Unveiling the landscape of Mottness and its proximity to superconductivity in 4Hb-TaS₂

Abstract

Mott physics lies at the heart of many intriguing quantum phenomena. Recently, van der Waals materials emerge as a powerful platform to explore these correlated electronic states, yet tracking how such a Mott state develops and interacts with neighboring phases remains an experimental challenge. Here we use scanning tunnelling spectroscopy to study a filling-controlled Mott state and its interplay with superconductivity in 4Hb-TaS₂, which interleaves strongly correlated 1T-TaS₂ layers and superconducting 1H-TaS₂ layers. By resolving the electronic spectral function across different filling levels driven by interlayer charge transfer, we quantitatively capture the continuous evolution of the Mott state, characterized by the emergence of Mott-Hubbard bands and the systematic suppression of the central quasiparticle peak. Moreover, while the 1H layers exhibit a uniform, fully opened superconducting gap, the heavily correlated electrons in the 1T layers act destructively against pairing, creating nanoscale, non-superconducting paramagnetic puddles. Our findings provide a quintessential visualization of the iconic Hubbard model and establish layered heterostructures as an ideal playground for designing exotic correlated quantum phases.

4Hb-TaS₂ is composed of alternating strongly correlated 1T-TaS₂ layers and superconducting 1H-TaS₂ layers. Here, the authors demonstrate that the 1T-TaS₂ layer is near the border of the Mott criterion and exhibits non-superconducting, paramagnetic puddles at the nanoscale.

Introduction

The Mott insulator is a paradigmatic example to study the relevant role of electron correlations. It represents the localization of electrons at half band-filling when the interaction energy of electrons—characterized by the Coulomb repulsion U—dominates over their kinetic energy characterized by the bandwidth W ^1,2. The vicinity of such Mott transitions is believed to host exotic many-body quantum states, including unconventional superconductivity^3,4, quantum spin liquids^5,6, and strange metallicity⁷. Although many efforts have been made to understand the microscopic basis of Mott physics, key features in many interesting doping regimes remain difficult to access experimentally.

Recently, two-dimensional van der Waals (vdW) materials have emerged as highly tunable, strongly correlated electronic systems by twisting or hetero-stacking, thus opening a new avenue for exploring the landscape of Mott physics and realizing correlated states that are not foreseeable from single layers alone^8–16. The 4Hb polytype of tantalum disulfide (4Hb-TaS₂) is one case in point¹⁷: it is a naturally occurring bulk vdW heterostructure composed of alternating 1T- and 1H-TaS₂ layers (Fig. 1a). The 1H layer is superconducting and features spin-valley locking of the Ising type^18,19. The 1T layers host a strong $\sqrt{13}\times \sqrt{13}$ superstructure under which every 13 Ta atoms are reconstructed into a Star of David (SoD) cluster, each holding one Ta-5d electron (if unperturbed) localized on the central Ta ion. These localized electrons are believed to bear large onsite Coulomb interactions compared with their intralayer hopping amplitude, therefore giving rise to a Mott insulator and a candidate quantum spin liquid on a triangular lattice^20–22. However, such a Mott state is susceptible to out-of-plane stacking in bulk 1T-TaS₂, where the interlayer dimerization of the SoD clusters leads to a band insulator with an even number of electrons in the Ta-5d orbitals^23–26.

Fig. 1. Atomic structure, charge density wave, and depleted narrow band in 4Hb-TaS₂.

a Crystalline structure of 4Hb-TaS₂, which interleaves strongly correlated 1T-TaS₂ layers with superconducting 1H-TaS₂ layers. The right panels denote schematics of electronic structures for each layer, where the red/blue arrows denote opposite spin orientations and the blue, red, and orange regions represent the narrow band, lower, and upper Hubbard bands, respectively. b Topography of the 1H termination showing $3\times 3$ CDW modulation. Insert: superconducting gap obtained at 0.1 K. c Topography of the 1T layer showing $\sqrt{13}\times \sqrt{13}$ CDW where every 13 Ta atoms are reconstructed into a SoD cluster. The inset shows its Fourier transform, in which the CDW peaks are marked by circles. d dI/dV spectra obtained along the line shown in (c). e Calculated band structure of monolayer 1T-TaS₂ with$\sqrt{13}\times \sqrt{13}$ CDW. An isolated narrow band can be found at E_F. STM setup conditions: b V_S = −10 mV, I_t = 1 nA. c V_S = −500 mV, I_t = 1 nA. d V_S = −800 mV, I_t = 2 nA, V_mod = 10 mV. H high, L low.

