Direct visualization of stacking-selective self-intercalation in epitaxial Nb_1+xSe_2 films

Domain: earth_science
Published: 2024-03-21
Editorial outcome: accept

Abstract
Two-dimensional (2D) van der Waals (vdW) materials offer rich tuning opportunities generated by different stacking configurations or by introducing intercalants into the vdW gaps. Current knowledge of the interplay between stacking polytypes and intercalation often relies on macroscopically averaged probes, which fail to pinpoint the exact atomic position and chemical state of the intercalants in real space. Here, by using atomic-resolution electron energy-loss spectroscopy in a scanning transmission electron microscope, we visualize a stacking-selective self-intercalation phenomenon in thin films of the transition-metal dichalcogenide (TMDC) Nb 1+xSe 2. We observe robust contrasts between 180°-stacked layers with large amounts of Nb intercalants inside their vdW gaps and 0°-stacked layers with little detectable intercalants inside their vdW gaps, coexisting on the atomic scale. First-principles calculations suggest that the films lie at the boundary of a phase transition from 0° to 180° stacking when the intercalant concentration x exceeds ~0.25, which we could attain in our films due to specific kinetic pathways. Our results offer not only renewed mechanistic insights into stacking and intercalation, but also open up prospects for engineering the functionality of TMDCs via stacking-selective self-intercalation.

Introduction
Stacking and intercalation represent two of the most versatile tuning knobs for modifying and engineering the properties of two-dimensional (2D) van der Waals (vdW) materials 1–3. Stacking as a control parameter includes varying the lateral registry or twist angle between adjacent layers, to realize, for example, exotic electronic phases on a moiré superlattice 4,5. Layers from different compounds can also be stacked to fabricate heterostructures to achieve functionalities such as atomically sharp p-n junctions and interlayer excitons 6,7. Intercalation involves inserting atoms or molecules into the vdW gap between two layers, either by synthetic routes or by electrochemistry 8–11. The intercalants serve a manifold role, either as stored ions for battery applications 10, or as a means to transfer additional charge carriers or tune interlayer coupling, possibly resulting in new superconducting 12,13 or magnetic states 14,15. While the individual potentials of stacking and intercalation have hardly been exhausted, a natural extension is to explore synergistic combinations of these two tuning parameters. One possibility is to utilize intercalation to stabilize alternative stacking arrangements. For example, Li intercalation of MoS 2 changes the structure from a 2H polytype with trigonal prismatic coordination of the Mo atoms and 180° rotation between successive layers to a 1T polytype with octahedral coordination of the Mo atoms and 0° rotation between successive layers 16. Another possibility is to utilize stacking sequences to selectively intercalate between layers or regions of interest. For example, in a heterostructure composed of graphene and hexagonal boron nitride (hBN) layers, Li atoms intercalate the graphene-graphene and graphene-hBN interfaces, while avoiding the hBN-hBN interfaces, resulting in a layer-selective intercalation 17,18.

Transition-metal dichalcogenides (TMDCs) are particular among the 2D vdW materials in that they exhibit a self-intercalation phenomenon. In the synthesis of MX 2, where M is a transition metal atom and X = S, Se, or Te, an excess starting amount of M may either result in X vacancies, or M atoms incorporated into the vdW gap 19–22. Early studies showed that TMDCs, especially with group-5 metal atoms, i.e., M = V, Nb, or Ta, undergo complex transformations of stacking polytypes upon excess M stoichiometry 23,24. For example, bulk samples of Nb 1+xS 2 and Nb 1+xSe 2 undergo a transition from a 2H a polytype with 180° stacking of layers to a 3R polytype with 0° stacking when x crosses a threshold around 0.03–0.07, presumably because the 3R polytype better accommodates the increasing number of Nb intercalants in its interstitial voids 24–27. With larger values of x, polycrystalline samples with 2H, 2H a, and 3R polytypes and Nb intercalants have been stabilized 24, but less is known about this regime. In essence, the cooperative behavior of stacking and intercalation is already realized “naturally” in the rich chemistry and polytypism of M 1+x X 2, but the mechanistic details remain hidden, and the behavior remains to be exploited for applications. To determine the precise atomic position and chemical state of the intercalants in a mixed-phase sample with various stacking configurations, cross-sectional scanning transmission electron microscopy (STEM) with sub-angstrom resolution is ideal 28–36 and avoids the problem of interlayer averaging present in other techniques, such as x-ray diffraction 24–27 or Raman spectroscopy 37,38. To exploit the cooperative behavior of stacking and intercalation for technological purposes, it is useful to reproduce the previously synthesized M 1+x X 2 compounds as thin films, which offer large surface areas, precise thickness control, amenability to lithography and plentiful pathways for properties engineering 32,39–42. A comparative study using thin films may also elucidate the role of growth kinetics in tuning stacking and intercalation.

We employ a thin-film approach, together with STEM and first-principles calculations, to offer a fresh perspective on the Nb 1+xSe 2 system. With the high spatial resolution afforded by STEM, we observe that thin films with an average x~0.29 comprise a nanoscale phase mixture of NbSe 2 layers stacked with both 180° and 0° in-plane rotations. The 180°-stacked layers are highly self-intercalated with Nb at the octahedral interstitial sites, with likely several tens of percentage occupancy, whereas the 0°-stacked layers have few resolvable intercalants at their octahedral interstitial sites. Our results go beyond simply imaging intercalants or different stacking structures to establishing a correlative relationship between the two. We further evaluate the roles of thermodynamics and kinetics in these observations. Density functional theory (DFT) confirms that the energetically favorable stacking orientation shifts from 0° back to 180° when the self-intercalation exceeds a threshold x~0.25. To reach this threshold, however, kinetic pathways that are distinct from the thin films appear to be crucial. Attempts to replicate these observations with Nb 1+xSe 2 crystals grown via chemical vapor transport (CVT) result in a homogeneous phase of intercalated, 0°-stacked layers with an average x of at most ~0.20. The Nb intercalants reduce the size of the Fermi hole pockets and suppress superconductivity in NbSe 2, and these modified properties may form the basis for fabricating junctions and nanostructures upon achieving more precise control of stacking and self-intercalation.

Results
Basic characterization
Thin films of Nb 1+xSe 2 were deposited on c-cut sapphire substrates via a “hybrid” pulsed laser deposition technique (hPLD) 43,44. Figure 1a illustrates the working principle of hPLD, which combines the laser ablation of refractory Nb metal with thermal sublimation of low-vapor-pressure Se to achieve adsorption-controlled growth, similar to that in molecular beam epitaxy (additional details are given in the Methods section). The growth process was monitored in situ by reflection high-energy electron diffraction (RHEED). During film deposition, the substrate spots disappear as new streaks emerge, indicating the formation of 2D, crystalline Nb 1+xSe 2 (Fig. 1b, c) (see Supplementary Fig. 1 for additional RHEED patterns and Supplementary Table 1 for growth parameters). Scanning tunneling microscopy (STM) (Fig. 1d) reveals a hexagonal lattice of bright spots corresponding to the topmost Se atoms on the surface NbSe 2 layer (Fig. 1e). The topography shows clear background inhomogeneity, an effect which we later attribute to an inhomogeneous distribution of subsurface Nb intercalants 45 (see Supplementary Fig. 2 for additional STM images). High-angle annular dark-field (HAADF) STEM images (Fig. 1f, g) show the cross-section of an 8–9 layer thick film, sandwiched between the sapphire substrate and a protective Se capping layer (see Supplementary Fig. 3 for additional STEM images in different magnifications). Each NbSe 2 layer, arranged as a Se-Nb-Se triple layer, can be fully visualized with atomic resolution. When viewing along the [1–100] direction of sapphire, we mainly observed two kinds of cross sections of the triple-layer structure: (1) Two Se atoms located directly above and below each other, but shifted laterally with respect to the Nb atom (Fig. 1f). (2) Two Se atoms located directly above and below each other, and also vertically aligned with the Nb atom (Fig. 1g). The first cross-section corresponds to the [11–20] projection of NbSe 2 and confirms that the individual NbSe 2 layers adopt the metallic 1H phase with trigonal prismatic coordination of the Nb atoms, whereas the second cross-section corresponds to the [1–100] projection of NbSe 2 (see Fig. 1e). These two distinct cross sections imply that the Nb 1+xSe 2 film is composed of domains rotated primarily by 30° with respect to each other, which is typical of our samples (see Supplementary Fig. 4 for low-energy electron diffraction (LEED) patterns of additional films). When we cut along the [11–20] direction of sapphire, we again observe these two kinds of NbSe 2 cross sections, which confirms that they correspond to 30°-rotated domains (see Supplementary Fig. 5).

