{'fraction_non_alphanumeric': 0.039107646821663754, 'fraction_numerical': 0.009676118801236392, 'mean_word_length': 4.7026819923371646, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Multiple Symmetry-Protected Dirac Nodal Lines in A Quasi-One-Dimensional Semimetal

Nodal-line semimetals (NLSMs) contains Dirac/Weyl type band-crossing nodes extending into shapes of line, loop and chain in the reciprocal space, leading to novel band topology and transport responses. Robust NLSMs against spin-orbit coupling typically occur in three-dimensional materials with more symmetry operations to protect the line nodes of band crossing, while the possibilities in lower-dimensional materials are rarely discussed. Here we demonstrate robust NLSM phase in a quasi-one-dimensional nonmagnetic semimetal TaNiTe5. Combining angle-resolved photoemission spectroscopy measurements and first-principles calculations, we reveal how reduced dimension can interact with nonsymmorphic symmetry and result into multiple Dirac-type nodal lines with four-fold degeneracy. Our findings suggest rich physics and application in (quasi-)one-dimensional topological materials and call for further investigation on the interplay between the quantum confinement and nontrivial band topology.

Here, we report the realization of robust Dirac nodal lines (DNLs), i.e., nodal lines with four-fold degeneracy, in a quasi-one-dimensional (Q1D) nonmagnetic semimetal TaNiTe5. Combining angle-resolved photoemission spectroscopy (ARPES) and density functional theory (DFT) calculations, we reveal that the interplay between nonsymmorphic symmetry and Q1D geometry results into multiple DNLs robust against SOC, as presented by three key features: (1) four-fold degenerate nodes (Dirac cones) at the boundary (Z point) of the bulk Brillouin zone (BZ); (2) these Dirac cones extend through the whole 3D BZ along T − Z − T line and form DNLs; (3) multiple nodal loops in Z − A − R plane. The consistency between ARPES measurements and DFT calculations justifies the above claims and provides direct evidence of the firstdiscovered Q1D NLSM phase robust against SOC in TaNiTe5. Our results open a door for topological states of matter in Q1D materials and call for further investigation on the interplay between the quantum confinement and nontrivial band topology. Single crystals of TaNiTe5 adapt an orthorhombic layered structure with a space group (No. 63) [47][48][49]. The lattice constants can be inferred from powder Xray diffraction (XRD) (Fig. S1) and single crystal XRD results (Table S1)  to recent report [47]. The Hall resistivity shows generally positive slope with field and clearly non-linear behavior, suggesting multiple Fermi surfaces and hole-type carriers.

Lattice structure and characterization
All these deduced electronic features are confirmed by ARPES data discussed below. To uncover the topological properties of TaNiTe5, we start from DFT calculation with the lattice constants obtained from our XRD results. Fig. 2 Interestingly, these strongly dispersed bands along A − Z − R path appear in pairs, forming Type-Ⅰ Dirac cones on point Z, Type-Ⅱ Dirac cones on point R, and cross each other several times forming Type-Ⅱ Dirac cones in between, which are also highlighted in colors in Fig. 2(b). Further DFT calculation confirms that all Dirac cones connect each other forming nodal lines and nodal loops on " = # $ (Z − A − R) plane, as shown in Fig. 2(c). We prove that these DNLs are protected by nonsymmorphic symmetry in the presence of strong SOC in TaNiTe5, providing evidence of robust NLSM phase in a Q1D system (see Supplementary materials for details). Our ARPES measurements provide direct evidence of these multiple DNL features.

Multiple Dirac nodal lines in Q1D TaNiTe5
We first analyze the Dirac cone at bulk Z point and DNLs along T − Z − T line as indicated in Fig. 3(a). Fermi surface and bands measured by ARPES and projected from DFT calculation are shown in comparison in Fig. 3(b, c). For ARPES measurement, the photon energy was selected as 50 eV, so it approximately covers the Γ − Z − A plane, see Fig. S2 for systematic photon energy-dependent data. Satisfactory agreement between experiment and theory is reached considering the detailed Fermiology and spectrum. In particular, the four-fold Dirac cone crossing at the bulk Z point (as discussed in Fig. 2) can be clearly resolved by ARPES, as marked in Fig. 3(c) by green arrows. This measured Dirac cone corresponds to the calculated one shown in green lines in Fig. 2(b). The calculated Dirac cone shown in red lines is above the Fermi level and the one in blue lines is too weak to be resolved (blue arrows in Fig. 3(c)).
Judging from the highlighted dispersion in the curvature plot, this Dirac crossing is gapless at Z point. Furthermore, in Fig. 3(d) we present the spectra of this Dirac crossing at different & planes measured by varying the incident photon energy. It is clear that this Dirac crossing remains gapless across the 3D BZ, composing a DNL from Z to T point as indicated by the green curves in Fig. 2(c) and Fig. 3(a). It is noted that this DNL shows clear dispersion along Z − T line in DFT (Fig. 2(b)  Considering the nodal loops locating in T − Z − A plane, we can also find strong evidence of their corresponding Dirac crosses from the satisfactory match between ARPES and DFT. In Fig. 4(a) bottom panel, the nodal loops from three pairs of bands close to the Fermi level are shown in T − Z − A plane with red, blue, green colors as in Fig. 2(c). ARPES spectra and DFT dispersion along ! (Z → A) direction are shown in comparison in Fig. 4(b, c, d). In the present DFT energy-momentum window ( Fig.   4(b)), two Dirac crosses can be identified for the green pair of bands, four Dirac crosses for the blue pair and three for the red, with all the band pairs containing both type I and type II Dirac cones. The dashed ellipses in Fig. 4(b) point out regions where the Dirac gaps are too small to be resolved in ARPES spectra. Except that, all the features predicted by DFT can be identified in the ARPES spectra, as emphasized in Fig. 4(c) and 4(d)by arrows colored correspondingly. The existence of multiple type I and type II Dirac crosses along ! (Z → A) direction provides strong evidence for the nodal loops shown in Fig. 4(a).
Further evidence of these Dirac crosses can also be derived from the ARPES spectra along " (parallel to Γ − Z − Γ) direction at different values of ! . As shown in Fig.   4(e), ARPES spectra along " direction at different ! positions present evolution of the Dirac crosses corresponding to the nodal loop shape. When the ! positions of the spectra, as specified by red circles in Fig. 4(a) bottom panel, coincide with the nodal loops, gapless Dirac crosses can be identified directly in the 2D curvature spectra. These Dirac crosses are also emphasized by arrows whose colors correspond to the band pairs.

Summary
Combining ARPES measurements, DFT calculations and symmetry analysis, we have demonstrated how reduced dimension can interact with nonsymmorphic symmetry and reshape the band topology in a Q1D semimetal. The resulting multiple robust Dirac crosses and DNLs against SOC suggest fertile physics in lowerdimensional topological systems [50][51][52]. Compared to their 3D and 2D counterparts, Q1D topological materials could be better suited for device exploitation due to their reduced dimensionality, especially in devices utilizing coherent spin transport [53,54].
Our work would stimulate further effort in exploring these rich physics and applications in Q1D topological materials.