Main

Increased research into 2D materials has heralded a new branch of condensed-matter physics concerned with the description of electrons in atomically thin structures. So far, research efforts have primarily focused on 2D monolayers2 and their hetero-stacked structures3, in which new properties can be engineered by generating superlattices of different moiré wavelengths. However, these hetero-stacked structures are currently produced by bottom-up methods that are low yielding and show poor reproducibility16. An alternative method of compositional tuning involves the intercalation of foreign atoms into the van der Waals (vdW) gap that is sandwiched by the chalcogen atoms; this has been shown to induce pseudo-2D characteristics in bulk crystals and modify their electronic properties4,6,7. Depending on the interlayer stacking registries, the vdW gaps in transition metal dichalcogenides (TMDs) contain either octahedral and tetrahedral vacancies or trigonal-prismatic vacancies13, which provide docking sites for a diverse range of intercalants. Examples of successful intercalants include alkali metals8,9,10 such as Li, Na and K; transition metals17,18,19,20,21 such as Cu, Co, Ni, Fe and Nb; noble metals22,23,24 such as Ag, Au and Pt; as well as Sn and various organic molecules25,26,27. Charge transfer from the intercalants7—or increased spin–orbit coupling due to the presence of heavy atoms7,24,28—can enhance superconductivity10, thermoelectricity25 or spin polarization7. Intercalation is typically achieved using post-growth, diffusion-limited processes, either electrochemical or in the solid state. A well-defined intercalated phase with long-range crystalline order is difficult to obtain by such methods and usually requires harsh treatment conditions21,22,29. Moreover, an intercalation phase diagram that correlates the density and spatial distribution of the intercalated atoms with the mesoscopic properties of the intercalation compound is currently lacking. Compared with the intercalation of foreign atoms into a TMD, the intercalation of native atoms—those that are present in the TMD itself—has so far received little attention11,29,30. Such self-intercalated TMD compounds may exist as local energy minima in the region of the intercalation phase diagram in which a metal-rich stoichiometry is promoted by growth conditions involving metal atoms at high chemical potential. However, growth windows of TMDs using high metal chemical potentials have so far remained relatively unexplored31,32.

In this work, the growth of 2D TMDs using both molecular beam epitaxy (MBE) and chemical vapour deposition (CVD) methods was investigated under high metal chemical potentials. We discovered that—independent of the growth method used—a metal-rich chemical potential promotes the self-intercalation of a metal (M) into MX, MX2 or M2X3 layered 2D compounds (M, metal; X, chalcogen), producing covalently bonded MxXy compounds. We term this class of materials ic-2D. Taking TaS2 as an example, the intercalated Ta atoms occupy the octahedral vacancies in the vdW gap to form distinct topographical patterns, as verified by atomic resolution scanning transmission electron microscopy–annular dark field (STEM–ADF) imaging. By varying the ratio of intercalating atoms to octahedral vacancies in the vdW gap, we grew TaxSy or TaxSey films and quantified the extent of Ta-intercalation using σ, the percentage of initial total vacancy sites that are occupied by intercalated atoms. Our results indicate that self-intercalation is common to a broad class of vdW crystals, and it offers a powerful approach through which to transform layered 2D materials into ultrathin, covalently bonded ic-2D crystals with ferromagnetic properties.