In 4Hb-TaS₂, the interleaving of 1H superconducting layers can eliminate interlayer dimerization but at the expense of suffering marked electron transfer from the 1T layer to the 1H layer. This results in an almost empty narrow band in the 1T layer^27,28, and consequently, there is little room for Mottness or other strongly correlated effects. Nevertheless, the superconductivity in 4Hb-TaS₂ exhibits a series of highly unconventional features, including signatures of broken time-reversal symmetry²⁹ and multicomponent order parameters^30,31, topological edge modes³², residual specific heat²⁹, and a puzzling magnetic memory effect manifested in the spontaneous vortex phase³³. Most of these phenomena occur in lightly Se-doped samples and imply a critical role of electron correlation. In comparison, the spectroscopy data for non-superconducting 1T/1H-TaS₂ bilayer films exhibit a Mott gap feature together with a narrow zero-bias peak, which has been interpreted in terms of the local moment of 1T layer being Kondo-screened by the itinerant electrons of 1H layer^18,34–36. A recent first-principles study puts forward an alternative explanation that diminishes the role of screening by the 1H electrons and suggests a doped Mott insulator whose doping level depends on the distance between the layers³⁷. As such, the relevant physics of 1T/1H systems seems to critically depend on the charge transfer that controls the electron filling of the 1T layer, and the interlayer hybridization that determines the interplay between 1T and 1H electrons. This raises two central questions in 4Hb-TaS₂: first, how does the correlation effect develop for the 1T-electrons, specifically, to what extent does Mott physics govern the low-energy states, and second, how do such correlations subsequently influence superconductivity? The absence of a clear characterization of the electronic state has led to a strong dependence on theoretical input to clarify the underlying physics, which calls for systematic spectroscopy studies.

Here, we use scanning tunneling microscopy and spectroscopy to reveal the fate of 1T-electrons in 4Hb-TaS₂. Taking advantage of the subtle charge transfer between the 1T and 1H layers, we successfully track the evolution of single-particle spectral function continuously from ~0.2 electrons per SoD cluster toward half-filling with an unsurpassed energy resolution. Systematic measurements and analyses enable us to quantitatively determine the emerging Mott–Hubbard gap along with the diminishment of the central quasiparticle peak. These observations, taken together with our dynamical mean-field theory (DMFT) calculation, place the system near the borderline of the Mott criterion. Moreover, we provide spectroscopic evidence that this renormalization of the quasiparticle states locally alters the superconducting gap potential and gives rise to nonsuperconducting puddles with local moments in the 1T layer.

Results

Single crystals were synthesized with a low selenium concentration (4Hb-TaS_1.99Se_0.01) as described in previous reports^18,27–33. The structural and transport characterizations are shown in Supplementary Note 1, which confirms the $\sqrt{13}\times \sqrt{13}$ charge density wave (CDW) transition at 315 K and the superconducting transition at approximately 3.0 K. Cleaving naturally exposes the sulfur surfaces of both the 1T and 1H terminations, and these two types of surfaces can be distinguished morphologically and spectroscopically. For the 1H termination, both the atomic and 3 × 3 CDW periodicities are apparent in the STM topography (Fig. 1b). The differential conductance (dI/dV) spectrum shows a uniform V-shaped metallic character in the normal state (Supplementary Note 2). A superconducting gap of ${△}_{SC}^{1H}\approx 0.4\mathrm{meV}$ is observed below $T_C$ with a hard, “U”-shaped bottom (inset of Fig. 1b), indicating a nodeless gap function for these 1H layers. Notably, the strong $\sqrt{13}\times \sqrt{13}$ superlattice characteristic of the 1T layer (Fig. 1c) is also imprinted onto the 1H layer, indicating a remarkable interaction between adjacent layers. For the 1T termination, the majority of the dI/dV spectra exhibit a pronounced peak slightly above the Fermi energy (E_F), as shown in Fig. 1d. This peak corresponds to the isolated narrow band of the Ta-5d electrons with the $\sqrt{13}\times \sqrt{13}$ CDW order, as supported by our first principal calculation (Fig. 1e, a slab calculation of 1T/1H bilayer can be found in Supplementary Note 3), which has shifted above E_F owing to the charge transfer^27,28. The peak width at half height allows us to estimate the bandwidth of this narrow band, and we find that $W_0\approx 80\mathrm{meV}.$ By integrating the spectral weight below E_F and calculating its proportion to the total weight of this narrow band, we find that approximately 0.2 electrons remain in each SoD cluster (Supplementary Fig. 6). These observations set a good starting point for further exploration.