Stacking-selective self-intercalation
A close-up HAADF-STEM image of a film region (Fig. 1h) not only reveals each Nb and Se atom column with exquisite resolution but also manifests an additional row of atoms intercalated between the vdW gap of two NbSe 2 triple layers. The intercalant atoms are vertically aligned with the Nb atoms above and below and appear at every site, although with different intensities. The varying brightness at each intercalation site indicates varying concentrations of intercalants because the HAADF-STEM image is a cross-sectional average and its signal intensity is proportional to the mass of materials. Both center-of-mass and 2D Gaussian fitting methods are applied to precisely determine the positions of each atomic column in STEM images (see Supplementary Fig. 6 on the quantification of simulated STEM image of 2H-NbSe 2 as a reference). We observe clear, local structural modifications induced by the intercalant row, including an expansion of the out-of-plane spacing between adjacent NbSe 2 layers (Fig. 1i). (XRD measurements over a macroscopic area consisting of many intercalated regions confirm an overall increase in the average interlayer spacing, consistent with previous polycrystal studies of Nb 1+xSe 2 24; see Supplementary Fig. 7.) There is also an increase in the Se-Nb-Se bond angle for the two NbSe 2 layers surrounding the row of intercalants and a third NbSe 2 layer above (Fig. 1j).

To determine the chemical identity of the intercalants, we performed atomic-resolution electron energy-loss spectroscopy (EELS) for the cross-section shown in Fig. 2. The EELS spectra (Fig. 2a, b) reveal the Se-L 2,3 edge at the Se capping layer (1) and the Nb-L 2,3 edge at the intralayer Nb site (4) and intercalation site (3). A weak Se-L 2,3 signal is present in spectra (2), (3), and (4), presumably due to dechanneling and the ensuing beam broadening of neighboring Se atomic planes 46,47. EELS spectrum images of the Al-K, Se-L 2,3, and Nb-L 2,3 edges (Fig. 2c–e) and their composite map (Fig. 2f) show the distribution of constituent elements at the atomic scale (see Supplementary Fig. 8 for extracted EELS spectra). The row-averaged signal profiles (Fig. 2g) show maxima in the Nb signal corresponding to the intralayer Nb planes and intercalated layers. The intercalants are unambiguously established to be Nb atoms, thus pointing to a self-intercalation phenomenon in our Nb 1+xSe 2 films. We estimate based on x-ray photoelectron spectroscopy (XPS) that on average, the global x value of our thin films is roughly 0.29 (see Supplementary Figs. 9, 10, and Supplementary Table 2). Further information can be derived by spatial mapping at the Nb-N 2,3 edge at even lower energies (Fig. 2h–j). The EELS spectra (Fig. 2i) reveal small but systematic differences between the intralayer Nb and the Nb intercalants: For the intercalants, the onset, volume, and peak of the Nb-N 2,3 edge are shifted to lower energies (red, green, and black arrows in Fig. 2i, which can also be visualized in the first derivative of the line scan maps (Fig. 2j). Both the intralayer Nb and the Nb intercalants are cationic 48, but the shift to lower energies for the Nb intercalants indicates that they have a slightly reduced positive valence state and are more weakly bonded to the neighboring Se atoms. This observation highlights the extreme sensitivity of STEM-EELS in resolving minute chemical differences at the atomic scale.

Figure 3 encapsulates the main finding of this paper, which is a stacking-selective self-intercalation in our Nb 1+xSe 2 films with an average x~0.29. Four HAADF-STEM images are presented (Fig. 3a–d). The films show layers that are stacked with either 180° and 0° in-plane rotation, as indicated by the red and blue arrows. We find that different lateral regions of the film show predominant 180° (Fig. 3a, b) or 0° stacking (Fig. 3c, d), but within each such region, there are also changes in stacking rotation from layer to layer. The 180°-stacked layers have the same lateral registry as the 2H a polytype of bulk, pristine NbSe 2 (Fig. 3e). The Nb atoms are all vertically aligned, but since each layer rotates by 180°, a unit cell consists of two NbSe 2 layers. The stacking motif of Nb atoms is AA’, where the two A’s indicate the identical lateral position of Nb atoms, and the prime indicates a 180° rotation. For the 0°-stacked layers, we find that the Nb atoms in adjacent layers undergo a lateral shift. In the top four layers of Fig. 3c, the stacking motif is AB, meaning that the Nb atoms of every second NbSe 2 layer are realigned vertically (Fig. 3f). This corresponds to a known but rare 2H b polytype of Nb 1+xSe 2 24,49. In Fig. 3d and the bottom four layers of Fig. 3c, we observe that the periodicity is four NbSe 2 layers, with stacking motif ABAC (Fig. 3g). According to the Ramsdell notation, the corresponding polytype is 4H (4 layers per unit cell, hexagonal symmetry), but what we observe does not correspond to any of the known 4H polytypes (4H a, 4H b, 4H c, and 4H dI, 4H dII 49). We tentatively label the polytype as 4H x, and highlight the utility of STEM in resolving such fine differences between 2H b and 4H x polytypes with 0° stacking, which would be otherwise difficult to distinguish with XRD. We note that in Fig. 1h, the 0°-stacked layers show a stacking motif of ABC, which corresponds to the 3R polytype of NbSe 2. To summarize, we observed a total of four polytypes: 2H a-AA’, which we refer to as a 180°-stacked polytype, and 2H b-AB, 3R-ABC, and 4H x-ABAC, which we collectively refer to as 0°-stacked polytypes.

The striking point in Fig. 3 is not only the stacking variation in our Nb 1+xSe 2 films, but the selective preference of Nb intercalants for the 180°-stacked regions. Here, the Nb intercalants are always vertically aligned with the Nb atoms in adjacent layers, meaning that they occupy the octahedral site in the vdW gap (Fig. 3e). Meanwhile, there is little detectable concentration of intercalants in the 0°-stacked regions. The contrast is stark when comparing Fig. 3a and Fig. 3b with predominant 180° stacking and many intercalants to Fig. 3c, d with predominant 0° stacking and very few intercalants. The difference is also evident in the interlayer spacing, which expands with the presence of Nb intercalation and increases for greater concentration of intercalants (Fig. 3a–d). Sharp contrasts in intercalant concentration are also evident on a layer-by-layer basis. In Fig. 3b, all the pairs of layers except one have 180° stacking and many intercalants, and the only pair with 0° stacking has a barely intercalated vdW gap with reduced interlayer spacing. In Fig. 3c, all the pairs of layers except one have 0° stacking and little intercalants, and the only pair with 180° stacking shows a clear row of intercalants with enhanced interlayer spacing. Again, in Fig. 1h, the vdW gaps between 0°-stacked layers are barely intercalated, whereas the single vdW gap with a significant presence of intercalants lies between two 180°-stacked layers. (See Supplementary Fig. 11 for an example of a lateral transition from 180° stacking with many intercalants to 0° stacking with little intercalants.)

