Recently, a new type of quantum materials, so called Dirac semimetals (DSs), were discovered and intensively investigated for their rich physics and broad application potentials.^[1–8] Different from regular insulators or metals, DSs are systems that host Dirac points (DPs, robust degeneracy points between conduction and valence bands) and Dirac fermions in their electronic structure and possess intriguing electronic transport behaviors such as high bulk carrier mobility and extremely large magnetoresistance.^[4,5,9,10] The robustness of the Dirac points is usually protected by the crystal inversion or time reversal symmetry (e.g., in two-dimensional DS graphene^[11] and three-dimensional DS Na³Bi^[2,4] and Cd³As^2[3,5–8]). Breaking the symmetry in DS would induce a topological phase transition and achieve other nontrivial phases. For example, three-dimensional (3D) Weyl semimetal^[12–16] can be realized by breaking either time reversal symmetry or inversion symmetry in 3D DS.

More recently, a new type of DSs named Dirac line-node semimetals (DLNSs) were predicted in crystals with non-symmorphic symmetry (such as glide planes or screw axis). Unlike the previously studied DSs which contain discrete DPs, the additional symmetry in DLNSs induces and protects a band degeneracy at the Brillouin zone boundary, leading to one-dimensional (1D) Dirac line nodes.^[17] The degeneracy at the line node is robust against perturbations (such as spin-orbit coupling effect (SOC)). Moreover, the DLNS is predicted to host unusual electric transport properties since 1D Dirac line-nodes are a more significant feature in the band structure and can have stronger contributions to the physically observable properties of the material (e.g., in electric transport).^[18–21]

The line nodes have been predicted in various compounds, including the non-symmorphic compound ZrSiS and its isostructural family WHM (W = Zr, Hf, or La; H = Si, Ge, Sn, or Sb; M = O, S, Se or Te).^[22] Previous band structure measurements on ZrSiS^[19,23,24] and the related compounds ZrSiTe^[25] and HfSiS^[26,27] by angle-resolved photoemission spectroscopy (ARPES) have found signatures of the Dirac line-nodes and the surface states. However, since the previous measurements were taken with a few discrete photon energies, a more convincing identification of the bulk and surface states and detailed measurement on the line nodes are required. Furthermore, to better investigate the transport properties originated from the Dirac line-nodes, it would be desirable to manipulate the bulk and surface electronic states including the line-node structure in ZrSiS. All of these become the goals of our work.

In this work, we systematically studied the electronic structure of ZrSiS using high-resolution ARPES with broadly tunable photon energies. The measurement across multiple BZs identified a complete set of electronic structure, including the bands coming from both the bulk and surface electronic states. Especially, we identified the Dirac line node along the X–R direction, which proves the DLNS property in ZrSiS. Moreover, by surface potassium doping, we clearly observed the different evolution behaviors of the surface and bulk bands. We further noticed that the Dirac line node remains intact after the surface doping, proving the robustness from the symmetry protection. Our finding provides detailed information on the electronic structure of ZrSiS and proposes a method for manipulating its electronic structure for future investigations and applications.

Single crystals of ZrSiS were grown by a chemical vapor (iodine (I₂) as a transport agent) transport method in a two-step process. First, the polycrystalline ZrSiS powders were synthesized by direct solid-state reaction using high-purity elementals Zr, Si, and S in cleaned quartz ampoules. The stoichiometric amounts of ternary mixture were heated to 1100 °C and maintained at this temperature for 7 days to make the reaction complete. Then, we could obtain the single phase products after the samples were quenched to room temperature. Second, the as-prepared polycrystalline ZrSiS powder together with I₂ was sealed in a quartz tube. Then the quartz tube was kept in a two-zone furnace for 10 days with the growing temperature profile of 1150–1000 °C. The metallic luster crystals were obtained for ARPES measurements.^[20]

The ARPES experiments were performed at the beamline I05 of the Diamond Light Source (DLS), beamline 10.0.1 of the Advanced Light Source (ALS) and beamline 13U of the National Synchrotron Radiation Laboratory (NSRL), Hefei, China, all of them were equipped with Scienta R4000 analyzers. The measurement sample temperature and pressure were 10 K (20 K in ALS) and lower than Torr, respectively. The angle resolution was 0.2°, and the overall energy resolutions were better than 15 meV. The samples were cleaved in situ along the (001) plane.

The band structure and Fermi surface of bulk and slab ZrSiS were calculated by the OpenMX code^[28] within the framework of the density functional theory in the generalized gradient approximation.^[29] The bases are s³p²d², s²p²d¹, and s³p³d²f¹ for Zr, Si, and S elements, respectively. The energy cutoff for real-space integration is 250 Ry.

