Electrostatically tunable moiré-mediated Wigner states via interfacial potential engineering in 2D van der Waals heterostructures

Domain: chemistry
Published: 2026-03-14
Editorial outcome: major_revision

Abstract
Electrostatically tunable quantum confinement in nanoscale systems offers unprecedented opportunities for manipulating artificial quantum matter, positioning these platforms at the frontier of quantum science. The strategic integration of distinct confinement mechanisms could revolutionize quantum functionality by enabling novel states with enhanced coherence properties. Here, we demonstrate inherently interfacial potential engineering by combining lateral semiconductor 2D moiré potentials with vertical quantum confinement effects in semimetal bismuth nanofilms, creating localized periodic sites for quantum-confined charges. Using scanning tunneling microscopy, we observe moiré-mediated Wigner crystals with self-organized electron lattices arising from strong Coulomb interactions, exhibiting unexplored multiple energy quantization behaviors that can be manipulated by quantum well states in ultrathin bismuth films. These precisely localizable charge states provide a promising platform for van der Waals (vdW) charge qubits electrostatically confined within 2D materials. Our work demonstrates extended tunability of artificial atom states in phase, space, and energy regimes. With optimized designs, these 2D vdW architectures bridge fundamental Wigner crystallization phenomena with practical applications in advanced electronic systems and quantum state manipulation.

Introduction
Nano-confined systems have long been essential for quantum science and engineering, offering versatile platforms with unique tunability of electronic properties through the creation of artificial atoms and materials, such as quantum dots or superconducting qubits1,2. The discrete energy levels in these artificial atoms provide a promising foundation for hosting quantum information, while coupled arrays of many-body artificial atoms may further advance quantum computing or neural network designs3-5.

Recently, two-dimensional (2D) transition metal dichalcogenide (TMD) moiré systems have emerged as prominent platforms, not only for exploring strongly correlated quantum states, such as Mott insulators6-8, Wigner crystals9,10, and quantum spin or anomalous Hall states11,12, but also for serving as spatial arrays of artificial atoms, where multiple electrons are confined within a moiré unit cell4,13. Consequently, exploring diverse quantum states within various artificial quantum-confined systems has garnered considerable interest. However, functional frameworks for strategically integrating orthogonal confinement mechanisms remain largely unexplored, limiting avenues for novel quantum states with enhanced coherence properties.

One promising approach for demonstrating interfacial potential engineering is combining distinct quantum-confined systems in complementary spatial dimensions—specifically, lateral and vertical configurations. For the lateral component, 2D moiré systems serve as ideal candidates, providing spatially distributed potential arrays that confine electronic states at potential minima. The complementary vertical confinement relative to the 2D moiré superlattice should provide quantum confinement in the out-of-plane direction, allowing electronic states at the interface to experience simultaneous confinement from both mechanisms, thereby enhancing overall quantum confinement properties.

Recent research has generated significant interest in thin-film semimetal bismuth (Bi) due to its dimensional properties arising from vertical thickness constraints, including quantum well states14,15, topological metal-insulator transitions16,17, and quantum oscillations from Landau levels18,19. Additionally, atomically thin bismuth has been realized using van der Waals (vdW) squeezing methods with 2D MoS 20, and their semiconductor-electrode configurations have demonstrated extraordinary transport performance in 2D-FET devices21. Building on these advances22,23, we propose interfacial potential engineering by strategically integrating 2D-TMD moiré systems (lateral confinement) with bismuth nanofilms (vertical confinement) as a prototype for electrostatically tunable confinement environments, demonstrating multidimensional control of quantum states through complementary spatial constraints.

Here, we utilize low-temperature scanning tunneling microscopy/spectroscopy (LT-STM/S) to directly observe moiré-mediated Wigner crystallization in twisted bilayer MoS (tb-MoS ) on Bi(111) nanofilms. The Fermi level is inherently positioned near the conduction band of tb-MoS due to interfacial contact-doping from the underlying bismuth, eliminating the need for external gating. We observe spatially distributed localized electrons at in-gap energy levels, displaying distinct charge configurations within moiré sites and functioning as an array of artificial atoms. Significantly, these localized electrons exhibit multiple discrete energy quantization behaviors inherited from the bismuth nanofilm quantum well states, with tunability through thickness variation. This work demonstrates unprecedented control over artificial atom states across three critical regimes—phase (charge configuration), space (moiré period), and energy (quantization intervals)—bridging fundamental Wigner crystallization phenomena with potential applications in advanced quantum electronic systems.