In contrast to the homogeneous metallic state of the 1H layer, the low-energy spectral feature of the 1T layer is highly diverse among different SoD clusters. For example, Fig. 2a shows an STM topography with a 100-by-100-nm field of view (FOV), which contains approximately four thousand SoD clusters. The obtained electronic spectrum at the center of each cluster reveals that, in addition to the common depleted narrow band feature, ~13% of the clusters show a prominent zero-bias peak flanked by two broader peaks, reminiscent of the Kondo resonance observed in 1T/1H-TaS₂ bilayer films^16,34–36 and consistent with a previous report²⁸. A series of intermediate states are also observed, as shown in Fig. 2b. Through dI/dV mapping, we found that these low-energy states are distributed in the center of the SoD clusters, whereas between the clusters they exhibit depleted narrow band features despite weak intensity (Supplementary Figs. 8 and 9). The in-phase distribution suggests that these varying low-energy electronic features should stem from the narrow band, whose electron filling somehow changes among different clusters. These observations are also consistent with calculations showing that the narrow band mainly stems from the central Ta orbital inside a cluster^38,39, and moreover, the doped electron is largely trapped inside the cluster. In fact, their electron-doping nature can be directly revealed by the spectral line shapes at relatively high energies. For example, focusing on the broad peak located at ~0.5 eV below E_F, as shown in Fig. 2c, we find that it progressively shifts to negative binding energies, from clusters showing the depleted narrow band to those with zero-bias peaks. As such, this direct link clarifies that the low-energy spectral function reflects an evolution of the narrow band upon increasing electron filling.

Fig. 2. Evolution of the narrow band with varying electron filling.

a Topographic image of a large FOV at the 1T termination. The apparent shapes of the SoD clusters exhibit high diversity owing to their different spectral features. b Representative dI/dV spectra obtained at the centers of different SoD clusters. c Energy shift of the broad peak (at approximately 0.5 eV below E_F) for the spectra in (b), indicating an increase in the electron filling of each cluster from top to bottom. The red lines show the Gaussian fitting, and the vertical lines indicate the energy positions of the broad peaks. d A false color map of the normalized dI/dV spectra obtained at the center of one hundred clusters, which are sorted according to the exact energy of the broad hump near −0.5 eV. The dashed white line tracks the shift of the remote band, whereas the dashed yellow lines mark the Hubbard bands. e Integral of the density of states from −250 meV to 250 meV in (d). STM setup conditions: a V_S = −500 mV, I_t = 1 nA; b, c V_S = −1 V, I_t = 2.5 nA, V_mod = 2 mV; d V_S = −1V, I_t = 2.5 nA, V_mod = 2 mV.

Next, we turn to the origin of such electron doping. A recent calculation has found that the charge transfer between the 1T and 1H layers highly depends on the chemical composition and the interlayer distance⁴⁰. In these 4Hb-TaS₂ samples, 0.5% of the sulfur atoms were replaced by selenium to stabilize the crystal. If we assume that each SoD cluster (13 Ta and 26 sulfur atoms) contains no more than one selenium substitution (which is reasonable because of the ultralow Se concentration), ~13% of the clusters are influenced, and Se defects can suppress the charge transfer to the host clusters⁴⁰. This hypothesis was further confirmed by two controlled experiments (Supplementary Note 4). First, the proportion of clusters hosting a zero-bias peak significantly increases in samples with higher Se concentrations, suggesting that Se substitution can indeed inhibit charge transfer. Second, the proportion of these clusters with zero-bias peak markedly decreases when an in-plane tensile strain is applied to the sample. This is because an in-plane tensile strain would, in principle, reduce the interlayer distance so that it can promote charge transfer and lead to more “empty” clusters in the 1T layer. Therefore, the electron filling level in each cluster is highly influenced by charge transfer at a subtle balance of selenium substitution and interlayer spacing (a detailed discussion can be found in Supplementary Note 4). This situation is unique and allows an in-depth study of the filling-controlled electronic state here. More importantly, the doping effect deviates from that of conventional metallic systems and shows strong spatial inhomogeneity as in cuprates^41–43. This feature comes from the weak screening of the electron Coulomb potential in a strongly correlated system.