We first describe the self-intercalation of native atoms—that is, Ta—into a TaS2 bilayer during MBE deposition on a silicon wafer, as a means to demonstrate the formation of an ic-2D film via octahedral vacancy filling of a 2D bilayer material. Wafer-scale Ta-intercalated TaS2 bilayer films were grown on 2-inch, 285-nm SiO2/Si wafers in a dedicated MBE system14. Ultra-pure Ta and S molecular beams were evaporated from an e-beam evaporator and a sulfur cracker cell equipped with a valve, respectively (Fig. 1a, b). We could routinely grow 2H-phase TaS2 bilayer films using a high S chemical potential—that is, a Ta-to-S flux ratio of around 1:10 (Fig. 1a, Supplementary Fig. 1)—for 3 h and a substrate temperature of 600 °C. When the Ta:S flux ratio was increased to 1:6 (Fig. 1b, c), the film became non-stoichiometric with respect to TaS2 owing to the excess of Ta atoms. A fingerprint of the Ta-rich environment is the presence of Ta adatoms (Fig. 1d) occupying the centre of the honeycombs (Fig. 1e) or situated on top of the Ta sites (Fig. 1f) in the monolayer TaS2 film, as observed by STEM when the growth was interrupted partway through (Supplementary Fig. 2). When Ta and S are continually supplied in the appropriate ratio, the Ta adatoms become embedded in the TaS2 structure, occupying the octahedral vacancies between two S layers (Fig. 1g). The ic-2D crystals therefore have a sequential, TaS2-Ta-TaS2-Ta layer-by-layer growth mechanism; as such, multilayer or bulk-phase ic-2D crystals can be readily accessed simply by increasing the growth time. The thermodynamic stability of such intercalated phases was assessed using energy-composition phase diagrams generated through density functional theory (DFT) calculations (Fig. 1h). It was found that stoichiometric H-phase TaS2 is formed only under S-rich conditions (when the chemical potential of sulfur, μS, exceeds −5.3 eV), whereas at higher Ta:S flux ratios (low μS), various Ta-intercalated TaxSy configurations—ranging from Ta9S16 (25% Ta intercalation) to Ta8S12 (66.7% Ta intercalation)—entered a thermodynamically stable state.

Fig. 1: Self-intercalation in TaS2 crystals.
figure 1

a, b, Schematic showing the growth of pristine TaS2 (a) and self-intercalated Ta7S12 (b) by MBE under a low and a high Ta-flux environment, respectively. The lower Ta flux produces stoichiometric TaS2, whereas a higher Ta flux generates a self-intercalated phase. c, Photographs of monolayer TaS2 and bilayer Ta7S12, grown by MBE on a 2-inch SiO2/Si wafer. d–f, Atomic-resolution STEM–ADF image of monolayer TaS2 under Ta-rich conditions (d), showing an abundance of interstitial Ta atoms at the centre of honeycomb (e) or on top of the Ta site (f). In e, f, the corresponding atomic models are depicted on the right. g, Schematic depicting the layer-by-layer growth of ic-2D crystals. h, Calculated formation energies of various self-intercalated TaxSy phases with intercalation concentrations of 25%, 33.3%, 50%, 66.7% and 100%, as a function of the chemical potential of sulfur. Scale bars: d, 2 nm; e, f, 0.5 nm.

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Notably, a Ta:S flux ratio of approximately 1:6 produced a \(\sqrt{3}a\times \sqrt{3}a\) superlattice of Ta atoms (Fig. 2a) sandwiched between two TaS2 monolayers. The extent of intercalation (σ) was 33.3%, and the overall stoichiometry of the crystal became Ta7S12, as corroborated by both the real-space STEM image (Fig. 2b) and the corresponding fast Fourier transform (FFT) pattern (Fig. 2c). Image simulation and sequential STEM images capturing the diffusion of intercalated atoms showed that the periodically arranged bright spots in the STEM image were induced by the intercalation of Ta (Fig. 2d, Supplementary Information section 1, Supplementary Videos 1, 2). We also collected STEM cross-section images (Fig. 2e, f) to verify the existence of an intercalated Ta atomic layer in the vdW gap of ic-2D films grown by CVD.

