab$ plane.

Figure 2

Pressure-dependent optical conductivity ${\sigma }_1$ with the Drude-Lorentz fitting and the corresponding contributions at 0 GPa for (a) $\mathbf{E}\parallel ab$ and (b) $\mathbf{E}\parallel c$. Arrows mark the most pronounced pressure-induced changes in the spectra. Inset of (a): comparison between the experimental and both DFT and BSE calculated interband conductivity ${\sigma }_{1,\text{interband}}$ at 0 GPa.

Figure 3

(a),(b) Comparison between the experimental and DFT interband conductivity ${\sigma }_{1,\text{interband}}$ at 2.0 and 7.0 GPa, with the total fitting curve and the fitting contributions for the experimental ${\sigma }_{1,\text{interband}}$ at 7.0 GPa, for $\mathbf{E}\parallel ab$ and $\mathbf{E}\parallel c$, respectively. Insets of (a),(b): comparison between DFT and BSE theoretical results and experimental interband conductivity ${\sigma }_1$ at 7.0 GPa for $\mathbf{E}\parallel ab$ and $\mathbf{E}\parallel c$, respectively. (c) Temperature-dependent high-energy optical conductivity for $\mathbf{E}\parallel ab$. The arrow marks the temperature-induced shift of the $L4$ peak. (d) Comparison between the temperature ($T$) and pressure ($P$) dependence (both experimental and theoretical) of the frequency position of the $L4$ peak. (e) Pressure-dependent frequency position and oscillator strength (osc. str., inset) of the peaks $F1$ and $F2$. (f) Volume $V$ of the unit cell and lattice parameters $a$ and $b$ as a function of pressure. The error bars represent three times the estimated standard deviation. The solid line is a fit with a Murnaghan-type EOS (see text).