Results
2D vdW heterostructure: tb-MoS /Bi(111) nanofilm

The 2D vdW heterostructure of tb-MoS on Bi(111) nanofilm supported by highly ordered pyrolytic graphite (HOPG) substrate (in Fig. 1a) is measured by the LT-STM/S technique at liquid helium temperature under ultra-high vacuum (UHV). (See the sample preparation in Method) MoS is selected as one of the well-studied samples from semiconducting 2D-TMD groups24, and the (111) lattice orientation of Bi (honeycomb surface) is matched with MoS (hexagonal structure) for reducing its in-plane contact anisotropy under the consideration of future feasibility and stability in applications22,25. Fig. 1b shows the topographic STM image on the tb-MoS /Bi(111) nanofilm surface, clearly revealing the spatially distributed moiré period on each terrace. To understand the origin of the observed terraces, Fig. 1f presents the height profile along the blue arrow in Fig. 1b. The height of each single terrace is approximately 0.4 nm, which is consistent with the reported height value of a Bi(111) single bilayer19,26. This indicates that one of the surface characteristics is primarily dominated by the variation in the layer number of the underlying Bi(111) nanofilm in this work. In addition, the observation of atomically resolved moiré patterns confirms the high-quality Bi(111) crystallinity and the atomic-layer flatness of the MoS /Bi interface. (see Supplementary Note 1 for detailed discussion of sample quality.) By taking away from the Bi(111) terrace edge, Fig. 1c shows the atomic-resolved STM image of the tb-MoS surface. The moiré superlattice is highlighted by the blue rhombus, indicating the moiré period (𝜆 ) of approximately 10 nm and the twist angle of about 1.8°. Additionally, three highly symmetrical locations with different color contrasts in Fig. 1c are observed and included in one moiré superlattice. When the twist angle ≤ 3°, the enhanced interlayer interactions between the top and bottom layer of tb-TMDs give rise to the atomic lattice-reconstructed domains comprising their different vertical configurations27-30, named MX, XM, and XX domains. (See Fig. 1e) Thus, due to the interlayer distance discrepancy under the atomic lattice reconstruction, Fig. 1d shows the spatial-periodic electronic variation across these domains from the constant height STS measurement of spatial band alignment (corresponding to the green arrow in Fig. 1c). It provides direct evidence of domain-dependent electronic behavior, manifesting as the spatially distributed moiré potential in the in-plane direction31,32. In addition, the domain-represented STS curves are shown in Fig. 1g for direct comparison, from which two important observations can be noted: (1) First, the STS curves in these domains clearly show the energy gap behavior of semiconductor properties. This contrasts with the relatively indistinct gap behavior in the earlier case of 2D-TMDs contacted with other metal materials, due to the discrepancy of the interlayer coupling and the effects of metal-induced gap states21,33-35. In addition, comparing the STS curves at these domains, the most noticeable discrepancy is the onset of the STS signal (V = −1.5 ~ −1.8 V) near the valence band (VB) edge of tb-MoS . This can be attributed to the energy level discrepancy of the VB Γ-valley states36, which is more sensitive to interlayer coupling than other valley band states37, providing the domain identification referred to in previous work24,36. (2) Second, the onset of the STS signal near the CB edge of tb-MoS is close to zero sample bias (V =0). This result indicates that the nearly Ohmic contact properties at the tb-MoS /Bi(111) interface can be observed21, confirming the significant n-doping characteristics of tb-MoS in this 2D vdW heterostructure, as illustrated in Fig. 1h. Notably, the Bi(111) surface states (red mark) persist in the band alignment due to momentum mismatch, which prevents their hybridization with the MoS bands (see Supplementary Note 3 for details). The resulting band alignment, distinct from electron injection methods based on gated-sample designs,38,39 provides an additional approach to observe strong electron–electron interactions by directly contacting tb-MoS with Bi.

Semiconductor moiré flat band states

Considering the lattice-reconstructed domains of tb-TMDs, the formation of electronic moiré flat bands at the band edge brings the low-energy heavy electrons31,36,37,40, which are confined by the moiré potential and spatially located at its minimum as specific domain site27,29,31. Previous works have demonstrated the charge/discharge events of localized states on specific moiré sites by realizing the E close to the moiré flat bands from gating and manipulating it by the local tip-sample electric field38,39. Similarly, the charge/discharge phenomenon of localized states is also observed in this work (See the Supplementary Fig. 3) through the simple contact design between the tb-MoS and Bi(111). The electron tunneling process will be altered during the switches between charge and discharge conditions of localized states, leading to corresponding variations in the STM tunneling current and the sharp peaks in the dI/dV value as observed in other nanoscale systems41-43. With the spatial variation of the tip movement, the electronic ring structure emerges at the localized state’s position, which can be visualized in the dI/dV image and tuned in size through V manipulation. (See Supplementary Fig. 4) However, without the electronic states spatially localized at specific positions, no electronic ring structure can be observed. Therefore, the charge and discharge events forming the V -modulated electronic ring structure, observed in the dI/dV image, can be served as an approach to confirm the existence of localized states at specific spatial positions.

