I n step with the resurgent interest in 2D materials, there have been extensive efforts toward engineering additional levels of confinement and, thus, lower dimensionality in fewand monolayer van der Waals bonded 2D structures. The greatest successes have been achieved in the fabrication and synthesis of graphene nanoribbons (GNRs), where rational bottom-up synthesis has been accomplished using the selfassembly of molecular precursors. 1,2 This has enabled the growth of GNRs with specific edge structures 3 and atomically precise widths, 4 as well as single GNR heterojunctions with engineered band alignment 5 and topology. 6 Exciting physics is similarly predicted to arise when 2D transition metal dichalcogenides (TMDs) are further constrained toward onedimension (1D), 7 including the emergence of metal-insulator transitions, 8 enhanced thermoelectric performance, 9 ferromagnetism, 10,11 and tunable band gaps. 8 However, the synthesis or fabrication of TMD NRs has lagged far behind that of GNRs both in terms of quality and width control. Past studies have relied upon top-down fabrication methods that require lithography and etching processes, 12,13 which results in NRs with widths greater than 50 nmtoo large to observe quantum confinement effects and with a high degree of structural disorder. 14 Molecular beam epitaxy has been used for the fabrication of ultranarrow MoSe 2 NRs, 15,16 but this method has little flexibility in implementation (e.g., substrate choice). Other bottom-up techniques, including chemical vapor deposition and vaporliquid-solid growth, have recently been used to grow MoS 2 NRs, 17,18 resulting in ribbons with average widths >50 nm, again too large to access predicted quantum phenomena.

The templated growth of 1D nanomaterials using multiwalled carbon nanotubes (MWCNTs) has been successfully demonstrated for a variety of materials including elemental metals, 19 halides, 20 trichalcogenides, 21,22 and molecular chains, 23 where the synthesis generally results in nanowireor chain-like structures. Nanoribbons have also been observed in nanotubes filled via solution based processes. 24,25 Here, we extend the method to ribbon-like morphologies, and demonstrate the growth of 2H-TaS 2 NRs with a simple vapor phase process. TaS 2 is a metallic TMD, which hosts multiple charge-density-wave (CDW) phases, [26][27][28] a Mott insulator state 29 and possible quantum spin liquid, 30 making it a unique material for the study of strongly correlated physics under extreme dimensional constraint. [31][32][33] We achieve TaS 2 NRs with thicknesses down to the monolayer limit (typical layer numbers are between 1 and 3), widths as low as 2.5 nm, and lengths greater than 100 nm. The MWCNT sheath fully encapsulates the TaS 2 NR, protecting it from interaction with the environment. The growth produces NRs with controllable widths, clean NR surfaces and edges and enables easy handling (e.g., solution-based processing) and subsequent imaging of the structure and detailed atomic registry of NRs with transmission electron microscopy (TEM) and aberrationcorrected annular dark-field scanning transmission electron microscopy (ADF-STEM). Furthermore, we observe and investigate previously unknown and unique periodic atomic superstructures defined by ordered defect arrays. Firstprinciples calculations are used to elucidate the electronic structure of the NRs and atomic superstructure, revealing the presence of flat bands localized at the defect boundaries and edges.

TaS 2 NRs are grown within MWCNT using chemical vapor transport (CVT), described in detail in the Supporting Information. In brief, MWCNTs are first opened at the end via oxidation at high temperature; 34 the opened nanotubes are then coated onto the inner surface of a quartz ampule, which is filled with elemental Ta, S, and an iodine transport agent and sealed under vacuum. Synthesis is carried out in a gradient furnace in a manner similar to that used for single crystal TMD growth via CVT. We surmise that the growth mechanism is similar to the conventional vapor transport growth mechanism for MX 2 materials but subject to the additional geometrical constraint of the NT interior diameter.

Figure 1A shows a schematic of a monolayer TaS 2 NR within a carbon nanotube (for simplicity, a single-wall nanotube is shown), in both plan and end views. Figure 1B-D shows microscopy images of the as-synthesized material.