In Fig. 2d, we have sorted more than one hundred typical dI/dV spectra according to the exact energy of the broad hump near −0.5 eV. We note that the involvement of these high-energy spectral features is essential for the analysis: first, they are reliable indicators of the actual amount of electron doping, and second, their spectral weights offer a basis for normalizing the dI/dV spectra, thus enabling a meaningful comparison of the low-energy density of states (DOS) among different clusters. The resulting false color map (Fig. 2d) depicts a full picture of how the nearly empty narrow band, with increasing electron filling (note the collective shift of the high-energy band features marked by the dashed white line), transforms into two shallow sub-bands below and above E_F, along with the sharpening and vanishing of the central peak. For better visualization, several representative spectra are plotted in Fig. 3a, which capture the main characteristics of the evolution. The symmetrical transfer of spectral weight from the original quasiparticle band (the narrow Ta-5d band) to the incoherent part (upper and lower Hubbard bands; abbreviated as UHB and LHB, marked by dashed yellow lines), at first glance, follows the prediction for a Mott transition, which will be tested in detail later.

Fig. 3. Characteristics of the spectral function of a filling-controlled Mott state.

a A series of dI/dV spectra selected from Fig. 2d that are sorted by the increased electron filling per cluster. The red and yellow arrows mark the metallic peak and the Hubbard bands, respectively. b Typical dI/dV spectrum close to half-filling, where three peak-like features can be seen. The solid lines are Lorentzian fits to the peaks: dark blue line, LHB; brown line, UHB; cyan line, central narrow quasiparticle peak. c U extracted from the positions of the LHB and UHB, plotted as a function of electron filling (according to the position of the LHB, see Supplementary Note 6). The inset shows the positions of the LHB and UHB. The yellow shaded area indicates that the value of U falls within this range. d Evolution of the spectral weights for the LHB and UHB with increasing electron filling. e The spectral weight of the central quasiparticle state with increasing electron filling, and f the FWHM of the central peak. The FWHM is obtained via Fano fitting. The color scales in (c–e) denote data from different samples. g DMFT calculations with quantum Monte–Carlo solvers under the condition U/W ~ 1.67. h HWHM of the central quasiparticle peak at different temperatures (see Supplementary Note 8). The light gray line denotes the expected temperature-dependent HWHM for a Kondo peak based on the Anderson impurity model (T_K ~ 40 K).

The unprecedented full set of spectroscopic data with high-energy resolution enables us to extract several key parameters of this evolution. To proceed, we focus our analyses on the energy range of $\pm 0.25\mathrm{eV}$, which includes the most relevant information of the isolated narrow band. The total spectral weight in this range, obtained by integrating the local DOS, remains roughly unchanged with electron filling (Fig. 2e). However, the narrow-band feature becomes sharper upon doping, with its maximum pinned near E_F (marked by red arrows in Fig. 3a); its intensity then decreases when the UHB and LHB start to develop (yellow arrows in Fig. 3a). In this region, we can extract several key parameters, including the onsite Coulomb U and positions of the LHB (ε) and UHB (ε+U), as well as the widths and spectral weights of the Hubbard bands and the central peak, by fitting these three features with Lorentzian line shapes (Fig. 3b, more fitting data are shown in Supplementary Note 5). We plot the results versus electron filling; this is done by employing ε as a measure of electron doping, since we find that it has a linear relationship with the position of high-energy features (Supplementary Note 6). The first direct observation is that while both LHB and UHB shift in energy with doping, a constant onsite $U\cong 190\pm 10\mathrm{meV}$ is found in the entire dataset (Fig. 3c), and a similar value has been found for the AC stacked termination in bulk 1T-TaS₂²⁵. When the LHB overlaps with the central peak, it carries more spectral weight than the UHB does, but the difference decreases with electron doping and almost disappears toward half-filling (Fig. 3d). Concurrently, the central peak becomes sharper (as indicated by its full width at half maximum, FWHM; Fig. 3f) and vanishes (its spectral weight, Fig. 3g), as it undergoes significant renormalization by onsite U.