Fig. 2: Compositional engineering of TaxSy and TaxSey with different concentrations of intercalated Ta.
figure 2

a, b, Atomic-resolution STEM–ADF images of self-intercalated Ta7S12, grown by MBE, showing the well-defined \(\sqrt{3}a\times \sqrt{3}a\) superstructure (a), and an enlarged image (b). c, The corresponding FFT pattern of a, with \(\sqrt{3}a\) superspots highlighted by orange circles. d, Atomic model of self-intercalated Ta7S12. e, f, STEM cross-section view of 100% Ta-intercalated Ta9Se12 (e) and its corresponding simulated image derived from the DFT-optimized atomic model (f). g–j, Atomic-resolution STEM images of 25% Ta-intercalated Ta9S16 (g), 50% Ta-intercalated Ta10S16 (h), 66.7% Ta-intercalated Ta8Se12 (i) and 100% Ta-intercalated Ta9Se12 (j) ic-2D crystals. k–n, Left, enlarged STEM images corresponding to the regions highlighted with white boxes in g–j, respectively; right, the corresponding FFT patterns; bottom, the corresponding atomic models. Scale bars: a, g–j, 2 nm; b, e, k–n, 0.5 nm.

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The homogeneous Ta7S12 phase was grown directly on a 2-inch silicon wafer (Supplementary Fig. 3). The Ta7S12 film was formed by the coalescence of nano-domain crystals (around 50 nm) separated by mirror twin boundaries or tilted grain boundaries (Supplementary Information section 2). The amorphous islands and gaps seen in the STEM images were attributed to the poor stability of TaxSy and to sample damage incurred during transfer. Energy dispersive X-ray spectroscopy (EDS) and electron energy loss spectroscopy (Supplementary Fig. 4) verified that the film was composed solely of Ta and S, with no foreign elements, and X-ray photoelectron spectroscopy (Supplementary Fig. 5) confirmed that the chemical stoichiometry agreed very well with Ta7S12. The Raman spectra of the film exhibited two prominent \({{\rm{E}}}_{{\rm{g}}}^{3}\) and \({{\rm{A}}}_{{\rm{1g}}}^{3}\) peaks at 300 cm−1 and 400 cm−1, respectively, matching those of H-phase TaS2 films. The fingerprint of the intercalation was a series of minor peaks in the 100 cm−1 to 170 cm−1 range (Supplementary Fig. 6), which were absent in pure H-phase TaS233 and are attributed to the covalent bonds between the intercalated Ta atoms and their octahedrally coordinated S atoms (Supplementary Fig. 7).

25% Ta-intercalated TaS2 has a stoichiometry of Ta9S16 and was produced at a slightly lower Ta chemical potential than Ta7S12, corresponding to a Ta:S ratio of around 1:8. The intercalated Ta atoms occupy the octahedral vacancies in every \(2a\times \sqrt{3}a\) unit length, and this phase was distinguished by the square symmetry of the intercalated atomic lattice (Fig. 2g, k, Supplementary Fig. 8). When the Ta:S flux ratio was further increased to 1:5, a Ta10S16 phase (σ = 50%) was successfully grown (Fig. 2h). The intercalation concentration—the percentage of total vacancy sites that were occupied—was determined to be exactly 50% via atom counting (Supplementary Fig. 9). Notably, this phase is characterized by atomic chains that are interconnected over a short range, forming an overall glassy phase. Clear diffusive rings were observed in the proximity of the first-order FFT spots (Fig. 2l, Supplementary Fig. 10), confirming this short-range ordered structure34. When the Ta:S flux ratio was further increased, the glassy phase was retained, but the short atomic chains became denser before fully evolving into a complete atomic plane when σ reached approximately 100% (Supplementary Fig. 11). The use of growth conditions intermediate between those that give rise to high-symmetry phases resulted in phase separations, and atomically sharp domain boundaries separating two high-symmetry phases were apparent (Supplementary Information section 3).