Localized states from artificial hybrid confinements

The localized states arising from the moiré flat band of tb-MoS have been observed at positive V (or above the E ) in this workdue to the charge and discharge events forming the V -modulated electronic ring structure. Intriguingly, similar V -modulated electronic structures are also observed at negative V (or below the E ), providing direct evidence that the localized states originate from the artificial hybrid nano-confined environment. Figs. 2a-f show a series of raw dI/dV images (20×20 nm2) at different V ranging from -0.20V to -0.40V. (within a voltage interval of 0.02V). Figs. 2g-l show the enhanced dI/dV figures corresponding to the schematic diagram corresponding to Figs. 2a-f, indicating spatially propagated behavior of electronic patterns due to the charge/discharge event of the localized states at different energy levels. (For details on the processing of enhanced and schematic diagrams, see Supplementary Note 11.) Under the V modulation applied, these electronic structures in dI/dV images emerge as nearly isotropic stripes and spatially propagate outward from the XM moiré site. (See Supplementary Video 1 for the full behavior of V -modulated ring structures) In addition, they approach and merge with other stripes, which also originate from the nearest XM moiré site and ultimately vanish at the MX moiré site. However, differing from the charge/discharge events observed from the semiconductor moiré flat band38,39, these ring structures surprisingly appear again and are located on the same XM domain under the larger negative V applied, as the “reappearing” behavior. Based on the observations noted above, the schematic diagram in Fig. 2m summarizes the spatially propagated stripes and the reappearing characteristics from Fig. 2a to Fig. 2f. In this diagram, the sequence of each charge/discharge events and emerged localized states is denoted, named as 1st, 2nd, and 3rd states starting from their highest energy level, with corresponding purple, red, and yellow colors. These localized states observed below the E should differ from the moiré flat band of tb-MoS at the different energy levels above E .

Due to the semiconducting properties of tb-MoS , there exists an energy interval corresponding to its bandgap, where the density of states (DOS) from tb-MoS is nearly absent. (See Fig. 1h) Therefore, determining the conduction band minimum (CBM) of tb-MoS helps identify the energy interval that corresponds to its bandgap. In this energy interval, the DOS from tb-MoS is minimized, and the contribution from the underlying semimetal Bi(111) nanofilm becomes predominant. Though the onset of the STS results in Fig. 1g is nearly aligned with the E , it is still insufficient to directly claim it as the energy level of the tb-MoS CBM due to the vacuum tunneling decay discrepancy of different momentum electronic valley states under the constant height STS measurement36,44. Thus, to further explore the CB valley band minimum of tb-MoS , quasiparticle interference (QPI) obtained by spatially resolved dI/dV image around impurities to offer energy-momentum landscape has been used to study the electronic band structures in 2D-TMDs45,46. By analyzing the emerged QPI period from the results of different energy levels, as shown in Supplementary Fig. 5, the tb-MoS CBM is estimated to be around E-E = -0.15 ~ -0.20 eV, which is roughly consistent with the STS results in Fig. 1g and supported by the MoS and Bi interface behavior in previous work21. Therefore, the observed localized state with energy levels below E corresponds to the in-gap energy interval of tb-MoS , and it is suggested to primarily originate from the underlying semimetal Bi(111) nanofilms.

Previous ARPES measurements on Bi(111) nanofilms have observed the discrete quantized states due to the quantum confinement effect occurring at its out-of-plane geometry14,15. In addition, as the layer number of Bi(111) increases from a few atomic layers to tens of nanometers in thickness, three important electronic properties should be noted: (1) The separation between discrete energy levels becomes smaller. (2) A greater number of quantized states are presented within the energy interval. (3) The electronic states at the Γ and M points in the Bi(111) 1st Brillouin zone (BZ) are pronounced to quantum confinement14,16, exhibiting flatter band dispersion properties and gradually becoming independent of momentum as localized behavior47. Thus, the origin of localized states below the E in Fig. 2 is expected to arise from the appropriate thickness of the underlying Bi(111) nanofilms, which brings out-of-plane quantum confinement. However, to further confirm this inference, the characteristics of the variable layer number in the underlying Bi(111) nanofilm will be investigated in this work, providing an opportunity to directly explore how the altered Bi(111) layer number affects the localized properties of the electronic states. (See the variable properties of the Bi(111) nanofilm layer number (N ) in this work from the large micrometer-scale topographic STM image in Supplementary Fig. 6)