Within regions with many successive rows of intercalants between 180°-stacked NbSe 2, such as Figs. 2a and 3a with five and six successive rows of intercalants, respectively, we observe signs of staggering. In Fig. 2a, the first, third, and fifth vdW gaps away from the sapphire substrate have a larger concentration of intercalants, whereas the second and fourth vdW gaps have a lower concentration of intercalants. In Fig. 3a, the second, fourth, and sixth vdW gaps away from the sapphire substrate have a larger concentration of intercalants, whereas the first, third, and fifth vdW gaps have a lower concentration of intercalants. This alternation in intercalant concentration can also be seen in the row-averaged ADF signal profiles of Figs. 2a and 3a, where the local maxima corresponding to the Nb intercalants alternate in peak height.

Electronic structure and properties
With a view toward possible control of electronic structure by intercalants, we investigated how the Nb intercalants modify the well-known electronic structure and properties of NbSe 2. Figure 4a, b present angle-resolved photoemission spectroscopy (ARPES) intensity cuts of a Nb 1+xSe 2 film along Γ-M and Γ-K-M. The positions of the bands closest to the Fermi energy were extracted from energy and momentum distribution curves and are marked as circles. Even when probing a small area of the sample with a diameter of 10–30 µm, we unavoidably averaged over 180°- and 0°-stacked layers with high and low amounts of Nb intercalants, as well as some rotated domains. To model the inhomogeneous film with DFT, we utilized a NbSe 2 slab with four NbSe 2 layers and a vacuum region (Fig. 4c). The inner two layers have 180° stacking with 100% Nb intercalation, whereas the outer two layers have 0° stacking and no Nb intercalants, which is a simplification of the actual situation. The overall structure retains 1×1 in-plane periodicity, so no unfolding of the bands is required, and the overall concentration of Nb intercalants, x=0.25, is relatively close to the experimental estimate of ~0.29. Figure 4d, e shows the calculated bands projected onto the pristine (blue) and 100%-intercalated (red) layers of the slab, corresponding to (a) and (b). The bands are projected onto the pristine (blue) and 100%-intercalated (red) layers. The arrows show the relative shift of the actual experimental bands compared to the calculations. f Resistivity (ρ) vs. temperature (T). Right axis: Sheet resistance per NbSe 2 layer. Inset: log(T)-like upturn at low temperatures. The magenta straight line is a guide to the eye. g Magnetoresistance (MR) below 20 K. The magnetic field (μ 0 H) is applied perpendicular to the plane of the film. The calculated blue bands for the pristine NbSe 2 layers form Fermi-hole pockets at Γ and K. The corresponding red bands for the intercalated NbSe 2 layers exhibit a downward shift as large as 0.8 eV, implying effective electron doping. The ARPES bands lie between these two limits of zero and 100% intercalation. The donation of electrons from Nb intercalants is consistent with their cationic valence states seen by EELS (Fig. 2i). Electrical transport measurements of a Nb 1+xSe 2 film reveal metallic behavior with no superconductivity down to temperatures as low as 0.4 K and current densities as low as 3.8 A/mm2, which is in contrast to the superconductivity observed in pristine NbSe 2 crystals and films (Fig. 4f). Below 20 K, the resistivity shows an upturn with logarithmic temperature dependence (inset of Fig. 4f). The upturn likely corresponds to weak localization, as a concomitant low-field negative magnetoresistance emerges below 20 K (Fig. 4g) (see Supplementary Fig. 12 for conductivity analysis). The sheet resistance per layer of the intercalated film lies between 2.4 and 3.1 kΩ over the measured temperature range. These values fall below but are close to the quantum resistance h/(2e)2~6.5 kΩ 50, which is often the critical value above which a superconductor-to-insulator transition is triggered in a 2D system due to Cooper pair localization. The suppression of superconductivity could be in part related to the disorder induced by Nb intercalants. Furthermore, electron transfer from Nb intercalants reduces the size of hole pockets and lowers the density of states at the Fermi energy, which in turn decreases any superconducting transition temperature. The Nb intercalants could possibly also be magnetic and act as pair-breaking scatterers 32.

Methods
Filmgrowthandparameters
Nb 1+xSe 2 films were grown on c-cut sapphire (aluminum oxide, Al 2 O 3) substrates via hybrid pulsed laser deposition (hPLD) in ultrahigh vacuum 44,52. A pulsed KrF excimer laser (Coherent LPX PRO 210F) was utilized to ablate pure niobium (99.9%) targets at a repetition rate of 1–5 Hz. Pure selenium (99.999%) was evaporated from a Knudsen cell at a flux of roughly 2 Å/s, which was measured with a quartz crystal microbalance. The Nb:Se flux ratio was roughly 1:1800. The depositions were carried out at different temperatures for a few hours, followed by annealing both with and without selenium flux. After annealing, additional selenium could be deposited on the film at room temperature for capping, which protected the films. The detailed growth conditions and in-situ RHEED monitoring of the films are listed in the supplemental information (see Supplementary Fig. 1 and Table 1).

Bulkcrystalgrowth
Single crystals of Nb 1+xSe 2 were grown by chemical vapor transport with iodine as the transporting agent. Powder samples were prepared by heating mixtures of Nb (99.9%) and Se (99.999%) in an evacuated silica tube at 800 °C for one day. The powder sample and iodine (5 mg/cm3) were sealed in a silica tube and heated in a two-zone furnace for 10 days with the temperature of the source and growth zones fixed at 1000 °C and 700 °C, respectively. The typical size of the crystals obtained was 2×2×0.2 mm. Starting Nb:Se compositions of 1.08:2, 1.25:2, and 1:35:2 yielded actual crystals of Nb 1.11 Se 2, Nb 1.17 Se 2, and Nb 1.20 Se 2, as determined by energy dispersive x-ray spectroscopy.

XRD
XRD measurements were performed to confirm the interlayer distance of the Nb 1+xSe 2 films, as well as to determine the film thickness from Kiessig fringes. We used a Huber four-circle diffractometer equipped with a Cu Kα source and a Mythen 1D detector from Dectris.

STM and atomic force microscopy (AFM)
STM measurements were performed using a customized room-temperature system from Unisoku. W tips were prepared by electrochemical etching, followed by in-situ sharpening with electron beam heating. In order to obtain a pristine surface for constant-current imaging, a Se capping layer was deposited on the film, prior to removal of the sample from the hPLD chamber. The Se capping layer was then removed via heating inside the STM load lock to expose a fresh surface. AFM measurements were performed in an ambient environment using a Bruker system with the PeakForce Tapping mode. Different surface morphologies can be observed for the Nb 1+xSe 2 films with different thicknesses.