To verify that ic-2D films could be produced by methods other than MBE, we used CVD to grow self-intercalated TaxSey crystals using excess Ta precursors. The crystal domains of these films were in the micrometre range—considerably larger than the nanosized domains grown by MBE (Supplementary Fig. 12). A typical Ta8Se12 crystal (σ = 66.7%) is depicted in Fig. 2i. Notably, it possesses a Kagome lattice belonging to the P6 wallpaper symmetry group. A well-defined \(\sqrt{3}a\times \sqrt{3}a\) periodic lattice can be unambiguously identified in the atomic-resolution STEM image (Fig. 2m; for the simulated image, see Supplementary Fig. 13). At even higher Ta chemical potential we successfully synthesized Ta9Se12 crystals (σ = 100%), in which the trigonal prismatic vacant sites in AA-stacked Ta9Se12 were fully occupied (Fig. 2j)—as seen from the top view (Fig. 2n) and side view (Fig. 2e, Supplementary Fig. 14) STEM images. By precisely controlling the metal:chalcogen ratio during growth, we can prepare a full range of Ta-intercalated TaxSey or TaxSy compounds with intercalation levels ranging from σ = 25% to over 100%, as verified by EDS (Supplementary Fig. 15, Supplementary Table 1).

In ic-2D films, the intercalated Ta atoms are octahedrally coordinated to the S6 cage, as opposed to the trigonal-prismatic coordination that is adopted in pristine TaS2. Charge transfer from the intercalated Ta atoms to the TaS2 host layers creates new electron ordering and modifies the Ta d-band splitting. Because the amount of charge transfer is dependent on the concentration of the intercalant, the system can be tuned. To investigate whether ferromagnetic order is present in the intercalated samples, magneto-transport measurements were carried out on MBE-grown Ta7S12 (σ = 33.3%) with a predominantly 2Ha stacking registry (Fig. 3a, Supplementary Fig. 16) and bilayer thickness (Supplementary Fig. 17). Figure 3c shows the temperature-dependent resistivity, in which a non-saturating upturn is observed below 30 K owing to the disorder-induced metal–insulator transition in the polycrystalline sample35. Linear magnetoresistance up to 9 T is observed at low temperatures in Ta7S12 (Fig. 3d), owing to density and mobility fluctuations36. The anomalous Hall effect (AHE) arises from the interplay of spin–orbit interactions and ferromagnetic order, and is a potentially useful probe of spin polarization. We observed AHE in Ta7S12 in addition to the linear ordinary Hall effect (OHE). Figure 3e shows a nonlinear Hall effect in the proximity of zero magnetic field and a linear OHE at high field. Although both multiband conduction and the AHE contribute to the nonlinear Hall effect, the observed linear OHE suggests single-carrier (hole) conduction in Ta7S12 and thus excludes multiband transport as the origin of the nonlinear Hall effect37,38. The nonlinear Hall effect is therefore ascribed to AHE, which arises from ferromagnetism in conductors39. After subtracting the linear OHE, anomalous Hall resistance of up to 0.75 Ω is observed at 1.5 K; this decreases with increasing temperature and disappears at 10 K, which is in line with Monte Carlo simulations based on the Ising model (Supplementary Fig. 18).

Fig. 3: Ferromagnetism in Ta-intercalated Ta7S12 ic-2D crystals.
figure 3

a, Atomic-resolution STEM–ADF image of a typical self-intercalated Ta7S12 film. This image was collected using a half-angle range from about 30 mrad to 110 mrad to enhance the contrast of S. b, Optical microscopy image of a Ta7S12 Hall bar device encapsulated with hexagonal boron nitride. c, Resistivity of the Ta7S12 ic-2D crystal as a function of temperature. d, e, Temperature-dependent magnetoresistance (d) and Hall resistance (Rxy) (e) of Ta7S12 under an out-of-plane magnetic field. f, Contour plot of charge density difference in Ta-intercalated Ta7S12. g, h, Orbital-resolved spin-up (g) and spin-down (h) band structures of the intercalated Ta in Ta7S12. i, Top view (top) and side view (bottom) spin density isosurface of Ta-intercalated Ta7S12. j, Calculated magnetic moments as a function of the Ta-intercalation concentration (σ) in 2Ha-stacked nonstoichiometric TaxSy. μB, Bohr magneton. Scale bars: a, 0.5 nm; b, 20 μm.

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The effects of self-intercalation on the electrical properties of TMDs were further assessed in Ta8Se12 (σ = 66.7%), which forms a Kagome lattice. It was found that the intercalation of Ta atoms and the formation of Kagome lattices stabilize the charge-density wave states. The temperature-dependent Hall signal reveals an AHE below 15 K and confirms ferromagnetic order in Ta8Se12 (Supplementary Fig. 19, 20).