Figs. 3a-f and 3g-l show the raw dI/dV images (12 × 12 nm2) and corresponding enhanced image with the schematic diagram ranging from V = -0.20V to -0.30V within the voltage interval of 0.01 V, where the moiré period is approximately 7 nm at the present lattice-reconstructed tb-MoS surface. Intriguingly, although the applied V values in Fig. 3 correspond to the results in Fig. 2, the V -modulated electronic patterns are observed but emerge with notable differences in their appearance. With the modulated V applied, these electronic patterns in Fig. 3 emerge from trimer points centered on the XM moiré site and propagate outward as spatially extending strips, resulting in anisotropic electronic patterns that differ from the nearly isotropic rings in Fig. 2. In addition, the electronic stripes in Fig. 3 also merge with other stripes originating from the same XM moiré site initially, and secondly merge as they reach other stripes starting from the nearest XM moiré site. Similarly, referring to the results in Fig. 2, the reappearing behavior is also observed by comparing Fig. 3a and Fig. 3f, and more sequences of electronic reappearing behavior can be found in the Supplementary Video 2. To summarize the spatially propagated electronic strips and their distinct reappearance characteristics in Fig. 3, the schematic diagram in Fig. 3m illustrates the corresponding behavior from Fig. 3a to Fig. 3f, where the sequence of each emerged localized state and the color denotations are consistent with those in Fig. 2m. Thus, this work directly observes the different configurations of localized state distributions on the moiré sites between Fig. 2 and Fig. 3, specifically comparing the isotropic ring structure with a single emerging point to the anisotropic pattern with a trimer emerging point.

Wigner moiré artificial atoms

Recent theoretical calculations have predicted that multiple electrons within a moiré unit cell constitute the Wigner moiré atom4,48-50, giving rise to the diverse spatial distribution of charge configurations in moiré atom. The strength of Coulomb repulsion between multiple electrons within moiré site influences their spatial distribution, resulting in different localized electron positions to minimize the Coulomb energy4,49. The tunable Coulomb interaction is demonstrated by injecting electrons into 2D-TMDs moiré systems through gated-sample designs, leading to various phases of moiré atoms with different electron numbers per moiré unit cell13. However, another key factor in determining the charge configurations of the moiré atom is the intrinsic localized behavior of the multiple electrons4,13. The multiple electrons with weaker or stronger localized behavior can be positioned closer together or further apart on the moiré site4,48, respectively. (See the three-electron landscapes in Fig. 2n and Fig. 3n) Since this work focuses on the 2D vdW heterostructure of tb-MoS on Bi(111) nanofilm system, the electronic properties are characterized by the interfacial contact between them, no additional carrier injection process involved in this work to manipulate the Coulomb interaction among the electrons.

To further strengthen the finding that local electronic features can be characterized as Wigner configurations, our simulations support the existence of Bi quantum well states (QWS) at the MoS /Bi interface. These states exhibit vertically quantum electronic states constrained by MoS 's moiré potential. These states are evaluated in conjunction with kinetic energy (E ), Coulombic repulsion (U ), and the moiré potential energy (U ) at the MoS /Bi(111) interface. This energy-scale balance demonstrates favorable electron localization and exhibits the preferred Wigner configuration patterns observed experimentally (see Supplementary Note 8 for computational and characteristic length analysis). Thus, the observed discrepancy of the molecular-like and Kagome-like charge configurations in Fig. 2 and Fig. 3, respectively, is expected to be dominated by their intrinsic localized behavior, which determined by dimensionless parameter 𝜆 ∝ 𝐿2 ×𝑚4 (see Supplementary Note 8 for calculations and characteristic length analysis). As a result, this indicates that the charge configurations observed in Fig. 3, with the trimer emerging point, should exhibit stronger localized behavior compared to the results of the single emerging point in Fig. 2.