LEED, XPS, and ARPES
LEED, XPS, and ARPES measurements were performed in two systems. The first system includes a SPECS ErLEED 150 instrument and a Kratos AXIS Ultra spectrometer with a monochromatized Al Kα source, with which we obtained LEED (Supplementary Fig. 4a, b) and XPS data (Supplementary Figs. 9, 10). The second system is a NanoESCA (Scienta Omicron), with which we obtained both LEED (Supplementary Fig. 4c, d) and ARPES data (Fig. 4a, b, and Supplementary Fig. 4e, f). The ARPES data in Fig. 4a, b were acquired with a single shot as a cube (k x-k y-E B) with an energy resolution of 50 meV using a non-monochromatized HeI UV-source. All LEED, XPS, and ARPES measurements were done at room temperature. To preserve the sample surface, films were capped with a Se layer, which was subsequently removed by heating at 250–300 °C for 10–30 min prior to measurements.

We fit the Se 3d XPS core level spectra using the CasaXPS software 53. The fitting functions were primarily composed of Gaussian-Lorentzian mixtures on top of a Shirley background. For the Nb and Se 3d 3/2 and 3d 5/2 core levels, we constrained the doublet ratio to be 2:3 and fixed the doublet splitting to literature values 54, while the FWHM was left as a free-fitting parameter. We calibrated the binding energies to the Fermi edge observed in a valence band spectrum of the film. To determine the band positions in the ARPES intensity cuts, we took the maxima from a combination of energy distribution curves and momentum distribution curves. Assuming that the photoelectrons in ARPES come from roughly three times the inelastic mean free path, which is approximately 1 nm for electrons with kinetic energies in the range of 15 eV 55, and an interlayer distance of roughly 0.65 nm, most of the signal comes from the top five layers, which covers the majority of the entire film thickness.

Transport measurement
We performed transport measurements on 5 mm × 5 mm thin films with two methods and obtained similar results. In the first method, we removed the selenium capping and evaporated six gold electrodes onto the exposed Nb 1+xSe 2 film in a Hall bar geometry. We used a wire bonder to connect gold wires with a diameter of 50 μm between the film electrodes and the pads on the puck. In the second method, we mechanically removed portions of the Nb 1+xSe 2 film to define a Hall bar geometry. The film remained capped with a Se layer, so we attached gold wires by scratching away the Se capping at contact points and applying silver epoxy. We collected the resistivity and magnetoresistance data using the resistivity option of a Physical Property Measurement System (PPMS) from Quantum Design. The measurements were carried out in the He-3 insert of the PPMS, with a base temperature of 300 mK and a maximum magnetic field of 14 T. We symmetrized the magnetoresistance data with respect to the field direction.

Scanning transmission electron microscopy
STEM specimens in a cross-sectional orientation were prepared by a focused ion beam technique. Prior to the ion cutting and milling process, the surface of the Se-capped Nb 1+xSe 2 thin film was coated with electron beam-deposited Pt and ion beam-deposited Pt to protect the material from ion beam damage 56.

STEM studies were conducted using a spherical aberration-corrected STEM (JEM-ARM200F, JEOL Co. Ltd.) equipped with a cold field-emission gun and a DCOR probe Cs-corrector (CEOS GmbH) operated at 200 kV. The STEM images were obtained by an annular dark-field (ADF) detector with a convergent semi-angle of 20.4 mrad and collection semi-angles of 70−300 mrad. In order to make precise measurements of lattice constants, ten serial frames were acquired with a short dwell time (2 μs/pixel), aligned, and added afterward to improve the signal-to-noise ratio (SNR) and to minimize the image distortion of HAADF images. EELS acquisition was performed by a Gatan GIF Quantum ERS imaging filter equipped with a Gatan K2 Summit camera with a convergent semi-angle of 20.4 mrad and a collection semi-angle of 111 mrad. EELS 2D spectrum imaging was performed with a dispersion of 0.5 eV/channel and 1436 eV drift-tube energy with a 4000-pixel wide detector for the simultaneous acquisition of signals of Se-L 2,3, Al-K, and Nb-L 2,3 edges. The EELS line scan was performed with a dispersion of 0.1 eV/channel and 45 eV drift tube energy with a 4000-pixel wide detector for the simultaneous acquisition of signals of Nb-N 2,3, Nb-M 2,3, Nb-M 4,5 and Se-M 4,5 edges. The raw spectrum image data were denoised by applying a principal component analysis (PCA) with the multivariate statistical analysis (MSA) plugin (HREM Research Inc.) in Gatan DigitalMicrograph and then smoothed using a spatial filter in Gatan DigitalMicrograph. The first and second derivative analyses of EELS spectra were conducted using a built-in function in Gatan DigitalMicrograph. HAADF-STEM images of 2H a-phase NbSe 2 were simulated using the abTEM code 57. Atomically resolved HAADF-STEM images have been quantified, where the coordinate positions of Nb and Se ions were determined by a combination of center-of-mass and 2D Gaussian fitting in high-resolution HAADF images, and then used to calculate the interlayer spacing between adjacent NbSe 2 layers and Se-Nb-Se angles in NbSe 2 layers 58,59.

Density functional theory
To evaluate the phase stability and electronic structure of the pristine and intercalated NbSe 2, DFT calculations were performed using the Vienna Ab initio Simulation Package (VASP) based on the projected augmented wave method 60,61. The electron exchange-correlation function was described by the Perdew-Burke-Ernzerhof (PBE) parametrization of the generalized gradient approximation (GGA). The wave functions were expanded on a plane-wave basis with a cutoff energy of 520 eV using a k-mesh density of 50 Å−1. The tolerance of total energy convergence for self-consistent field calculations was set to be 10−5 eV. All structures were fully optimized until the maximal Hellmann–Feynman forces on atoms were less than 0.01 eV/Å. The Becke88 optimization (optB88) was used to accurately account for non-local vdW forces 62.

Data availability
Relevant data supporting the key findings of this study are available within the article and the Supplementary Information file. All raw data generated during the current study are available from the corresponding authors upon request.