We performed DFT calculations in order to understand the origin of the magnetization in self-intercalated Ta7S12. Perfect bilayer 2Ha-stacked TaS2 (Supplementary Fig. 21) possesses a non-magnetic ground state, in which ferromagnetism can be induced by the double exchange mechanism40, triggered by the charge transfer from intercalated Ta to pristine TaS2 (Fig. 3f). When the intercalated Ta adopts a \(\sqrt{3}a\times \sqrt{3}a\) superstructure, six S atoms bond with one intercalated Ta atom to form an octahedral unit in the vdW gap. By contrast, each S atom is shared by three Ta atoms in the pristine TaS2 layer. This difference in local bonding arrangement induces charge transfer from the octahedral-coordinated intercalated Ta atom to the prismatic-coordinated Ta atom in the TaS2 layer (Fig. 3f). In pristine H-phase TaS2, the Ta d orbitals and the S p orbitals are well separated in terms of energy, with the states at the Fermi level having mainly Ta \({d}_{{z}^{2}}\) and Ta \({d}_{{x}^{2}}\) characteristics (Supplementary Fig. 21). In Ta7S12 (σ = 33.3%), the intercalated Ta atoms introduce additional spin-split bands across the Fermi level, and a magnetic ground state develops (Fig. 3g, h). The magnetic moments are localized on the d orbitals of the intercalated Ta atom, as evidenced by the calculated intercalated Ta orbital-resolved spin-up and spin-down band structures in Fig. 3g and Fig. 3h, respectively. The states at the Fermi level comprise the prismatic-centred Ta \({d}_{{z}^{2}}\) orbitals hybridized with the spin-up band of the \({d}_{{x}^{2}-{y}^{2}}\) orbital of the intercalated Ta. However, only the intercalated Ta atoms exhibit a net spin density, as illustrated in Fig. 3i, in which the top view spin density isosurface matches the shape of the \({d}_{{x}^{2}-{y}^{2}}\) orbital. In addition, the non-magnetic 3a × 3a charge-density wave state of Ta7S12 can be ruled out owing to its relative instability compared with the ferromagnetic state41.

The existence of a magnetic moment correlates with a large degree of charge transfer between the intercalated Ta and the TaS2 layers. Strong charge transfer occurs when the proportion of intercalated Ta atoms is low, whereas charge transfer becomes relatively weak in a heavily intercalated (Fig. 3j) compound, in accordance with the calculated charge difference and the variation of Bader charge on the Ta atoms (Supplementary Fig. 22, Supplementary Table 2).

To investigate whether the self-intercalation phenomenon occurred for other TMDs, we performed a high-throughput DFT study of 48 different intercalated TMD bilayers, using a semi-automated workflow for maximal consistency and veracity42. Specifically, we considered TMDs of the transition metals Mo, W, Nb, Ta, Ti, Zr, Hf, V, Cr, Mn, Fe, Co, Ni, Pd and Pt, as well as Sn, and the chalcogens S, Se and Te (Fig. 4a) at σ values of 33.3% or 66.7%. Out of this set of TMDs, we observed that 14 bilayer configurations—Ti8S12, Ti8Se12, Ti8Te12, Co7S12, Co7Se12, Co7Te12, Nb7S12, Nb7Se12, Nb7Te12, Mo7S12, Mo7Se12, Ta7S12, Ta7Se12 and Ta7Te12 (highlighted by specific σ values and chalcogens in Fig. 4a and Supplementary Table 3 for magnetic moment)—develop ferromagnetic order upon self-intercalation, whereas their parental MX2 bilayers are nonferromagnetic. Notably, group V and group VI TMDs exhibit strong ferromagnetism after self-intercalation (Fig. 4b). MX2 bilayers that are intrinsically ferromagnetic—that is, VX2, CrX2, MnX2 and FeX2—retain ferromagnetism upon self-intercalation (highlighted by orange triangles in Fig. 4a). Among the 14 self-intercalated 2D ferromagnets that we generated, the formation energies of 12 of these—the two exceptions being MoS2 and MoSe2—were lower than or similar to those of the non-intercalated materials (Supplementary Figs. 23, 24), indicating that self-intercalation is energetically feasible.