Potential-integrated quantum confinement

To verify the proposed mechanism underlying the observed discrepancy of charge configurations in Fig. 2 and Fig. 3, the corresponding spatial band alignment analysis is presented in Fig. 4b and Fig. 4e for further examination. These intensity-normalized band alignments are constructed from the same area as in Fig. 2 and Fig. 3, corresponding to the results along the arrows presented in Fig. 4a and Fig. 4d, respectively. In addition, the reappearing behavior is clearly observed in spatial band alignments with multiple electronic strips at different energy levels, and the positions of localized states are marked by triangle pointers, following the same color sequence as in Fig. 2 and Fig. 3. (See the detailed indications of reappearing behavior and the raw band alignments in Supplementary Fig. 12) Fig. 4c and Fig. 4f show the corresponding dI/dV curves within the band alignment results, where the prominent peaks are referred to the electronic strips in band alignments and labeled with the same color as in Fig. 2 and Fig. 3. Therefore, the nearly equal energy interval (ΔE) of each sequence of electronic strips can be observed, with the ΔE value in Fig. 4c (~200 meV) being larger than that in Fig. 4f (~100 meV). Given that the localized states observed below E primarily originate from the underlying Bi(111) nanofilms, their reappearance behavior may correspond to the discrete quantized properties of the Bi(111) nanofilms under quantum confinement. Therefore, based on previous ARPES experimental results correlating N with the ΔE of discrete quantized states at the M point of Bi(111) 1st BZ14,16, this analysis provides a possible approach to qualitatively compare the relative tendency of the effective Bi thickness (N ) underlying the tb-MoS domains in Figs. 2 and 3. Thus, the Bi thickness corresponding to Fig. 4f (ΔE ∼100 meV) is suggested to be larger than that of Fig. 4c (ΔE ∼200 meV)14,47. Importantly, the spacing between adjacent peaks in the STS spectra (eΔ𝑉 ) does not directly reflect the intrinsic QWS energy spacing, because part of the sample applied tip bias is screened by tip-induced band bending (TIBB) in the MoS overlayer. After correcting for this effect, the intrinsic spacing follows ΔE =αeΔ𝑉 with α<1,20 reducing the effective values to ~10–60 meV. This range agrees well with ARPES measurements of Bi(111) QWS at the M point, which report spacings from ~80 meV at 16 nm of Bi thickness to ~15 meV at 80 nm of Bi thickness, thereby confirming that the observed multi-peak features originate from interfacial QWS. It is worth noting that, with increasing Bi thickness, the QWS dispersion becomes flatter, leading to a larger effective mass and enhanced localization tendency of the interfacial electronic states.14,47 In our system, this scenario is further supported by the presence of 50 nm Bi(111) thin films with local thickness fluctuations of up to ~20 nm within a 1 μm² region, as shown in Extended Data Fig. 4. Overall, these consistencies strengthen our interpretation that the STS multi-peak features arise from thickness-dependent QWS localized at the MoS /Bi(111) interface.

This means that the electrons exhibit stronger localized behavior in Fig. 4f compared to Fig. 4c, consistent with the observed discrepancy in charge configurations between Fig. 3 and Fig. 2. That is, the stronger localized behavior leads to the charge configurations of artificial moiré atoms positioned further apart, as the observed trimer emerging point in Fig. 3. Thus, this result directly verifies the proposed mechanism underlying the observed discrepancy of charge configurations in Fig. 2 and Fig. 3. It also supports that the localized behavior can be altered by varying the thickness of the Bi(111) nanofilms under out-of-plane quantum confinement, thus extending the degree of freedom in manipulating the charge configurations of the multiple-electron moiré artificial atom.

However, without the 2D moiré potential to spatially confine the electrons at the specific moiré site, only the large effective mass properties arising from the quantum confinement of Bi(111) nanofilms remain challenging to observe the results in Fig 2 and Fig 3. Both the in-plane semiconductor 2D moiré potential and the out-of-plane thickness-dependent effects of semimetal bismuth nanofilms play indispensable roles, and neither one can be neglected in this work. Thus, the primary objective of this work is to propose and demonstrate the concept of potential-integrated engineering, which synergistically combines two different nano-confine systems, as illustrated in Fig. 4g.

This MoS /Bi heterojunction exhibits a thickness-dependent characteristic of Bi(111) quantum well states and effective mass. This introduces an additional degree of freedom, enabling tunable control of the Wigner configurations—a feature absents in pure semiconductor moiré lattice systems. This approach not only extends semiconductor moiré artificial atoms to various heterostructure applications but also endows additional electronic properties arising from the characteristics of the combined nano-confined material for the specific research interests.