The crystal structure of ZrSiS is shown in Fig. 1(a) (PbFCl structure type in the tetragonal P4/nmm space group (No. 129), with lattice constants a = b = 3.544 Å, c = 8.055 Å). In this system, square nets of Si form glide planes in the crystal, while the C_2x ( axis of the lattice is the screw axis, thus preserving two kinds of non-symmorphic symmetries.^[17] The relatively weak bonding between two neighboring Zr–S layers provides a natural (001) cleavage plane. According to the ab-initio calculation of the bulk band structure (Fig. 1(c)), all lines along X–R direction preserve degeneracy from the protection of glide mirror, screw axis, and inversion symmetry, thus forming degenerate lines, including the Dirac line-nodes formed from the crossing of the Dirac-like band. The bulk Brillouin zone (BZ) and the surface BZ of the (001) surface are shown in Fig. 1(d) where the predicted position of the Dirac line node (solid green line) is indicated.

Fig. 1.

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Fig. 1. (color online) Characterization of ZrSiS single crystals and Dirac line node. (a) PbFCl-type structure of ZrSiS crystal, lattice constants (a = b = 3.544 Å, c = 8.055 Å) and cleavage plane are labelled. (b) The schematics of Dirac node and Dirac line node in the momentum space. (c) Calculation results of the bulk band structure of ZrSiS along high-symmetry directions. The green line indicates the position of the Dirac line node. (d) Illustration of the Dirac line-node location (labelled by the solid green line) in Brillouin zone boundary along the X–R direction. In addition, the projected surface BZ of (001) plane is also labelled. (e) Core level photoemission spectrum of ZrSiS showing the characteristic Zr4s, Zr4p, and Si2p peaks. Left inset: cleaved surface of ZrSiS single crystal used in this study. Right inset: Laue pattern showing the high quality of the ZrSiS crystal. (f) Broad range photoemission spectral intensity map of the Fermi-surface covering more than one BZ, showing the correct symmetry and the characteristic of the FS.

After cleaving, large flat and shiny surfaces are exposed, which are ideal for ARPES measurements. The high quality of the crystal can also be verified by the Laue patterns and the core level photoemission spectrum which clearly shows the characteristic Zr_4s, Zr_4p, and Si_2p peaks (Fig. 1(e)). The broad Fermi surface (FS) mapping in Fig. 1(f) covering multiple BZs further confirms the high quality (001) cleavage plane, which allows us to carry out the study below.

To investigate the detailed electronic structure of ZrSiS, we focus on the first BZ by carrying out high-resolution ARPES measurements, and the results are shown in Fig. 2. The stacking plots of constant-energy contours in a broader binding energy range (Fig. 2(a)) show the electronic structure evolution around the point. From the detailed plot of the constant energy contours (Fig. 2(b)), we could clearly identify two sets of features: one is the large diamond-shaped FS, which is formed by the connected band structure at four points; the other is the elliptical electronic pocket centered at each point. While the first set of features can be well reproduced by our ab-initio calculations of the bulk bands (Figs. 2(b)(i)–2(b)(iv)), the second set of features could not be found in the bulk band calculations, suggesting their bulk and surface origins, respectively.

Fig. 2.

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Fig. 2. (color online) General electronic structure of ZrSiS. (a) Stacking plots of constant-energy contours in broader binding energy range show the band structure evolution. (b) Top row: photoemission spectral intensity map showing the constant energy contours of bands at (i), 0.25 eV (ii), 0.5 eV (iii) and 0.75 eV (iv), respectively. Bulk states (BS) and surface states (SS) are labelled. Bottom row: corresponding calculated constant energy contours at the same binding energies as in the experiments above. (c) 3D intensity plot of the photoemission spectra centred around point. High symmetry cuts are exposed. (d) Broad range high symmetry cut along the – – direction (i), with their corresponding calculated bulk band structure (ii). BSs and SSs are labelled on the data and zoomed in surface states near the Fermi level (iii). (e) High symmetry cuts along the – (i) and – – (iii) directions and corresponding calculated bulk band structures ((ii), (iv)). SS is labelled in the data.