Fig. 4: A library of ic-2D crystals.
figure 4

a, Periodic table showing metal (blue) and chalcogen (red) combinations that form ic-2D crystals according to our DFT calculations; the list is not exhaustive. Blue triangles indicate that self-intercalation can be experimentally realized, whereas grey triangles indicate that intercalation was not successful under our experimental conditions. MX2 structures with intrinsic ferromagnetism are highlighted with orange triangles. b, Atomic models, obtained from DFT calculations, of ic-2D crystals that exhibit ferromagnetism. c–e, STEM–ADF images of V-intercalated V11S16 (c), In-intercalated In11Se16 (d) and Fe-intercalated FexTey (e). f–h, Left, enlarged STEM images of c–e, respectively; right, the corresponding FFT patterns. Scale bars: c–e, 2 nm; f–h, 0.5 nm; FFT patterns in f–h, 5 nm−1.

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To validate our theoretical predictions, we attempted to grow a wide variety of ic-2D materials (Fig. 4a). In this figure, blue triangles indicate that the self-intercalation can be experimentally realized11,12, whereas grey triangles indicate that intercalation was not successful under our experimental conditions. We succeeded in growing several ic-2D crystals—namely V11S16 (Fig. 4c, Supplementary Fig. 25), In11Se16 (Fig. 4d, Supplementary Fig. 26) and FexTey (Fig. 4e, Supplementary Fig. 27)—by either CVD or MBE. The topological features and corresponding FFT patterns of these crystals are depicted in Fig. 4f–h. The intercalated V11S16 has a 2a × 2a superstructure, and the intercalation concentration was estimated at 75% (Fig. 4f). In11Se16 also showed a 2a × 2a superstructure; however, in this case, the intercalated In atoms reveal a signature honeycomb structure (Fig. 4g). The crystal structure of self-intercalated FexTey was complicated—additional Fe atoms were found to be intercalated into the atomic network of the pristine FeTe matrix as interstitials, because telluride-based TMDs offer the largest spacing between the host atoms43. Upon intercalation, the FexTey phase reveals new symmetries, as confirmed by the emergence of superspots in the FFT pattern (Fig. 4h). A similar complex intercalation network was also observed in VxTey (Supplementary Fig. 28).

We have developed a robust method to engineer the composition of a broad class of TMDs, by means of self-intercalation with native metal atoms during growth. Because the main principle is the application of high chemical potential of metal atoms to provide the driving force for intercalation during growth, this technique should be compatible with most growth methods. The metal intercalants occupy octahedral vacant sites in the vdW gap, and distinct stoichiometric phases are produced depending on the levels of intercalation. High-throughput DFT simulations—supported by growth experiments—show that the self-intercalation method is applicable to a large class of 2D layered materials, thus enabling a library of materials with potentially new properties to be created from existing layered materials. Owing to the versatility with which the composition can be controlled, it is possible to tune—in one class of materials—properties such as ferromagnetism and the formation of spin-frustrated Kagome lattices. The implication of this work is that bilayer (or thicker) TMDs can be transformed into ultrathin, covalently bonded 3D materials, with stoichiometry that can be tuned over a broad range by varying the concentration of the intercalants.