Code availability
All the codes used for this study are available from the corresponding authors upon request.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The manuscript by Hongguang Wang et al. reports a detailed atomic-resolufion STEM invesfigafion, combined with theorefical calculafions, on the study of the self-intercalafion mechanism in Nb-rich niobium selenide epitaxial films grown by PLD on sapphire substrates. Authors visualize a stacking-selecfive self-intercalafion process where excess Nb intercalants drive the formafion of 3R-AB stacking instead of AA’ stacking, in contradicfion to previous reports. After reading the manuscript, I see that authors intend to present this mechanisfic process as a universal phenomenon, which I don’t agree with and I think authors do not provide enough evidence to support that claim, therefore I cannot recommend the paper for publicafion in Nature Communicafions in the current state. However, I sfill think the findings are sound and it may be interesfing for the community. In the following I list of some quesfions to be addressed.\n1) As a general comment, I find very disturbing the notafion the authors use referring to 0º and 180º stacking instead of the convenfional 2H-AA’ and 3R-AB stacking. I suggest the authors to sfick to more widely accepted terminology instead of creafing new unnecessary notafions. Personally, I found the draft difficult to follow at some points due to this mafter.\n2) It is known from the literature that higher chemical potenfial of the metal during the growth process of TMDs favors the 3R stacking [Phys. Rev. B 93, 041420 (2016); Sci Rep 8, 2143 (2018); Adv. Mater. 2018, 30, 1704674; Nat Commun 9, 199 (2018)]. Authors indirectly discuss this in the parficular case of Nb-Se system in line 56, saying that x>0.07 induce a transifion from AA’ to AB stacking, cifing references [24-27]. However, generally, these studies were made on samples grown by chemical methods such as CVD or CVT, methods closer to equilibrium that allow more thermodynamically stable phases to nucleate. In the present work, samples are epitaxially grown by PLD, which allows layer-to-layer control and the possibility of stabilizing metastable phases and processes in non-equilibrium condifions. One wonders if the discrepancies authors try to debate between their findings on the origin of the stacking switching and the previously reported are simply due to the use of different growth methods, which allows new growth kinefics to happen and processes not observed before. The growth method is a key factor in controlling and realizing materials.\nThanks to more and more microscopy works, as the present one, we are finding out that most of the discrepancies found in literature in the last years regarding the intercalafion process, polytyping, seems to have the origin on the growth method employed. I think this issue should be properly addressed and discussed. In my opinion, this doesn’t invalidate their findings but the story of the paper, conclusions and abstract may change considerably. I think the author’s discoveries may not necessarily invalidate the previous findings, and I think there is not enough compelling arguments to present these observafions as a general mechanism. I invite the authors to review the manuscript in this regard and avoid generalizafion if they cannot provide an unambiguous comparison that supports their arguments.\n3) Confinuing with the growth condifions, I see the growth of the samples require temperatures as high as 600º C somefimes. The chalcogen Se is problemafic due to its low evaporafion temperature. Some experiments in V-Se samples showed that post-growth annealing at temperatures above 400 ºC results in a significant loss of Se [Adv Mater Interfaces 2020, 7 (15), 1–9; Adv Mater 2019, 31 (40), 1903779], inducing phase transifions or emerging ferromagnefism. This is important. Se evaporafion will imbalance the chemical potenfial (previous comment), thus Se vacancies may be another parameter to consider for the conclusions of the paper and the role of the Nb intercalafions. Have authors consider the possibility of Se vacancies during the growth or annealing process? How to make sure no Se was evaporated? How may change the formafion energies of different stacking types?\n4) On the other hand, I found interesfing Figure S2. If I understood correctly from the main text, the authors aftribute the bright atoms in the topographic STM image to the Se surface, and then the dark and bright contrast variafions to Nb intercalafions? In my understanding, in a topographic image, adatoms should show brighter than the Se surface and, if vacancies (Se here), as dark atoms. How can we understand this image? This means there are both adatoms and Se vacancies? This quesfion should be addressed; I am not sure what message is the image delivering.\n5) The STEM shows clear interlayer expansion when the vdW gap is filled with intercalafions. I found this hard to understand. Intercalants will create covalent bonds [Nature 581, 171-177 (2020)], therefore the large weakly bonded vdW gap should be eliminated or parfially eliminated. For instance, as an example from a sister family system, the c axis of VSe2 (1:2, vdW gap fully empty) and VSe (1:1, vdW gap fully occupied) is 0.613 and 0.578 nm, respecfively (~ - 6%). How can we understand the laftice expansion in the case of Nb-Se?\n6) The staggering of intercalants is quite interesfing. Here it is only shown for the case of 7–8-layer films. Is the same for the rest of samples? What about the thicker films? Seems to me this staggering mechanism may be very well connected with the PLD growth process, as discussed in comment 2. The formafion of intercalated-superstructures and twisfing has been also reported for CVD-grown Cr-Te nanoplates [Nano Left. 2021, 21, 9517−9525].", "reviewer_2": "The authors present a thorough invesfigafion of Nb1+xSe2 synthesized by PLD. They go beyond prior observafions and demonstrafions by correlafing the self-intercalafion with layer stacking, unambiguously idenfifying the nature and posifion of the intercalant, observing ARPES spectra that appears to be a mixture of 2Ha and 2Hb, reported on the electronic properfies. This work is well wriften and free of errors and unjusfified conclusions. I recommend publicafion as is.\nMinor comment:\nThe authors state the photon energy of their monochromated Al Kalpha source as 1486.6eV. While this is commonly reported in the literature, it is incorrect and likely a legacy of un-monochromated dual anode sources where the weighted average of the k-alpha1 (1486.7eV) and the k-alpha2 (1486.3eV) was used. Since a monochromator will be opfimized to the maximum intensity the result will be a k-alpha1 line at 1486.7eV. While the incorrect 1486.6 eV is quite prevalent throughout the literature (and even some vendor websites), I don’t think this error should be propagated to a nature journal. Unless the authors opfimized their monochromator away from the maximum intensity then the photon energy would be 1486.7 eV.\nThe authors can see the work by J. Schweppe R.D. Deslaftes T. Mooney and C.J. Powell as well as the LBL tables which both confirm the energy of the Ka1 line\nhttps://doi.org/10.1016/0368-2048(93)02059-U\nhttps://xdb.lbl.gov/Secfion1/Table_1-2.pdf\nOpfional suggesfion:\nWhen reviewing the SI, I noted that the results and interpretafion of the XPS and XRD data is similar and consistent with those reported recently by Litwin et al (for Nb1+xSe2)[1] and Bonilla et al (for VSe2)[2] and as such may warrant comparison. Since Bonilla et al also reported on the surface structure observed with STM it would be interesfing to consider whether are all observafions are consistent.