Having obtained detailed knowledge of the evolution of low-energy spectral functions, we now discuss the relevant picture of the correlation effect in 4Hb-TaS₂. The 1T layer exhibits a Mott insulating state only when it is very close to half-filling. In our experiments, it is clear that the majority of the SoD clusters are significantly away from half-filling, and the continuous evolution of the spectral function shown in Fig. 2d suggests a primary role of the local doping effect in 1T layer. Indeed, this evolution can be well captured by our DMFT calculations with quantum Monte Carlo (Fig. 3g) and numerical renormalization group solvers (“Methods”; Supplementary Note 7); we have solely considered the correlating electrons of the 1T narrow band here and reproduced the low-energy three-peak feature with varying electron filling. Although our simplified model calculation deviates from the tunneling peaks due to the solver and approximations, it is fruitful to compare the theoretical results with our experimental data, and the results indicate that the changes in the low-energy spectral function are indeed consistent with the general signatures of a doped Mott system.

The clusters with Se-substitution are near half-filling, in which local moments can form; the central zero-energy peak can be a typical Kondo resonance peak, if the local moments are screened by 1H electrons, or a remanent quasiparticle peak if the correlation is driven by the 1T electrons. To shed light on the underlying physics, we compare our results with those of other typical T/H bilayer systems with Kondo physics. In those systems, the 1T layer remains in a uniform, half-filled Mott state due to less charge transfer, and the itinerant electrons for screening are thus the 1H electrons; this gives rise to a typical two-band Kondo system with Kondo temperatures $T_K$~18-40 K, and the Kondo resonance peak appears uniformly in real space^{16,34–36,44}. In crystalline 4Hb-TaS₂, the interlayer distance of T/H is approximately 0.6 nm (Supplementary Fig. 1), which is relatively smaller than that of bilayer films (typically 0.8 nm in refs. ^16,34). If the screening electrons are still from the 1H layer, this smaller distance, and consequently, larger interlayer hybridization, will lead to a higher $T_K$ in the Se-doped clusters. However, we found that the half width at half maximum (HWHM) of the central peak here is generally an order of magnitude smaller than that of these bilayer Kondo systems, and does not saturate but decreases linearly with decreasing temperature from 4.2 to 0.3 K (Fig. 3h). To estimate the Kondo temperature from the data, we removed the extrinsic broadening effect caused by Fermi–Dirac broadening of the tip and voltage modulation for lock-in detection⁴⁵ and fitted the HWHM with an empirical expression of $\Gamma =\sqrt{{\left(\alpha k_{B}T\right)}^2+{\left(2k_B{T}_K\right)}^2}$. The estimated $T_K$ is approximately 4 K (Supplementary Note 8), which is much lower than that of the bilayer Kondo systems. Furthermore, with the knowledge of $\left(\epsilon ,U,W_0\right),$ the Kondo temperature can be calculated with the Anderson impurity model as $k_B{T}_K=\omega W_0\sqrt{U/4W_0}\exp \left(-\pi ∣\epsilon ∣∣\epsilon +U∣/W_{0}U\right)$ with $\omega =0.4128$ being the Wilson number. The prediction power of the Anderson impurity model with this procedure has been experimentally verified in a recent STM work⁴⁶; in our case, since all the microscopic parameters are experimentally accessible, $T_K$ can be directly calculated to be ~40 K near half-filling (Fig. 3h). This value is basically similar to that of typical T/H Kondo systems^{16,34–36,44}, whereas in our system the DMFT calculations of a doped Mott state provide a better match to the reduced peak width than the single Anderson impurity model (Supplementary Note 8).

The significantly reduced Kondo energy scale of the central peak, together with the fact that it always connects to the LHB, leads us to attribute it to the remnant, narrowing metallic peak as in the Brinkman–Rice picture of Mott transitions⁴⁷, where the vanishing width of the central peak indicates the divergence of the effective mass of electrons approaching half-filling (Supplementary Fig. 16). In fact, the evolution in Fig. 2d directly shows how the spectral weights of the narrow band transfer to the Hubbard bands and leave a remaining quasiparticle peak at E_F. Therefore, our data indicate an inhomogeneous, doped Mott state^48–50 in the 1T layer of 4Hb-TaS₂; that is, the correlation and doping effect of 1T electrons play a dominant role. This picture is reasonable since there are still d-electrons occupying the same 1T layer due to the doping effect. In general, the full system should be properly described by a periodic Anderson model⁵¹, with the d-orbitals corresponding to the 1T layer and the p-orbitals to the 1H layer³⁷. On the other hand, for the specific question addressed here, this periodic Anderson model can be simplified to an effective Hubbard model, in which the p-orbital of the 1H layers primarily acts as charge reservoirs that control the filling of the 1T layer, as suggested in ref. ³⁷. To further check this, we have extended the calculation by incorporating the 1H component into the model, and the results obtained from this periodic Anderson model with the 1H contribution and those from the pure 1T Hubbard model remain in qualitative agreement with each other (Supplementary Fig. 15). This consistency validates that the essential physics in this regime is governed by the Hubbard interaction $U$ within the 1T layer. The ratio $U/W_0~2$ places the system near the borderline of the Mott criterion.

