Observation of Nodal-Line Plasmons in ZrSiS

Nodal-line semimetals (NLSMs), a large family of new topological phases of matter with continuous linear band crossing points in the momentum space, attract considerable attention. Here, we report the direct observation of plasmons originating from topological nodal-line states in a prototypical NLSM ZrSiS by high-resolution electron energy loss spectroscopy. There exist three temperature-independent plasmons with energies ranging from the near- to the mid-infrared frequencies. With first-principles calculations of a slab model, these plasmons can be ascribed to the correlations of electrons in the bulk nodal lines and their projected surface states, dubbed nodal-line plasmons. An anomalous surface plasmon has higher excitation energy than the bulk plasmon due to the larger contribution from the nodal-line projected surface states. This work reveals the novel plasmons related to the unique nodal-line states in a NLSM.

Figure 1

(a) Crystal structure of ZrSiS with thin solid lines depicting a unit cell and yellow plane representing the cleavage plane. (b) LEED pattern on the (001) surface of ZrSiS, obtained at room temperature with an incident beam energy of 125 eV. (c) Fermi surface in the bulk Brillouin zone encapsulating nodal lines in electron or hole pockets. The diamondlike nodal line at $k_z=\pi$ plane is demonstrated by the yellow lines as an example. The cyan plane above is the surface Brillouin zone. (d) Band structures of ZrSiS along the $\overline{\mathrm{\Gamma }}\overline{\mathrm{X}}\overline{\mathrm{M}}$ path around $\overline{\mathrm{X}}$ point from the tight-binding model. The gray lines are the projection of bulk bands, while the blue and red lines are the surface states (the HSS and the FSS, with the details in the text).

Figure 2

Typical 2D momentum-energy mappings of HREELS along (a) the $\overline{\mathrm{\Gamma }}\overline{\mathrm{X}}$ and (b) the $\overline{\mathrm{\Gamma }}\overline{\mathrm{M}}$ directions of ZrSiS at room temperature. (c),(d) Stacks of momentum-dependent EDCs along the $\overline{\mathrm{\Gamma }}\overline{\mathrm{X}}$ and $\overline{\mathrm{\Gamma }}\overline{\mathrm{M}}$ directions, respectively. The corresponding momentum values are listed on the right. The plasmon peak positions are indicated, with error bars from the fitting procedure described in the text.

Figure 3

(a) Extracted plasmon dispersions from the EDC stacks in Figs. 2. The dashed lines are the polynomial fittings. (b) Extracted plasmon linewidths (full width at half maximum, FWHM) along the $\overline{\mathrm{\Gamma }}\overline{\mathrm{X}}$ direction at room temperature (RT). (c) Comparison of dispersions along the $\overline{\mathrm{\Gamma }}\overline{\mathrm{X}}$ direction between RT and 35 K. (d) The dependence of peak positions on temperature. The peak positions of $\alpha$ are at $q=0.005{\AA }^{-1}$ while the peak positions of $\beta$ and $\gamma$ are at $q=0.020{\AA }^{-1}$. The error bars originate from the uncertainty of the fittings with different background subtractions.

Figure 4

(a) Schematic for the slab of ZrSiS for the DFT calculations. (b) Calculated electronic dispersions of the slab in (a) along the $\overline{\mathrm{\Gamma }}\text{−}\overline{\mathrm{X}}\text{−}\overline{\mathrm{\Gamma }}$ path around $\overline{\mathrm{X}}$ point. The gray solid lines are the surface projected bulk bands. The color bar indicates the position of the surface states in the slab. The green dashed line is the position of the experimental Fermi level obtained from ARPES. The blue arrow sketches the interband correlations between the HSSs and the FSSs, while the pink (orange) arrows correspond to the intraband correlations within the HSSs (within the projected nodal-line bands). (c) Comparison between the experimental plasmon peaks (dots) and the calculated loss functions (lines). (d),(e) The calculated Fermi surface at surface and center of the slab in (a), respectively. (f) Difference between (d) and (e). The red means the surface density is larger than the bulk one, and blue means the opposite. (g) The local density of states (DOS) of slab with red, black, and blue curves for surface, bulk, and their difference, respectively.