Lattice dynamics of Dirac node-line semimetal ZrSiS

We report a comprehensive study of lattice dynamics of the Dirac node-line semimetal ZrSiS single crystal by Raman spectroscopy and first-principles calculations. The weak covalent bonding between ZrSiS layers is confirmed by the absence of low-frequency shear or breathing Raman modes down to $15\mathrm{c}{\mathrm{m}}^{-1}$. All six Raman-active optical phonons are identified at 300 K, whose energies and symmetries match our phonon-dispersion calculations and polarized Raman measurements. The thermodynamic stability is verified from 77 to 300 K, and, with increasing temperature, sizable softening of Raman modes is observed with broadened profiles. The first-order temperature coefficients are found to be linearly dependent on temperature. Furthermore, using multiple excitation laser wavelengths of 488, 514.5, 568, 647, and 785 nm, we find that three out-of-plane Raman modes are all nondispersive, and their normalized intensity resonances at different laser energies can be attributed to the different interband transitions. Our work provides detailed information of ZrSiS lattice vibrations, as well as the coupling between ZrSiS lattice vibrations and its electronic states.

Figure 1

(a) Side view and top view of ZrSiS layered crystal structure. Si, Zr, and S atoms are in blue, green, and yellow, respectively. (b) Dominant atom displacements of Raman-active optical phonon modes and energies. (c) Calculated ZrSiS phonon-dispersion relation, and the phonon density of states with colored lines indicating the partial DOS from different elements. (d) Low-frequency Raman spectrum of ZrSiS single-crystal $ab$ plane (black) and side plane (perpendicular to the $ab$ plane, red) using 514.5-nm incident laser of 0.05 mW at ambient conditions.

Figure 2

(a) Raman spectra of single-crystal ZrSiS ($ab$-plane configuration) for selected laser polarization angles θ from the initial parallel polarized configuration. (b) Polar plot of $A_{1g}^1$, $A_{1g}^2$, and $B_{1g}$ Raman-mode intensities with respect to angle θ; the radial scale is 100 counts per grid. (c) Raman spectra of single-crystal ZrSiS under 514.5-nm laser irradiation with the different power. The vertical dotted lines are a guide for the eye.

Figure 3

Raman spectra of ZrSiS side plane at different temperatures from 77 to 300 K. Spectra are shifted vertically for clarity.

Figure 4

(a)–(f) Raman shifts and (g)–(l) FWHM of characteristic Raman modes of ZrSiS single crystal with respect to temperature. Three solid lines are the linear fittings of data from 77 to 300 K.

Figure 5

(a) Raman spectra of ZrSiS single crystal ($ab$-plane configuration) for excitation laser lines of 488, 514.5, 568, 647, and 785 nm. (b) Normalized $A_{1g}^1$, $A_{1g}^2$, and $B_{1g}$- mode intensities for five incident lasers. (c) Calculated ZrSiS electronic structure without SOC. (d) Brillouin zone of ZrSiS primitive tetragonal lattice; the Dirac cone line nodes are along the red line.