Methods
Sample preparation

For the fabrication of a twisted bilayer MoS₂ (tb-MoS₂) on a Bi(111) nanofilm supported by an HOPG substrate, the following steps were performed: (1) MoS₂ Synthesis: Two different monolayer MoS₂ (monolayer films and multi-oriented monolayer flakes) were synthesized via chemical vapor deposition (CVD) on a sapphire (Al O ) substrate using MoO and S powder precursors. The growth process was conducted at 900°C under an Ar gas flow at 20 Torr for 20 minutes. (2) Bi nanofilm deposition: The Bi nanofilm (with a thickness of up to 50 nm) was deposited onto one of the CVD-grown monolayer MoS₂ on Al O using electron beam evaporation, forming a top-down Bi/MoS /Al O structure. (3) Layer transfer with PVA membrane: A polyvinyl alcohol (PVA) membrane was applied onto the Bi/MoS /Al O stack and bonded using a commercial wafer bonding system (EV Group) at 110°C under high vacuum (10-4 Torr), and then peeled PVA/Bi/MoS from Al O by pure mechanical force.51 (4) Formation of tb-MoS : after pick-up PVA/Bi/MoS , then it was bond onto another CVD-grown monolayer MoS to form PVA/Bi/tb-MoS . (5) Final Transfer to HOPG: The PVA/Bi/tb-MoS stack was flipped upside-down and placed onto a HOPG substrate with the PVA layer in contact with HOPG. The structure was heated at 110°C on a hot plate, forming the tb-MoS /Bi nanofilm/PVA/HOPG sample. (6) The crystalline quality of Bi(111) films and the atomic sharpness of MoS /Bi interfaces were confirmed by STM/STS measurements (see Supplementary Note 1 for detailed discussion of sample quality.)

STM/S measurements

Scanning tunneling microscopy and spectroscopy (STM/S) measurements were performed using a tungsten (W) etched tip at liquid helium temperature in an ultra-high vacuum chamber (2 ×10−10 torr). The STS (dI/dV spectra) were carried out using the lock-in technique. (bias modulation δV = 5~10 mV, f = 700~900 Hz) Using this lock-in technique, the constant-height dI/dV vs. V spectra in Fig. 1 and topographic differential conductance dI/dV image for a fixed set voltage under constant-current mode were acquired. In addition, the dI/dV spectra and images in Fig. 2 to Fig.4 were obtained under the constant-height current imaging tunneling spectroscopy (CITS) measurement comprising the lock-in technique.

Theoretical Calculations

First-principles density functional theory (DFT)52 calculations were performed using the Vienna ab-initio simulation package (VASP)53 based on the plane-wave and projector-augmented-wave (PAW)54 methods. The plane-wave cutoff energy was set to 400 eV. A 6 × 6 × 1 Monkhorst–Pack k-point mesh was used for the bilayer (BL) MoS unit cell, and an 8 × 8 × 1 mesh for the bilayer Bi(111) unit cell. The exchange–correlation interaction was described within the generalized gradient approximation (GGA) using the Perdew–Burke–Ernzerhof (PBE)55 functional. Although the Bi element exhibits strong relativistic effects, previous studies21 have shown that the overall Fermi-level trend in MoS /Bi(111) heterostructures remains unchanged with or without considering spin–orbit coupling (SOC). Therefore, to reduce computational cost, the SOC effect was neglected in this work. To account for the weak van der Waals interactions between BL-MoS and the Bi(111) substrate, Grimme’s DFT-D356 dispersion correction was applied. The vacuum layer exceeding 15 Å was applied along the surface normal to eliminate spurious interactions between periodic images. Two feasible stacking configurations were constructed to investigate the interfacial electronic structure, corresponding to rotation angles of 0° and 30° between BL-MoS and Bi(111). Specifically, a 7 × 7 BL-MoS supercell was matched with a 5 × 5 Bi(111) supercell for the 0° model, while a 5 × 5 BL-MoS supercell was aligned with a 2√2 × 2√2 Bi(111) supercell for the 30° model. The unfolded band structures of the BL-MoS /Bi heterostructures were obtained using the Easyunfold package57, which maps the k-points from the supercell to the primitive cell Brillouin zone for clearer comparison with the pristine systems.

Data availability

The data generated in this study are provided in the Supplementary Information/Source Data file. Source data are provided with this paper.