Methods

Growth of self-intercalated TMD films by MBE

Ta-intercalated TaxSy films were grown in a dedicated MBE chamber (base pressure <6 × 10−10 torr). Before growth, the 2-inch SiO2 substrates were degassed in the same chamber at 500 °C for 2 h. Ultrapure Ta (99.995%, Goodfellow) and S powders (99.5% Alfa Aesar) were evaporated from a mini electron-beam evaporator and a standard sulfur valved cracker, respectively. The flux density of Ta was precisely controlled by adjusting the flux current. The temperature of the S cracker cell was maintained at 110 °C, and the flux density was controlled by the shutter of the cracker valve. The substrate temperature was maintained at 600–650 °C and the growth time was about 3 h for all thin films. Controlled growth of 25% Ta-intercalated Ta9S16, 33.3% Ta-intercalated Ta7S12 and 50% Ta-intercalated Ta10S16 films was achieved when the Ta/S ratio was set at around 1:8, around 1:6 and around 1:5, respectively. A slightly higher growth temperature facilitates the self-intercalation process. After growth, both Ta and S sources were turned off and the sample was further annealed for another 30 min before cooling to room temperature. In-intercalated InxSey samples were grown in a customized MBE chamber (base pressure <6 × 10−10 torr). Before growth, the 1 cm × 1 cm SiO2 substrate was degassed in the chamber at 600 °C for 1 h. Ultrapure In2Se3 powder (99.99%) and Se pellets (99.999%) were evaporated from a mini electron-beam evaporator and an effusion cell, respectively. The temperature of the Se effusion cell was set at 150 °C with a hot-lip at 220 °C. The substrate temperature was maintained at 400 °C and the growth time was about 2 h. Controlled growth of In11Se16 films was achieved when the In2Se3/Se ratio was set at around 1:3.

Growth of self-intercalated TMD films by CVD

Ta-intercalated TaxSey crystals were grown by CVD. Before growth, the SiO2 substrate was sequentially cleaned using water and acetone, followed by 5 min of O2 plasma. The furnace was purged by 300 standard cubic centimetres (sccm) of Ar gas for 5 min. Se powders and mixed Ta/TaCl5 powders were applied as precursors that were located upstream in a one-inch quartz tube. 40 sccm Ar and 10 sccm H2 was used as a carrier gas. The samples were grown at 800 °C for 30 min. After growth, the sample was cooled down quickly in a continuous stream of Ar. Controlled growth of 66.7% Ta-intercalated Ta8Se12 and 100% Ta-intercalated Ta9Se12 was achieved when the content of Se powders and mixed Ta/TaCl5 powders were 1 g/15 mg/1.5 mg and 1 g/30 mg/3 mg, respectively. V-intercalated VxSy crystals were grown by CVD. Before growth, the SiO2 substrates were treated by the same method as indicated for the growth of TaxSey. Two quartz boats containing 0.5 g S and 0.3 g VCl3 were loaded upstream of the one-inch quartz tube to dispense the precursors. The carrier gas was 40 sccm Ar together with 10 sccm H2. The sample was grown at 680 °C for 30 min. After growth, the sample was cooled quickly under the protection of 100 sccm Ar. Fe-intercalated FexTey crystals were grown by CVD. Before growth, the SiO2 substrates were treated by the same method as indicated for the growth of TaxSey. Two quartz boats containing Te (>99.997%) and FeCl2 (>99.9%) were placed upstream of the one-inch quartz tube to dispense the precursors. The sample was grown at 600 °C for 30 min. After growth, the sample was cooled quickly under the protection of 100 sccm Ar.

Sample characterization

X-ray photoelectron spectroscopy was performed using a SPECS XR 50 X-ray Al Kα (1,486.6 eV) source with a pass energy of 30 eV. The chamber base pressure was lower than 8 × 10−10 mbar. Raman spectra were collected at room temperature using the confocal WiTec Alpha 300R Raman Microscope (laser excitation, 532 nm).