\nhttps://doi.org/10.1116/6.0002593\nhttps://doi.org/10.1002/admi.202000497", "reviewer_3": "**THIS REPORT WAS WRITTEN IN COLLABORATION WITH REFEREE #4\nH Wang et al study the intercalafion of excess Nb within hybrid PLD grown Nb1+xSe2 thin films, and they observe a strong interacfion between the layer stacking order and intercalafion. Using atomically resolved STEM imaging and EELS analysis, the authors find that their films contain both 180° and 0° stacking, and that intercalants preferenfially occupy the octahedral sites between 180° stacked layers. Negligible intercalafion was found between 0° stacked layers. The experimental data suggest that Nb intercalants energefically prefer the octahedral 180° sites, and this is confirmed via DFT calculafions. The authors also argue that the presence of 0° stacking is driven by the inter-layer repulsion of Nb intercalants and a staging mechanism. The effects of intercalafion on the electronic properfies are invesfigated with ARPES and resisfivity measurements. Both the intercalafion of TMDs and the layer stacking in TMDs are topics of interest, and this manuscript presents an interesfing system where intercalafion and layer stacking cooperate in a non-trivial manner. The manuscript is well-wriften, and the characterizafion and analysis are complete. Below are some quesfions / comments for the authors.\n1. The term staging is most often associated with Li intercalafion into graphite, which progresses from stage 4, to stage 3, stage 2, and finally stage 1, which corresponds to fully intercalated graphite. Do the authors propose that similar stages occur for Nb1+xSe2? Have different stages been observed experimentally? The authors should clarify their use of the term staging.\n2. The authors propose that the 0° layer stacking is driven by the inter-layer repulsion of Nb intercalafion. So the 0° stacking forms to separate layers of fully intercalated 180° stacking. If this argument is accurate, then 0° stacking should only form in close proximity to intercalated 180° stacking. But the data in Fig. 3 seems to contradict this argument. In Fig 3d, the NbSe2 film is enfirely 0° stacked, except for a single layer of intercalated 180° stacking at the substrate interface. The topmost 0° stacked layers cannot be driven by an inter-layer Nb repulsion mechanism, since there is no Nb intercalafion nearby. A similar situafion is found in Fig. 3c.\n3. Have the authors grown hPLD thin films of stoichiometric NbSe2 (with no self-intercalafion) and studied the layer stacking? Is it possible that the hPLD growth condifions yield mixed layer stacking even in the absence of self-intercalafion?\n4. What is the lateral length-scale of the different layer stacking orders and intercalated layers? Do the authors have any wide field-of-view images showing changes in the layer stacking and intercalant structure? For instance, a lateral transifion from 0° stacking to 180° stacking? Alternafively, do the authors have any selected area electron diffracfion of the FIB’d samples, which would provide informafion on the layer stacking averaged across a large region?\n5. For the ARPES measurements, what is the penetrafion depth? Is the enfire film thickness being probed?\n6. The text references a yellow arrow in Fig. 2f, but the arrow is pink. Also, the text refers to an orange arrow in Fig. 2i, but the arrow looks green.\n7. For the Nb oxidafion state analysis, did the authors look at the fine structure of the Nb L-edge (Fig. 2b) to confirm their findings at the Nb N-edge? Does the N-edge offer advantages for chemical analysis compared to the L-edge?\n8. In Fig. 1g, how were the error bars calculated?", "reviewer_4": "**THIS REPORT WAS WRITTEN IN COLLABORATION WITH REFEREE #3\nH Wang et al study the intercalafion of excess Nb within hybrid PLD grown Nb1+xSe2 thin films, and they observe a strong interacfion between the layer stacking order and intercalafion. Using atomically resolved STEM imaging and EELS analysis, the authors find that their films contain both 180° and 0° stacking, and that intercalants preferenfially occupy the octahedral sites between 180° stacked layers. Negligible intercalafion was found between 0° stacked layers. The experimental data suggest that Nb intercalants energefically prefer the octahedral 180° sites, and this is confirmed via DFT calculafions. The authors also argue that the presence of 0° stacking is driven by the inter-layer repulsion of Nb intercalants and a staging mechanism. The effects of intercalafion on the electronic properfies are invesfigated with ARPES and resisfivity measurements. Both the intercalafion of TMDs and the layer stacking in TMDs are topics of interest, and this manuscript presents an interesfing system where intercalafion and layer stacking cooperate in a non-trivial manner. The manuscript is well-wriften, and the characterizafion and analysis are complete. Below are some quesfions / comments for the authors.\n1. The term staging is most often associated with Li intercalafion into graphite, which progresses from stage 4, to stage 3, stage 2, and finally stage 1, which corresponds to fully intercalated graphite. Do the authors propose that similar stages occur for Nb1+xSe2? Have different stages been observed experimentally? The authors should clarify their use of the term staging.\n2. The authors propose that the 0° layer stacking is driven by the inter-layer repulsion of Nb intercalafion. So the 0° stacking forms to separate layers of fully intercalated 180° stacking. If this argument is accurate, then 0° stacking should only form in close proximity to intercalated 180° stacking. But the data in Fig. 3 seems to contradict this picutre. In Fig 3d, the NbSe2 film is enfirely 0° stacked, except for a single layer of intercalated 180° stacking at the substrate interface. The topmost 0° stacked layers cannot be driven by an inter-layer Nb repulsion mechanism, since there is no Nb intercalafion nearby. A similar situafion is found in Fig. 3c. Can the authors comment on Fig 3 and the proposed staging mechanism?\n3. Have the authors grown hPLD thin films of stoichiometric NbSe2 (with no self-intercalafion) and studied the layer stacking? Is it possible that the hPLD growth condifions yield mixed layer stacking even in the absence of self-intercalafion?\n4. What is the lateral length-scale of the different layer stacking orders and intercalated layers? Do the authors have any wide field-of-view images showing changes in the layer stacking and intercalant structure? For instance, a lateral transifion from 0° stacking to 180° stacking? Alternafively, do the authors have any selected area electron diffracfion of the FIB’d samples, which would provide informafion on the layer stacking averaged across a large region?\n5. For the ARPES measurements, what is the penetrafion depth? Is the enfire film thickness being probed?\n6. The text references a yellow arrow in Fig. 2f, but the arrow is pink. Also, the text refers to an orange arrow in Fig. 2i, but the arrow looks green.\n7. For the Nb oxidafion state analysis, did the authors look at the fine structure of the Nb L-edge (Fig. 2b) to confirm their findings at the Nb N-edge? Does the N-edge offer advantages for chemical analysis compared to the L-edge?\n8. In Fig. 1g, how were the error bars calculated?"}, "author_response": "Response to the Reviewers and Revisions\nReviewer #1:\nThe manuscript by Hongguang Wang et al. reports a detailed atomic-resolution STEM investigation, combined with\ntheoretical calculations, on the study of the self-intercalation mechanism in Nb-rich niobium selenide epitaxial films grown\nby PLD on sapphire substrates. Authors visualize a stacking-selective self-intercalation process where excess Nb intercalants\ndrive the formation of 3R-AB stacking instead of AA’ stacking, in contradiction to previous reports. After reading the\nmanuscript, I see that authors intend to present this mechanistic process as a universal phenomenon, which I don’t agree\nwith and I think authors do not provide enough evidence to support that claim, therefore I cannot recommend the paper for\npublication in Nature Communications in the current state. However, I still think the findings are sound and it may be\ninteresting for the community. In the following I list of some questions to be addressed.