The bulk superconductivity of 4Hb-TaS₂, in which many fascinating phenomena have been reported^29–33, further provides a unique opportunity to study the manifestation of a doped Mott state in proximity to superconducting layers. To establish a benchmark, we first examine the superconductivity of the 1H layer. The measured dI/dV spectrum shows a rather uniform superconducting gap with a U-shaped bottom (Fig. 4a, c), providing strong evidence for a nodeless gap function of the 1H layer. We note that no visible Kondo signature or Yu–Shiba–Rusinov states are found in this layer, considering that 13% of the clusters show zero-energy peaks in the 1T layer (Supplementary Note 4). When moving to the 1T layer, we find a relatively weak, electron-hole symmetric gap with a V-shaped bottom near E_F. We attribute this gap feature to superconductivity for the following reasons (see Supplementary Note 9 for details). First, this gap disappears at higher temperatures above T_C and under out-of-plane magnetic field of 2 T (Fig. 4b and Supplementary Fig. 20). Second, we observed superconducting vortices on the 1T termination with an applied magnetic field of 0.1 T, where the gap feature was strongly suppressed inside the vortex core (Supplementary Fig. 21). Third, this gap feature is mostly clear for the clusters that are significantly away from half-filling, as we will show below, differentiating it from a dip-like feature of Fano line shape (Supplementary Note 9). The superconducting gap on the 1T layer has rarely been reported before. Interestingly, we find that the gap size ${△}_{SC}^{1T}$ dramatically varies between SoD clusters (Fig. 4d), being largely constant inside each of them. It takes a maximum value of ${△}_{SC}^{1T}\approx 0.3\mathrm{meV}$ on clusters featuring a depleted narrow band and collapses to zero (${△}_{SC}^{1T}\approx 0$) on those showing Hubbard bands. To better visualize the overall trends, we present the tens of low-energy spectra of different clusters in Fig. 4e after sorting them by the electron-doping level (see wide-energy spectra in Supplementary Note 10). One can see that with increasing electron doping, the superconducting gap gradually decreases and finally vanishes when LHB and UHB develop, leaving behind only the sharp metallic peak at E_F. As discussed in the Brinkman–Rice scenario, the hopping of low-energy quasiparticles is strongly renormalized owing to the large energy cost of changing electron occupation. The coupling between 1T and 1H also strongly depends on this renormalization. Therefore, if the superconductivity in the 1T layer comes from the proximity effect, the superconducting gap becomes weaker when the correlation effect of the SoD clusters becomes stronger, which is consistent with our experimental findings.

Fig. 4. Superconductivity dressed by the renormalization of the 1T layer.

a Superconducting spectra for the 1T and 1H terminations at 0.1 K. b Superconducting spectra for 1T termination under different conditions, up: at 3.0 K near T_C, down: at 2T above H_c2. The red arrows mark the peak of the narrow band. c, d False color maps of the spatially resolved dI/dV spectra for the 1H termination and 1T termination, and the traces are marked by the orange (c) and green (d) arrows in the corresponding topographic images. e False color map of superconducting spectra obtained from nearly 30 clusters at the 1T termination and sorting by electron filling. The red bars in (d, e) mark the peak of the narrow band. STM setup conditions: a 1H: V_S = −1.5 mV, I_t = 1 nA, V_mod = 20 μV; 1 T: V_S = −1.5 mV, I_t = 1 nA, V_mod = 20 μV; b V_S = −10 mV, I_t = 1 nA, V_mod = 50 μV; c V_S = −1.5 mV, I_t = 1 nA, V_mod = 20 μV; d V_S = −10 mV, I_t = 1 nA, V_mod = 50 μV; e V_S = −10 mV, I_t = 1 nA, V_mod = 50 μV.