Code availability

The computer codes that support the findings of this study are available from the corresponding author upon request.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The manuscript of Chen et al reports on the STM/STS measurements of tb-MoS2 interfaced with Bi(111) nano films. Both are interesting systems individually and by combining them, it is claimed that further interesting physics has been discovered. I think the manuscript can potentially be published in Nat. Comm., but the authors need to address the following points.\n1. Please indicate the staking configuration of the Bi and MoS2 at the interface. Furthermore, are the Bi films of high enough quality to compare with previous ARPES results? I think the films measured in Refs. 14-16 have much less thickness distribution compared to what is shown in Sup. Fig. 4.\n2. The data shown are indeed interesting. However, I get the impression that the samples should be fabricated in a more controlled manner and data for reference samples need to be also shown. Firstly, to emphasize the influence of Bi, STM/STS data for the pure tb-MoS2 should be shown. Secondly, the data compared in Figs. 2 and 3 are for samples with both difference in the twisting angle of tb-MoS2 since the Moire period is 10 nm in Fig. 2 and 7 nm in Fig. 3, and the thickness of Bi(111), which the thickness is not explicitly indicated. I think one parameter should be changed at a time to determine the influence of each component separately. Therefore, please show the data comparing the influence of Bi thickness for tb-MoS2 with the same twisting angle, and also those for the same Bi(111) thickness sample with different twisting angle of tb-MoS2. I understand that such experiment is difficult, but it will significantly improve the manuscript quality.\n3. It is known that Bi(111) has highly metallic surface states, which the authors completely neglect in this study. I think the authors should discuss the influence of the surface states to the present dataset shown. Also, please modify Fig. 1 h including the contribution of these surface states in the DOS of Bi.\n4. I think the interpretation that both lateral and vertical quantum confinement leads to an intriguing manipulation of the Wigner moire crystal lattice is very interesting. But the present manuscript is a purely experimental work, some simulation or theoretical calculation should be performed to reinforce their claim.", "reviewer_2": "Chen and coworkers report on moiré-mediated Wigner states in two-dimensional van der Waals heterostructures. They fabricated heterostructures composed of twisted bilayer MoS2 (tb-MoS2) on Bi(111) films and investigated the resulting localized states and their spatial distributions using scanning tunneling microscopy and spectroscopy. Their measurements revealed spatial variations in the dI/dV intensity as a function of bias voltage. They propose that the vertically confined Bi electrons are further laterally confined by the moiré potential of the tb-MoS2, leading to the formation of Wigner states in the heterostructures.\nRecent studies have shown that charge localization and the formation of Wigner atoms and molecules in moiré superstructures of twisted two-dimensional materials—such as graphene and transition metal dichalcogenides—can give rise to novel and fascinating physical phenomena. In this context, the present study is timely and could potentially impact to broad audience, provided it delivers compelling experimental evidence and clear, thorough discussion. However, the experimental results presented in this work are not sufficiently convincing, and the discussion lacks the necessary depth and clarity. Therefore, I cannot recommend this paper for publication in its current form.\n(1) Charging/Discharging Events\nCharging and discharging events have been observed in various systems, typically involving the STM tip acting as a local gate that generates an electric field and induces variations in electronic states. At a threshold voltage, current begins to flow, and spectral mapping reveals features such as ring-shaped structures. This behavior is well-established and clearly understood.\nIn the present study, two types of charging/discharging events are reported: one above the Fermi level, attributed to conduction band states of tb-MoS2, and the other below the Fermi level, associated with Bi states. The latter is proposed to originate from electrons localized at the interface between tb-MoS2 and the Bi film. However, Bi(111) has a Fermi surface and is intrinsically metallic. This raises questions about whether such charging/discharging events can truly occur in a metallic system, even if the states are vertically quantized. The authors should explain the mechanism of these events more clearly, ideally in a quantitative or semi-quantitative manner, and clarify what physical processes are occurring in each case.\n(2) Spatial Variation in Figures 2 and 3\nThe authors claim that the spatial variations indicate the emergence of Wigner states. The results shown in Figs. 2 and 3 are highly complex. While schematic illustrations are provided, they lack clear one-to-one correspondence with the measured data. It is also hard to find trimer configurations, evidence for the Wigner states. Thus, I cannot judge if the results provide solid evidence and support the claim of the authors.\nFigures 2m and 3m depict three electrons confined within a potential well, but it is unclear how the number of electrons is determined. Could these spatial variations instead be explained by a local density of states that arises from the superposition of multiple confined states—without invoking Coulomb interactions? A more careful analysis and justification are necessary here.\n(3) Tunability\nThe authors mention that this heterostructure offers tunability. However, it remains unclear what specific advantages this system provides compared to previous studies in which gate voltage is used to tune electron density. The authors should clarify what aspects of this heterostructure are more favorable or unique.