STEM sample preparation, image characterization and image simulation

The as-grown TMD films were transferred via a poly (methyl methacrylate) (PMMA) method under the protection of graphene. A continuous graphene film was coated on fresh Ta7S12 film to protect the surface oxidation via a conventional PMMA method. Subsequently, graphene/Ta7S12 composites were immersed in 1 M KOH solution to detach the PMMA/Ta7S12 composite from the SiO2 substrate, followed by rinsing in deionized water. The PMMA/graphene/Ta7S12 film was then placed onto a Cu quantifoil TEM grid that was precoated with continuous graphene film44. The TEM grid was then immersed in acetone to remove the PMMA films. Atomic-resolution STEM-ADF imaging was performed on an aberration-corrected JEOL ARM200F, equipped with a cold field-emission gun and an ASCOR corrector operating at 60 kV. The convergence semiangle of the probe was around 30 mrad. Image simulations were performed with the QSTEM package assuming an aberration-free probe with a probe size of approximately 1 Å. The convergence semiangle of the probe was set at around 30 mrad, and the accelerating voltage was 60 kV in line with the experiments. The collection angle for high-angle annular dark-field imaging was between 81 and 280 mrad and for medium angle annular dark-field imaging was from 30 to 110 mrad. The phonon configurations were set at 30 with defocus value of 0. The STEM–EDS were collected and processed in an Oxford Aztec EDS system.

Device fabrication and measurements

MBE-grown Ta7S12 and CVD-grown Ta8Se12 were selected to fabricate Hall-bar devices using e-beam lithography and e-beam evaporation of Ti/Au (2/60 nm). The MBE-grown Ta7S12 film was then etched into Hall-bar geometry using deep reactive-ion etching. The final devices were encapsulated with hexagonal boron nitride flakes using a dry-transfer method in the glovebox (both O2 and H2O less than 1 ppm), to avoid the degradation of Ta7S12 and Ta8Se12 under ambient conditions. Low-temperature transport measurements were carried out in an Oxford Teslatron system. All resistances were derived from four-terminal measurements using an SR830 lock-in amplifier, with a constant excitation current of 1 μA.

DFT calculations

First-principles calculations based on DFT were implemented in the plane wave code VASP45 using the projector-augmented wave potential approach. For the exchange and correlation functional, both the local density approximation and the Perdew–Burke-Ernzerhof (PBE)46 flavour of the generalized gradient approximation were used, and no discernible difference were found in the results. A kinetic energy cut off of 500 eV was used for the TaS2. A Monkhorst Pack47 k-grid sampling with a k-point density of 6.0 Å−1 was used for geometry optimization. For thin-film calculations, a vacuum thickness of 20 Å was added in the slab to minimize the interaction between adjacent image cells. Geometry optimization was performed with the maximum force convergence criterion of 0.005 eV Å−1. To treat the strong on-site Coulomb interaction of localized Ta d orbitals, we used Dudarev’s approach48 with an effective U parameter of Ueff = 3.0 eV. The zone centre phonon modes were calculated using density functional perturbation theory with the local density approximation functionals.

High-throughput DFT calculations

These were carried out with the electronic structure code GPAW49 following a semi-automated workflow for maximal consistency and accuracy42. The relaxations of the self-intercalated bilayers were done on a Monkhorst-Pack47 grid with a k-point density of 6.0 Å−1 using the PBE46 and BEEF-vdW functionals50 for describing exchange-correlation effects. A vacuum of 15 Å was used in the out-of-plane direction to avoid non-physical periodic interactions. The plane-wave expansion was cut off at 800 eV. All systems were relaxed until the maximum force on any atom was 0.01 eV Å−1 and the maximum stress on the unit cell was 0.002 eV Å−3. All systems were calculated in the intercalated structure with both a spin-paired calculation and a spin-polarized calculation. If the total energy of the spin-polarized structure was found to be more than 0.01 eV per atom lower than the spin-paired structure, the structure was concluded to be magnetically more stable than its non-magnetic counterpart. The atomic structures of calculated self-intercalated TMDs (33.3% and 66.7% intercalation concentration) are presented in Supplementary Fig. 29, in which the polymorphism of single-layer MoX2, WX2, NbX2 and TaX2 (X = S, Se and Te) reveals an H-phase, whereas the rest of the TMDs are T-phase, adopting an AA stacking polytype. MoX2 and WX2 adopt the AA′ stacking order whereas NbX2 and TaX2 adopt AB′ stacking. All intercalants occupy the octahedral vacancies in the vdW gap.