Discussion

The observation of correlation-dressed superconductivity has multiple ramifications. First, it results in a spatially inhomogeneous superconducting state in the 1T layer, and ~12% of the SoD clusters therein do not show a superconducting feature but instead exhibit a sharp zero-bias peak. Given the fully opened superconducting gap in the 1H layer (Fig. 4a, c), it is most likely that the residual density of state in the 1T layer is responsible for the signature in bulk thermal conductivity measurements⁵² (see Supplementary Note 4 for a discussion of the difference between the bulk and surface). Second, we characterized the central quasiparticle peak under external magnetic fields and found that it splits into two peaks with increasing magnetic field (Supplementary Note 11). The linear field dependence can be attributed to Zeeman splitting with a Landé factor of g ~ 2 for the localized electrons in these clusters (with ultra-small bandwidths after renormalization). Therefore, these nonsuperconducting clusters can be regarded as a unique type of paramagnetic “impurity” formed by electron correlations. These paramagnetic clusters could give rise to a negative Josephson coupling between the neighboring 1H and 1H’ layers (which are rotated 180 degrees relative to each other; Fig. 1a) when the spin-valley locking is considered⁵³: specifically, for momentum-conserved tunneling processes, the standard spin-independent tunneling amplitude could be significantly reduced owing to the opposite spin label between the H and H’ layers with spin-orbital coupling, and other spin-dependent processes can change the sign of the interlayer Josephson coupling (Supplementary Note 11). This provides a possible explanation for the unusual π phase shifts in the Little-Parks experiments^30,52. Third, the SoD clusters hosting local moments seem to exhibit spatial correlations, as they are locally arranged with a short-range order in real space (Supplementary Note 12). This suggests that although the proportion of these clusters is determined by Se substitution, their precise locations might be slightly redistributed by nonlocal Coulomb interactions^54,55. It remains to be seen whether any unconventional magnetic interactions can be established on the basis of such a spatial pattern that might be essential for the puzzling magnetic memory effect in 4Hb-TaS₂³³.

In closing, we have made use of subtle interlayer charge transfer to establish an ensemble of doped Mott insulators with a large variety of electron fillings in the 1T layer of 4Hb-TaS₂. This allows us to track the evolution of the single-particle spectral function continuously from 0.2 electrons per SoD cluster toward half-filling. Our spectroscopic data provide a systematic characterization of how a narrow band transforms into a Mott state by filling control, including the emergence of Mott–Hubbard bands and the narrowing of coherent peaks as in the famous Brinkman–Rice scenario. Remarkably, such renormalization ramifies the superconducting state of the 1T layer via locally closing the pairing gap and creating paramagnetic clusters, which sets the ground for understanding the unusual phenomena of the superconducting phase. Therefore, such vdW heterostructures provide new grounds to enrich the paradigm of doped Mott physics and represent exciting perspectives for engineering exotic quantum states.

Methods

Single crystal growth and characterization

High-quality single crystals of 4Hb-TaS₂ were prepared via the chemical vapor transport method. Appropriate amounts of Ta and S were ground and mixed with a small amount of Se (1% of the S amount). The powder was sealed in a quartz ampoule, and a small amount of iodine was added as a transport agent. The ampoule was placed in a two-zone furnace such that the powder was in the hot zone. After 30 days, single crystals with a typical size of 2.0 mm × 1.0 mm × 0.1 mm grew in the cold zone of the furnace. The chemical composition of the crystals was determined via energy dispersive X-ray spectroscopy and STM topographic images. Electrical transport measurements were carried out in a Quantum Design physical property measurement system (PPMS-14T). Electrical transport measurement in a conventional 4-lead configuration was realized by attaching four platinum wires to the (001) surface of the sample. The contacts were made with DuPont 4929 N conductor paste.

STM measurements

The STM data were acquired with a commercial CreaTec low-temperature system, and the subkelvin to 4 K studies were conducted on an Unisoku USM1300 or 1600 system. For the CreaTec low-temperature STM (Unisoku USM1300), single crystals were cleaved in situ under cryogenic ultrahigh vacuum at T ~ 30 K (T ~ 90 K) and immediately inserted into the STM head. Both Pt/Ir and tungsten tips were used in the experiments. The tungsten tips were annealed to a bright orange color in UHV, and their quality was checked on the surface of single-crystalline Au (111) prior to measurement. Spectroscopic data above 4 K were acquired using the standard lock-in technique at a frequency of 987.5 Hz under a modulation voltage of 2 mV, whereas data below 4 K were obtained using the same technique at a frequency of 987.5 Hz under a modulation voltage of 0.05–0.2 mV.