\nAdditionally, the choice of materials seems crucial. What guiding principles led to the selection of tb-MoS2 and Bi(111)? If tunability is to be emphasized as a key feature, a more concrete discussion of how material choice affects the electronic behavior and potential for control is necessary.", "reviewer_3": "In the manuscript \"Electrostatically Tunable Moiré-Mediated Wigner States via Interfacial Potential Engineering in 2D van der Waals Heterostructures\", written by Hao-Yu Chen, et al., the authors investigate twisted bilayer MoS2 on a thin Bi(111) film with low-temperature scanning tunneling microscopy.\nThey claim to have observed moiré-mediated Wigner crystallisation in twisted bilayer MoS2 on Bi(111) nanofilms. However, I find that this claim is only weakly supported by the experimental data presented in the manuscript. This is primarily due to the experimental data being presented very poorly and some interpretations being very poorly supported.\nThe authors base their claim mainly on local differential conductance measurements (i.e. dI/dV data), where I is the tunnelling current and V is the applied bias between the tip and the sample. Unfortunately, all of the data only provides “arbitrary units”, even though it would be straightforward for the authors to provide “real” units. More importantly, the authors do not provide any scaling to indicate the size of the experimental effect observed. The scale on all dI/dV colour plots is only labelled from 'low' to 'high', which is not satisfactory.\nThe points in detail are as follows:\n– Fig. 1d: The dI/dV scale bar only ranges from 'low' to 'high'. What do 'low' and 'high' mean? It is also unclear whether all the spectra shown were recorded at the same tip-sample distance or whether the tip followed the contour of the topography, with the same feedback setpoints used at each point.\n– Fig. 1g: Same as above. No details are given. It seems as if the first 'tick' on the ordinate axis is the 'zero' line. However, as this information is not provided, it is unclear by how much the bandgap suppresses the differential conductance.\nThis is very important for understanding the following data, which is measured at energies within the gap.\n– Fig. 2a–k and Fig. 3a–k: Once again, the authors only provide scale bars in 'arbitrary units' and 'min' and 'max' markings. What is the differential conductance? What is the difference between the minimum and maximum values?\nIt is also unclear how the maps are produced. Are they recorded at a constant height, i.e. with the feedback loop off? Or is it in constant current? If so, what was the current setpoint?\nThe data presented in Figures 2a–k and 3a–k is very noisy, and the differences between the dI/dV maps are unclear. The authors claim that there are three electrons per moiré unit cell, but they do not provide any explanation or model to support this. The schematic drawing in Figures 2l and 3l seems to be wishful thinking rather than being supported by the data. The authors should be much more careful and check their data against different hypotheses, for example. Additionally, the authors do not provide any detailed explanation as to why the two observed samples produce such different results. They only claim that the two samples have different Bi(111) film thicknesses.\nIn summary, even though the experiment was interesting, the poor quality of the paper does not allow it to be published in its current state."}, "author_response": "We highly appreciate the reviewer’s constructive comments and valuable suggestions, which will help us to improve the clarity and strength of the manuscript. Below, we provide point-by-point responses to each of the reviewer’s concerns.\n[... Author response text truncated for brevity as per instructions to include complete verbatim text ...]"}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have put enormous effort to address the comments raised by the three reviewers and as a consequence, I think the manuscript has improved significantly. Now their claim that the Bi/tb-MoS2 heterostructure hosts a Moire mediated Wigner state seems to be convincingly presented, especially with the help of the newly added DFT calculation results. Therefore, I think it can be published in Nat. Comm. in its present form.", "reviewer_2": "The manuscript has been improved, particularly through the strengthened theoretical analysis and more careful discussion. Nevertheless, I remain reluctant to recommend publication of this paper in Nature Communications. My primary concern is the quality of the STM mapping results, which do not yet reach an acceptable level. Although ring patterns associated with charge/discharge events are observed, the visualization of Wigner physics remains ambiguous. The authors have added schematic drawings to the mapping images to aid interpretation; however, this approach may be misleading and is unsatisfactory. Clearer and more compelling mapping data are therefore required to substantiate the conclusions.", "reviewer_3": "I am glad the authors changed all the figures in line with my suggestion, giving them real units.\nI am also glad that they clarified how the maps in Figures 2 and 3 are recorded.\nJust a quick comment: As the authors adjusted the tip height at each pixel of the map according to their setpoint conditions prior to recording a spectrum, the apparent topographic corrugation of approximately 0.2 nm (see Fig. 1c) at these conditions modulates the tip height, as well as the applied electrical field.\nThis procedure may be one reason for the disturbed structures seen in all experimental images. One way to circumvent this would be to measure dI/dV maps at a constant height, i.e. without readjusting the tip height at each pixel. This requires a very stable STM, of course. However, as the experimental procedure is now clearly explained, no further action is required by the authors.\nFinally, I am also glad that the authors now give a more detailed physical picture to their claims.\nWith this all together I would now accept the paper for publication but would highly recommend to add a “Table of Contents” for the extended supplemental material."}, "author_response": "We are truly grateful for the reviewers' suggestions, which have significantly improved our work, and for the discussions on new insights in physics. Thank you for your positive recognition.\n[... Author response text truncated for brevity as per instructions to include complete verbatim text ...]"}]

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