Figure 1B shows a plan view TEM image of a 5 nm wide NR, while Figure 1C shows an edge view TEM image of a 3-layer NR. The dashed yellow lines in Figure 1B and 1C delineate the inner walls of the MWCNT. The strong contrast (dark lines are the TaS 2 atomic planes) in Figure 1C is because of the edge-on orientation, resulting in greater sample thickness; the measured interlayer distance (∼0.7 nm) matches well with that of bulk TaS 2 (0.7 nm). 35 We further explore the detailed atomic structure and phase of the TaS 2 NR using atomic-resolution ADF-STEM imaging. A NR with width 3.8 nm is presented in Figure 2A, where the hexagonal lattice characteristic of (monolayer) prismatically coordinated TaS 2 is clearly visible. A zoomed in portion of the ADF-STEM image of the NR in Figures 1D is also shown in 2B. Figure 2C is a simulated STEM image of a monolayer of TaS 2 with prismatic coordination. Figure 2D compares the line intensity profile along the dashed green box in the experimental image of Figure 2B and that of a simulated STEM image of monolayer TaS 2 (Figure 2C). This match suggests the experimental image is that of a monolayer TaS 2 NR with prismatic coordination, consistent with the bulk 2H phase, and further, is inconsistent with simulations performed on bilayer TaS 2 . The presence of the prismatic phase is expected given the slow cool during synthesis, and the fact that the prismatic phase is the preferred phase at room temperature. The smallest NR width we have observed is 2.5 nm, and lengths of order 100 nm is not uncommon. The widest NR observed is 6 nm wide, and the average NR width is 3.8 nm. A histogram of NR widths is shown in Figure S1. In addition to strictly planar morphologies, some NRs also show curling at the edges (Figure 2E), presumably facilitated by the MWCNT confinement. The composition of the NRs is further supported by energy dispersive X-ray spectroscopy (EDS) (Figure 2G-I), which shows, over the width and length of the NR, a reasonably uniform distribution of Ta and S atoms. An ADF-STEM images of the mapped NR is shown for reference in Figure 2F. The (wider, as expected) carbon contribution is from the MWCNT. The EDS spectrum collected from the TaS 2 NR also clearly shows peaks of Ta and S (Figure S2); we also observe O (contamination), Si, and N (substrate), not shown in the displayed energy range. This further confirms the identity of the NR material.

We find that TaS 2 NRs can form not only with perfect atomic structure but also with striking periodic atomic superstructure, an example of which is presented in Figure 3. Figure 3A shows an atomic-resolution ADF-STEM image of a 3.3 nm wide TaS 2 NR containing an ordered, "zigzag"-like superstructure characterized by triangular domains of ideal TaS 2 lattice interrupted by boundaries of low STEM contrast. The zigzag structure is dramatically highlighted in a bandpass filtered version of the same image, presented in Figure 3B. The period of the perturbation is ∼9 unit cells.

Given the nature of bulk 2H-TaS 2 , one may hypothesize that the periodic features arise from CDW-type distortions. As we discuss in more detail below, DFT calculations indicate that the TaS 2 NRs considered here appear to support CDWs, but the CDW amplitudes are small and CDWs are not the origin of the dramatic zigzag superstructure. Furthermore, the presence of CDW phases in the TaS 2 NR is not verified experimentally in this work. Rather, the superstructure arises from linear defect arrays. The atomic structure of the defect arrays is calculated via first-principles calculations (see below), and the relevant candidate structure is shown in Figure 3C. The structure is characterized by zigzag tracks of linearly formed S vacancies. A STEM simulation of this structure is shown in Figure 3D (STEM simulation details can be found in the Methods section of ref 36) for comparison with the experimental image in Figure 3E. Intensity line profiles across the boundary (along the dashed green box) in both the simulated (Figure 3F) and experimental images (Figure 3G) match, showing a Ta-Ta distance of ∼0.47 nm at the boundary versus ∼0.32 nm within the ideal TaS 2 lattice.

We expand on the discussion of our first-principles calculations based on DFT regarding the TaS 2 NRs. We investigate the atomic and electronic structures of TaS 2 bulk and ML, and the obtained atomic and electronic structures of the (prismatically coordinated) 2H-bulk and ML configurations (Figure S3) are consistent with other studies. 37,38 We investigate the atomic and electronic structure of NRs with various widths. First, we start with the NRs without structural defects (i.e., no vacancies, substitutions, or adatoms). The atomic positions of all the constructed structures are relaxed by minimizing the total energy. The obtained atomic and electronic structures of a NR (W = 2.99 nm) are shown in Figure 4A-C. Because of the metallicity and 1D nature, CDWtype distortions and corresponding partial gap openings are predicted in all the structures with various widths, but as noted previously, they do not match and are not the origin of the observed superstructure. We exclude the possibility that the zigzag structure originates from CDW-type distortions and do not investigate the CDW phase any further, experimentally or theoretically. Figure 4A incorporates the predicted CDW distortions, but the amplitude of the distortions is too small to be readily apparent in the model, and furthermore, the CDW distortions are not commensurate with the experimentally observed zigzag pattern.