Band calculations and DMFT simulations

We employ the Vienna ab initio simulation package (VASP) code with the projector augmented wave method to perform density functional theory (DFT) calculations. The Perdew–Burke–Ernzerhof exchange-correlation functional was used in our calculations. The kinetic energy cutoff is set to 500 eV for expanding the wave functions into a plane-wave basis, and the energy convergence criterion is 10⁻⁸ eV. A Г-centered $18\times 18\times 2$ k-mesh is used in the DFT calculations. The atomic coordinates of the optimized computational models for Supplementary Fig. S5 follow those in ref. ³⁷.

After obtaining the band structure from DFT calculations, we take the band that crosses the Fermi surface as the non-interacting part of a single-band Hubbard model. In this model, the onsite interaction strength is set to 1.67 W (where W represents the bandwidth). The open-source TRIQS package is employed for DMFT calculations, and the continuous-time quantum Monte Carlo (QMC) algorithm based on hybridization-expansion (CT-HYB) is used to solve the impurity problem. To obtain the spectral function, we adopt the maximum entropy method to analytically continue the Green’s function from the Matsubara frequency axis to the real frequency axis. In addition, the numerical renormalization group (NRG) method is used as a solver for the quantum impurity model, and calculations are performed under the same model parameters as those used in CT-HYB.

In the DMFT framework, the Hubbard model is mapped onto an effective Anderson impurity model. By solving this impurity problem, one can extract key quantities such as the self-energy and Green’s function of the original lattice model. NRG and QMC are two widely used impurity solvers. The main distinction between them lies in the domain of their computations: the NRG works directly on the real-frequency axis and is well suited for zero-temperature systems, whereas the QMC works on the Matsubara frequency axis and suffers from the fermionic sign problem, which limits its applicability at very low temperatures. The results obtained via the two methods (QMC and NRG) are consistent with each other. While the two methods may differ in the fine details of the spectral function, they provide fully consistent results when it comes to key physical features such as the Mott transition, the positions of the upper/lower Hubbard band, and the presence and behavior of the quasiparticle peak. This is primarily because the QMC provides self-energy and Green’s function data on the Matsubara frequency axis, which must be analytically continued to the real-frequency axis to obtain spectral functions—a procedure that is numerically ill-posed and may introduce artifacts.

Author contributions

Zhenyu Wang and X.C. conceived the experiments and supervised this project. P.W., Zhuying Wang, and Y.Z. performed the STM experiments and data analysis with the assistance of W.M., S.Y., Y.M., Zeyu Liang, X.W., J.W., W.C., Zhuowei Liang, X.Z., and Y.O. M.S., Y.Z., and T.W. synthesized and characterized the samples. Z.C. and K.J. performed theoretical calculations. Zhenyu Wang, K.J., T.W., Y.O., and X.C. interpreted the results. Zhenyu Wang, P.W., K.J., and X.C. wrote the manuscript with input from all authors.

Peer review

Peer review information

Nature Communications thanks Viliam Vano and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

Funding

This work is supported by the National Natural Science Foundation of China (Grants No. 12488201 (X.C. and T.W.) and No. 52261135638 (Zhenyu Wang)), the Scientific Research Innovation Capability Support Project for Young Faculty (No. ZYGXQNJSKYCXNLZCXM-M25 (Zhenyu Wang)), the National Key R&D Program of the MOST of China (Grant No. 2022YFA1602600 (X.C., T.W., and Zhenyu Wang)), the Quantum Science and Technology-National Science and Technology Major Project (Grant No. 2021ZD0302802 (X.C., T.W., and Zhenyu Wang)), the HFNL Self-Deployed Project (No. ZB2025020200 (X.C., T.W., and Zhenyu Wang)) and the Systematic Fundamental Research Program Leveraging Major Scientific and Technological Infrastructure, Chinese Academy of Sciences under Contract No. JZHKYPT-2021-08 (X.C.).

Data availability

The STM data generated in this study are provided in the Supplementary Information/Source Data file. The data supporting the findings of this study are also available at 10.5281/zenodo.19949280. Additional data are available from the corresponding author upon request. Source data are provided with this paper.

Code availability

The code used for STM data analysis is available from the corresponding author upon request.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s41467-026-75274-4.