In addition to the constant energy contours, we focus on the dispersions along the high symmetry directions (Figs. 2(c)–2(e)). We compare the bulk bands between experiments and ab-initio calculations along the high symmetry directions ( – – , – , and – – , the excellent overall agreement allows us to identify the surface states (the observed bands not included in the bulk band calculations, as indicated by the green arrows in Figs. 2(d)(i) and 2(e)(iii)) from the bulk states (red solid curves in Figs. 2(d)(i) and 2(e)(iii)). Combining the constant-energy contours, we notice that the surface states form a parabolic shape around the point, while the bulk band dispersions (Fig. 2d(i)) form a linear crossing (Dirac point) sitting at at the point. Furthermore, we notice a small gap opening at the band crossing along the – direction due to the effect of SOC, showing nice agreement with the ab-initio calculations (Fig. 2(e)(ii)).

The surface and bulk nature of the electronic bands are further supported by the photon-energy-dependent measurement which probes the band dispersion at different k_z values. By a series of measurements at different photon energies, we clearly identify the surface and bulk bands in the FS at momentum space (Fig. 3(a)). For details, we choose four cuts and plot them in Figs. 3(b)(i)–3(b)(iv) with their respective k_z locations indicated by the magenta dotted lines ( to ) in Fig. 3(a). We clearly notice that while the parabolic type bands do not change with k_z, other features show variation with k_z, proving their origins from the surface and bulk, respectively. Moreover, we clearly observe that the Dirac node formed by linear band touching disperses with k_z and results in a line-node along the X–R direction (Figs. 3(c) and Fig. 3(d)). With measurements of fine k_z steps, the dispersion of the X–R line node could be reconstructed (by tracking the positions of the DP positions), as illustrated in Fig. 3(e), which shows good agreement with our calculations (solid green curve in Fig. 3(e)).

Fig. 3.

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Fig. 3. (color online) Kz measurements and Dirac line node in ZrSiS. (a) Plot of the constant energy contour at in –kz space. The bulk and surface state bands are indicated by the red and green arrows, respectively. Magenta dotted lines indicate the kz positions of four representing cuts shown in (b) and (d). (b) Detailed analysis of the four representing cuts, the surface bands and linear dispersions are marked. (c) The 3D BZ shows the constant energy contours (ky–kz plane and kx–ky plane) around the DP and illustrates the location of the Dirac line node (green solid line) in ZrSiS (X–R direction). (d) (i) Schematic of the Dirac line node along the kz direction (labelled by the green curve) with the grey planes which are corresponding to each cut in (b) and (d) (ii). The bright curves sketch the Dirac dispersions we observe in each cut as in (ii). (ii) Stack plot of the four cuts as in (b). Green curve indicates the dispersion of the Dirac line node. (e) The fitted DP positions (red dots) at various kz values, the green curve indicates the calculated dispersion along the X–R direction.

Finally, we demonstrate the modification of the electronic structure of ZrSiS by introducing alkaline metal onto the sample surface. The stacking plots of constant-energy contours (Fig. 4(a)) show the electronic structure evolution after surface potassium doping. By comparing the FS and high symmetry cuts ( – – and – – (Figs. 4(b)–4(d)), we clearly see that the bands identified as surface state bands shift away from significantly and change their shape and volume while the bulk state bands almost do not show much shift or change. Such different behaviors not only help us clearly identify the surface states bands and bulk states bands, but also demonstrate the effect of tuning the surface and bulk electronic structures in ZrSiS. Moreover, as the surface dopant appears as perturbative impurities, the fact that the Dirac point stays intact proves the robustness of the Dirac line-node under the protection of the non-symmorphic crystal symmetry.

Fig. 4.

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Fig. 4. (color online) Surface potassium doping results in ZrSiS. (a) Stacking plots of constant-energy contours in broader binding energy range in the K-doped sample. (b) Side-by-side comparison of (i) pristine and (ii) K-dosed data on the Fermi surface where we can easily distinguish SSs from the BSs. (c) Side-by-side comparison of the high symmetry cut along – – direction in the (i) pristine and (ii) K-dosed sample where the SSs are labelled. (d) Side-by-side comparison of the high symmetry cuts along – – direction in the (i) pristine and (ii) K-dosed sample where the SSs and BSs are labelled.

In summary, our systematic measurement of the electronic structure of the ZrSiS compound has obtained the full set of band structure in the BZ, including the electronic states originated from both the bulk and surface. Our measurement of the Dirac line node convincingly establishes that ZrSiS is a DLNS protected by non-symmorphic symmetry. Our in-situ K-doping data illustrates the different behaviors of the surface and bulk bands, as well as the robustness of the Dirac line-node. These band characteristics not only help us understand the intriguing transport properties in ZrSiS, but also point to methods in manipulating the electronic properties in DLNS.