We next construct and optimize numerous candidate structures of the NRs with various types of structural defects for the zigzag boundaries. The atomic positions of all the constructed candidate structures are relaxed again by minimizing the total energy. Among the various candidate structures, we find a defect structure of NRs with various widths that is energetically favored compared to other candidate structures and matches well with the experimental STEM data. After careful analysis of the energetics of all the obtained structures (described below) and comparison with the STEM data, we conclude that the zigzag boundaries are linearly formed S vacancies in the NRs. As described above, Figure 3 shows the obtained atomic structures of a TaS 2 NR with W = 3.34 nm, the experimental STEM data, and the STEM simulation using the structures obtained by DFT for comparison, which agree well with each other. Figure 4D-H show the atomic and electronic structures of a NR with the zigzag defect array (W = 3.08 nm) in vacuum. In Figure 4D, the atomic structure is presented with the zigzag defect array denoted by L 1 and L 2 , and the mirror planes denoted by M 1 and M 2 . Figure 4E andF show the band structure unfolded with respect to the unit-cell of the primitive ML and the projected density of states (PDOS), respectively. A partial gap opening around the K-point is observed as shown in Figure 4E and there are two flat bands near the Fermi energy, E F , (0.020 and 0.007 eV below E F ), denoted as ψ 1 and ψ 2 , respectively, in Figure 4E and F. The real-space wave function of the flat bands reveals that they are localized edge states as shown in Figure 4G andH. The state ψ 1 is localized at the lower edge and has odd parity with respect to the mirror symmetries M 1 and M 2 , while ψ 2 is at the upper edge and has even parity with respect to the mirror symmetries as shown in Figure 4G andH. A similar analysis is also performed on defect free and defective NRs of width 3.29 nm, the results of which are shown in Figure S4.

To analyze the stability of the NRs with various numbers of atoms in the unit-cell, we calculate the Gibbs free energy of formation, δG, of the obtained structures, which is defined as δG = E NR + n Ta μ Ta + n S μ S , where E NR is the total energy per atom of the NR, n Ta , and n S are the mole fractions of Ta and S atoms, respectively, and μ Ta and μ S are the chemical potentials of Ta and S, respectively. We choose μ Ta and μ S as the binding energies per atom of the α-Ta bulk and crown-shaped S 8 molecule, respectively. We find an interesting tendency that the structures with more S vacancies become more stable. For a quantitative analysis, we measure the ratio R of the number of Ta atoms to that of S atoms, which is defined as R = n S /n Ta . The NRs without structural defects have R = 2.14-2.20 > R bulk = 2.0, because the edges are S-terminated, and the confined nature of the NR. The presence of S vacancies reduces R, and the stable calculated structures agreeing well with the experimental data have R = 2.00-2.01 (Table 1). We note that other kinds of defect ordering, such as Ta adatoms, can also reduce R and thereby enhance structural stability. We speculate that stabilization of the structure afforded by driving R → 2 is the main driving force of the formation of the zigzag defects with S vacancies.

It is worth emphasizing the following: First, the encapsulation of the NRs in CNTs does not alter the electronic structures of the NRs significantly except for the slight changes of E F because of the charge transfer between NRs and CNTs. The calculated charge transfer q from CNTs to NRs is ∼0.02 e per Ta atom, where e is the electron charge. Second, the interaction between the CNT's inner wall and the NR's edges is mainly van der Waals interaction. No appreciable amount of covalent bonding is found between the NRs and the CNTs in the DFT calculations. Third, no significant magnetic moment is found in all of the fully magnetic calculations with spin-orbit interaction. Last, the presence of the time-reversal symmetry and mirror symmetry in the prismatic phase indicates the potential for interesting topological properties in these NRs.

In summary, we have demonstrated a method that enables the synthesis of ultranarrow TMD NRs via a simple and broadly deployable gas phase process, using MWCNTs to template their growth. Our method results in TaS 2 NRs with widths below 3 nm, and lengths greater than 100 nm, while reaching the ML limit. Further, the nanoconfined growth of the NRs results in the formation of ordered arrays of linear defects in the TaS 2 lattice. DFT calculations reveal the characteristics of the defect arrays with spatial symmetries and electronic structures with localized edge and boundary states. The reported nanotube templated growth represents a versatile platform for the synthesis of ultranarrow TMD NRs and the exploration of the materials under constraint in multiple dimensions.