\nOur response:\nWe thank the reviewer for their interest and thoughtful evaluation of our work. We agree that kinetics can play as much a\nrole as thermodynamics, and that our observations in Nb Se thin films grown by our hPLD technique may not be universal\n1+x 2\nto Nb Se prepared in other forms, such as bulk crystals. To clarify this point, we have performed comparative STEM\n1+x 2\nexperiments on a series of bulk Nb Se single crystals grown by chemical vapor transport (CVT). Please refer to our\n1+x 2\nresponse to Comment 2 for a detailed explanation.\nComment 1:\n1) As a general comment, I find very disturbing the notation the authors use referring to 0º and 180º stacking instead of the\nconventional 2H-AA’ and 3R-AB stacking. I suggest the authors to stick to more widely accepted terminology instead of\ncreating new unnecessary notations. Personally, I found the draft difficult to follow at some points due to this matter.\nOur response:\nWe regret any confusion caused by our notation. The reason we did not simply apply the terms 2H-AA’ and 3R-AB is that\nwe actually observed a total of four stacking polytypes: 2H-AA’ (180º stacking), 2H -AB (0º stacking), 3R-ABC (0º\na b\nstacking), and 4H -ABAC (0º stacking). In fact, in the thin films, 2H and 4H were more prevalent than 3R. Instead of\nx b x\nlumping the 2H and 4H polytypes into the 3R polytype, we decided to refer to these three simply as 0º-stacked polytypes,\nb x\nand the 2H polytype as a 180º-stacked polytype. Our intention was to make our description accessible to a more general\na\naudience who might not be familiar with the Ramsdell notation.\nActions taken:\nWe added an additional sentence in the subsection “Stacking-selective self-intercalation” to try to better clarify our notation\n(Page 8 in the main manuscript):\n“To summarize, we observed a total of four polytypes: 2H -AA’, which we refer to as a 180°-stacked polytype, and 2H -\na b\nAB, 3R-ABC, and 4H -ABAC, which we collectively refer to as 0°-stacked polytypes.”\nx\nComment 2:\nIt is known from the literature that higher chemical potential of the metal during the growth process of TMDs favors the 3R\nstacking [Phys. Rev. B 93, 041420 (2016); Sci Rep 8, 2143 (2018); Adv. Mater. 2018, 30, 1704674; Nat Commun 9, 199\n(2018)]. Authors indirectly discuss this in the particular case of Nb-Se system in line 56, saying that x>0.07 induce a\ntransition from AA’ to AB stacking, citing references [24-27]. However, generally, these studies were made on samples\ngrown by chemical methods such as CVD or CVT, methods closer to equilibrium that allow more thermodynamically stable\nphases to nucleate. In the present work, samples are epitaxially grown by PLD, which allows layer-to-layer control and the\npossibility of stabilizing metastable phases and processes in non-equilibrium conditions. One wonders if the discrepancies\nauthors try to debate between their findings on the origin of the stacking switching and the previously reported are simply\ndue to the use of different growth methods, which allows new growth kinetics to happen and processes not observed before.\nThe growth method is a key factor in controlling and realizing materials.\nThanks to more and more microscopy works, as the present one, we are finding out that most of the discrepancies found in\nliterature in the last years regarding the intercalation process, polytyping, seems to have the origin on the growth method\nemployed. I think this issue should be properly addressed and discussed. In my opinion, this doesn’t invalidate their findings\nbut the story of the paper, conclusions and abstract may change considerably. I think the author’s discoveries may not\nnecessarily invalidate the previous findings, and I think there is not enough compelling arguments to present these\nobservations as a general mechanism. I invite the authors to review the manuscript in this regard and avoid generalization if\nthey cannot provide an unambiguous comparison that supports their arguments.\nOurresponse:\nWWeethankandagreewiththerevieweroonnthisstatement.OurSTEMimagesdisclosethatepitaxialfilmsooffNNbb SSee neara\n11++x 2\nglobalx~0.29showananoscalecoexistenceooff180° stackedlayerswithalargenumberooffNNbbintercalants,perhapsseveral\ntensofpercentageoccupancy(consideringtheaveragexvalue),and00°°-stackedlayerswhosenumberooffNNbbintercalantsfalls\nclose ttoo the detection limi TToo evaluate the role kinetics and growth conditions play in these observations, and howthey\nrelate (if aatt all) ttoo previous bulk reports, wwee performed a newcomparative studyoonn single crystals ooff NNbb SSee grown bbyy\n11++x 2\nchemicalvaportransport(CVT).\nFigureRR11presentsaseriesooffHAADF STEMimagesforfourNb SSee crystalswithincreasingaveragevaluesooffx.AAttx=\n11++x 2\n00,,NbSe crystallizesiinnthe2H polytypewith180°stacking,andthevdWgapsareclearooffintercalants[Fig.RR11(a)].AAttx~\n2 a\n00..1111,theNbSe layersuniformlyadoptthe3Rconfigurationwith00°°stacking[Fig.RR11(b)].Therearefaintsignaturesooffsome\n2\nintercalantsinsidetheoctahedralvoidsooffthevdWgaps,perhapstoadegreethatiissqualitativelysimilarttoowhatwweeobserve\nbeteenthe00°°-stackedlayersofourthinfilms.AAsswweecontinuedtosynthesizecrystalswithincreasingxviaCVT,thedegree\nooffself-intercalationbegantosaturate.AAnninitialNb:Sestoichiometryooff1.25:2resultedinNNbb SSee crystalswithaveragex\n11++x 2\n~0.17,showingagainahomogeneous00°°-stackedphase,butwithmoreintercalantsinsidetheiroctahedralvoids[Fig.RR11(c)].\nAgreaterstartingNb:Sestoichiometryof1.35:2resultedinNNbb SSee crystalswithaveragex~0.20.Thesecrystalscontained\n11++x 2\ndomainsooffadditionalNNbb-SSeephases(seeSupplementaryFig.S13);nevertheless,iinntheregionswith1HlayersofNbSe ,wwee\n2\nstillobservedhomogeneous00°°stacking[Fig.RR11(d)].Thedegreeooffintercalationbetweenthe00°°-stackedlayershereseems\nttoobbeemuchggrreaterthanthe00°°-stackedlayersofourthinfilms[e.g.,Figs.1(g)oorr3(c)ooffthemaintext]],,butstilllessthanthe\n180° stacked layers ooff our thin films [e.g., Fig. 3(a) ooff the main text]].. Contrary ttoo our previous suggestion, wwee ddoo not\ninvalidate the previous bulk studies aatt low x, but reproduce them with STEM. IItt appears tthhaatt x iiss a crucial parameter.\nHowever, with the CVT crystals, wwee could not reach the higher x values comparable ttoo our thin films, aatt which highly\nintercalated,180°-stackedlayersbeginttooappearlocally.\nFigure RR11. Self intercalation iinn single crystal NNbb SSee grownvia chemical vapor transport. (a)–(d) HAADF STEM\n11++x 2\nimagesooffthecross-sectionooffbulkNNbb SSee withnominalx=00,,00..11,00..1177,and00..2200,respectively.Aclose-uuppoofftheregion\n11++x 2\nenclosedbbyytheyellowboxiissshownforeachpanel.\nTTooreconcilewhatwweeobserveiinnNNbb SSee grownviahPLDandCVTiinndifferentglobalxregimes,wweeperformednewDFT\n11++x 2\ncalculationsover a greater range ooffx values. WWee constructed supercellsooffbilayer NNbb SSee with180°(AA’) and 00°°(AB)\n11++x 2\nstackingswithNNbbintercalantsinsidetheoctahedralvoids.ThesupercellshadchemicalformulaeNNbb SSee ,NNbb SSee ,NNbb SSee ,\n2 4 1199 3366 9 1166\nNNbb SSee , and NNbb SSee , which correspond ttoo aann occupancy ooff the interstitial octahedral sites ooff 0%, 11%, 25%, 50%, and\n1100 1166 3 4\n100%. (For bilayer NNbb SSee surrounded bbyy vacuum, there iiss only one octahedral void per unit cell, ssoo the occupancy ooff\n11++x 2\noctahedralvoidsiissgivenbbyy2x,iinncontrasttobulkNNbb SSee , wheretheoccupancyiissgivenbbyyx..))AAtt00%%intercalation,the\n11++x 2\ntotalenergyafterstructuralrelaxationooff180° stackedbilayerNbSe iissonly2meVperformulaunitsmallerthanthatooff00°°-\n2\nssttackedbilayerNbSe [Fig.RR22(a)].TheneardegeneracyooffthesetwostackingsreflectstheweakinterlayercouplingooffvdW\n2\nnatureiinnNbSe ,butthepredictionooffaslightlymoreenergeticallyfavorable180°stackingisiinnlinewiththeobserved2H\n2 a\npolytypeiinnbulk,pristineNbSe .AAtt11%and25%intercalation ,the00°°-stackedbilayeriissactuallyloweriinnenergythanthe\n2\n180° stackedbilayer,butthesituationiissquicklyreversedaatt50%and100%intercalationnss, wherethe180° stackedbilayer\niissagainmorestable.DFTpredictstwopolytypetransformationswithincreasingx.\nFigure RR22. Proposed microscopic picture ooff stacking selective self-intercalation. (a) The difference iinn DFT total\nenergiesperformulaunitbetween180° and00°°-stackedbilayerNNbb SSee withavaryingconcentrationofNNbbintercalantsaatt\n11++x 2\nthe interstitialoctahedral sites. A negative (positive) value ooffE(180°) – E(0°) impliesthat the 180°(0°) structure iiss more\nstableandiissindicatedbbyythered(blue)colorooffthedatapointsandshadedregions.(b)DFT computedchangeiinntotalenergy\nuponintercalationintotheoctahedralvoidsooff180° and00°°-stackedbilayerNNbb SSee .(c)and(d)Proposedphasediagram\n11++x 2\nforNNbb SSee grownviahPLDandCVT,respectively.ThehPLD grownfilmslieaattthephaseboundarybetween00°°and180°\n11++x 2\nstacking,whereasourCVT growncrystalshavenotreachedthesecond180° stackedphase.\nWWee also computed the intercalation energyiinn Fig. RR22(b), defined aass ;E = [E(Nb SSee ) – E(NbSe ) – xxEE(Nb)]/ , where\nint 11++x 2\nE(Nb SSee )andE(NbSe )aretheDFTtotalenergiesafterstructuralrelaxationoofftheintercalatedandpristinestructuresand\n11++x 2\nE(Nb) iiss the DFT computed energy required ttoo take one NNbb atom from bulk Nb. IInn all but one case, ;E iiss negative,\nint\nmeaningthatself-intercalationactuallyreleasesenergy.Again,aattlowintercalantconcentrations,;E iissmorenegativefor\nint\n00°°stacking,butsomewherebetween25%and50%intercalation,thetrendreversesand;E iisslowerfor180°stacking.WWee\nint\nspeculatethatthe changeiinnthe favorableintercalationsite mightbbeedue ttooacrossingooff thepercolationthresholdaround\n33%,aattwhichpointtheiinn-planeinteractionooffintercalantsbecomessignificantandchangestheenergeticsooffthefavorable\nintercalation site. (SupplementaryFig. S14, S15 for additional DFT calculations includingbulk structures and alternative\nintercalationsites.)\nBasedoonntheequilibriumstructurespredictedbbyyDFT,wweemakeatentativepictureooffwhatiisstranspiringiinnthehPLD and\nCVT grownsamples.AAttlowx,asmallamountooffintercalationwillswitchthestablestackingorientationfrom180°ttoo0°.\nWWeecanreachbothsidesooffthisphasetransitioniinnourbulkcrystals,where pristinesamplewithx=0showshomogeneous\n180°stacking[Fig.RR11(a)],andaannintercalatedsamplewithx~0.11showshomogeneous00°°stacking[Fig.RR11(b)].Thenaatt\nhigher x, NNbb SSee becomes thermodynamically more stable with 180° stacking again. Within the parameter spac ooff our\n11++x 2\ngrowth conditions, wwee only observed this second transition iinn the thin films with x ~ 0.29, but aass a nanoscale phase\ncoexistenceooffhighlyintercalated,180° stackedlayersandsparselyintercalated,00°°-stackedlayers[Fig.RR22(c)].OurCVT\ngrown crystals could not reach the highly intercalated, 180° stacked phase, even aatt a local level probed bbyy STEM [Fig.\nRR22(d)].Whenwweesynthesizedcrystalswithatargetcompositionaasshighaassx=0.35,wweeonlystabilizedalayeredNNbb SSee\n11++x 2\nphase withx~0.20.Thethinfilmsmust havesomespecific kineticpathwaysthatenable themttoorealizeahighdegreeooff\nself-intercalationwith180°stacking,suchaassthehighkineticenergyoofflaser ablatedNNbbadatoms,oorrsmallerfilmdomains\noonntheorderooff~100nnmmwithplentyooffedgesandboundaries(seeSupplementaryFig.S16forAFMimages),whichbetter\nfacilitateatomicmotionandrearrangements.ThethinfilmsarealsomorepronettooalossooffSSeeiinnthehPLDprocess,which\ncouldprovideaannalternativeroutetowardsself-intercalationandstackingchange(removingSSeeratherthaninsertingNNbb,aass\nsuggestedbbyythereviewer))..Furtherexperimentalworkiissneededttoopindowntheexactmicroscopicmechanismsinvolved.\nActionstaken:\nBased oonn the new STEM experiments and DFT calculations, wwee have substantially revised the story ooff our manuscript.\nFiguresRR11andRR22arenowincludediinnthemainmanuscriptaassFigs.5(Page11)and6(Page12) Sectionsooffourabstract\n(Page11))andintroduction(Page33))havebeenrevised,aasswellaassthheeDiscussionsection(Pages1100-13)\nComment33::\nContinuing with the growth conditions, I see the growth of the samples require temperatures as high as 600º C sometimes.\nThe chalcogen Se is problematic due to its low evaporation temperature. Some experiments in V-Se samples showed that\npost-growth annealing at temperatures above 400 ºC results in a significant loss of Se [Adv Mater Interfaces 2020, 7 (15),\n1–9; Adv Mater 2019, 31 (40), 1903779], inducing phase transitions or emerging ferromagnetism. This is important. Se\nevaporation will imbalance the chemical potential (previous comment), thus Se vacancies may be another parameter to\nconsider for the conclusions of the paper and the role of the Nb intercalations. Have authors consider the possibility of Se\nvacancies during the growth or annealing process? How to make sure no Se was evaporated? How may change the formation\nenergies of different stacking types?\nOurresponse:\nThereviewerraisesaannimportantpoint.IIttcouldbbeethatthelossooffSSeeaatthightemperatures(equivalentttooaannincreaseooffthe\neffectiveNb:Seratio)providesanotherkineticpathwaybbyywhichself-intercalationtranspiresiinnthin-filmNNbb SSee .WWeeddoo\n11++x 2\nnot currently have any experimental handle oonn what happens during the intermediate stages ooff the thin film deposition\nprocess.WWeecansayexperimentally,though,thatiinnthefinalstateooffourthinfilmsaftergrowth, wweehavenotobservedaann\nabundanceooffSSeevacancies.WWeehaveattempteeddttooquantifytheamountooffSSeevacanciesseenaattthesurfaceooffourthinfilms\nvia STM imaging. IInn a 1100 × 5 nnmm field ooff view, four SSee vacancies can bbee observed out ooff roughly 561 SSee sites, giving a\nvacancyratio<0.8%(Fig.R3).IInntermsooffcomputingtheformationenergiesooffdifferentstackingtypes,wweethinkiittiissvalid\nttoo omit the influence ooff 0.8% SSee vacancies. In terms ooff reaction pathways bbyy which self-intercalation actually occurs,\nhowever,thelossooffSSeecouldplayaannimportantrole.\nFigureR3.SSeevacanciesoonnthesurfaceobservediinnaannSTMimage.FourvacanciesareidentifiedoonntheSSeesurface.Scale\nbar:2nm.\nActionstaken:\nWWeehavementionedthelossooffSSeeaassapossiblemechanismooffself-intercalationiinntheDiscussionsection(Page13)\n“ThethinfilmsarealsomorepronettooalossooffSSeeiinnthehPLDprocess,whichcouldprovideaannalternativepathwaytowards\nself-intercalationandstackingchange(removingSSeeratherthaninsertingNb)5511.”\nComment44::\nOn the other hand, I found interesting Figure S2. If I understood correctly from the main text, the authors attribute the bright\natoms in the topographic STM image to the Se surface, and then the dark and bright contrast variations to Nb intercalations?\nIn my understanding, in a topographic image, adatoms should show brighter than the Se surface and, if vacancies (Se here),\nas dark atoms. How can we understand this image? This means there are both adatoms and Se vacancies? This question\nshould be addressed; I am not sure what message is the image delivering.\nOur response:\nWe thank the reviewer for their comment about the nature of the contrast shown in Fig. S2. In STM topographic images, a\ncontrast may come from adatoms, vacancies, or an inhomogeneous background. As shown in Fig. R4(a), a vacancy is\nobserved as an isolated dark region with no local maximum, surrounded by a hexagon formed of six Se atoms [Ugeda, M.\net al. Nature Phys 12, 92–97 (2016)]. In Fig. R4(b), an adatom is observed as isolated, sharply bright atoms with a diameter\nof ~1 nm [Liebhaber, E. et al. Nat Commun 13, 2160 (2022)]. In Fig. R4(d), an inhomogeneous background gives rise to a\nmodulation on the length scale of nanometers without long-range order [Lasek"}]

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