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

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.

Combining distinct confinement mechanisms can enable the engineering of novel electronic states. Here, the authors integrate a moiré potential with vertical quantum confinement in a heterostructure composed of twisted bilayer MoS₂ on (111)-oriented Bi nanofilms, revealing experimental signatures of a Wigner crystal.

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 qubits^1,2. 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 designs^3–5. 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 insulators^6–8, Wigner crystals^9,10, and quantum spin or anomalous Hall states^11,12, but also for serving as spatial arrays of artificial atoms, where multiple electrons are confined within a moiré unit cell^4,13. 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 states^14,15, topological metal-insulator transitions^16,17, and quantum oscillations from Landau levels^18,19. Additionally, atomically thin bismuth has been realized using van der Waals (vdW) squeezing methods with 2D MoS₂²⁰, and their semiconductor-electrode configurations have demonstrated extraordinary transport performance in 2D-FET devices²¹. Building on these advances^22,23, 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 MoS₂ (tb-MoS₂) on Bi(111) nanofilms. The Fermi level is inherently positioned near the conduction band of tb-MoS₂ 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-MoS₂/Bi(111) nanofilm

The 2D vdW heterostructure of tb-MoS₂ 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) MoS₂ 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 MoS₂ (hexagonal structure) for reducing its in-plane contact anisotropy under the consideration of future feasibility and stability in applications^22,25. Figure 1b shows the topographic STM image on the tb-MoS₂/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 ~0.4 nm, which is consistent with the reported height value of a Bi(111) single bilayer^19,26. 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 MoS₂/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-MoS₂ surface. The moiré superlattice is highlighted by the blue rhombus, indicating the moiré period (${\lambda }_{moir\acute{\mathrm{e}}}$) of ~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 configurations^27–30, 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 direction^31,32. 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 states^21,33–35. In addition, comparing the STS curves at these domains, the most noticeable discrepancy is the onset of the STS signal (V_s $=$ $-$1.5~$-$1.8 V) near the valence band (VB) edge of tb-MoS₂. This can be attributed to the energy level discrepancy of the VB Γ-valley states³⁶, which is more sensitive to interlayer coupling than other valley band states³⁷, providing the domain identification referred to in previous work^24,36. (2) Second, the onset of the STS signal near the CB edge of tb-MoS₂ is close to zero sample bias (V_s$=$0). This result indicates that the nearly Ohmic contact properties at the tb-MoS₂/Bi(111) interface can be observed²¹, confirming the significant n-doping characteristics of tb-MoS₂ 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 MoS₂ 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-MoS₂ with Bi.

Fig. 1. STM measurement of twist bilayer MoS₂ on Bi(111) nanofilm heterostructure.

a The sample schematic diagram of twist bilayer MoS₂ on Bi(111) nanofilm supported by highly ordered pyrolytic graphite (HOPG) substrate. b The large STM image (120$\times$120 nm²) on the surface of tb-MoS₂/Bi(111) nanofilm heterostructure reveals the spatially distributed moiré period on each Bi(111) terrace. (Set point: +0.50 V, 200pA). c The atomically resolved STM image (30$\times$30 nm²) on the surface of tb-MoS₂/Bi(111) nanofilm heterostructure. (Set point: +0.50 V, 200pA) The moiré superlattice is highlighted by the blue rhombus, and the atomic lattice-reconstructed domains XX(black), XM(blue), and MX(red) are labeled. d The spatial band alignment obtained by the constant height STS measurement corresponds to the green arrow in (c). e Atomic structure of the three different lattice-reconstructed domains within a moiré unit cell, where the atoms at the top and bottom layers of tb-MoS₂ are vertically aligned with each other. f The height profile along the blue arrow in (b) reveals the height value of single Bi(111) terraces is ~0.4 nm. g The STS spectrum represents the three lattice-reconstructed domains, directly comparing electronic properties between these domains. h The schematic diagram of the density of states (DOS) for semiconductor MoS₂, semimetal Bi, and Bi surface state contact, shaded as green, blue, and red areas, respectively. The Fermi level in this system is close to the conduction band of MoS₂, consistent with the STS spectrum results in (g). (unit: nA/V = nS).

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 electrons^31,36,37,40, which are confined by the moiré potential and spatially located at its minimum as specific domain site^27,29,31. Previous works have demonstrated the charge/discharge events of localized states on specific moiré sites by realizing the E_F close to the moiré flat bands from gating and manipulating it by the local tip-sample electric field^38,39. Similarly, the charge/discharge phenomenon of localized states is also observed in this work (See the Supplementary Fig. 5) through the simple contact design between the tb-MoS₂ 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 systems^41–43. 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_s manipulation. (See Supplementary Fig. 6) 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_s-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-MoS₂ have been observed at positive V_s (or above the E_F) in this work due to the charge and discharge events forming the V_s-modulated electronic ring structure. Intriguingly, similar V_s-modulated electronic structures are also observed at negative V_s (or below the E_F), providing direct evidence that the localized states originate from the artificial hybrid nano-confined environment. Figure 2a–f shows a series of raw dI/dV images (20$\times$20 nm²) at different V_s ranging from −0.20 V to −0.40 V. (within a voltage interval of 0.04 V). Figure 2g–l shows the enhanced dI/dV figures corresponding to the schematic diagram corresponding to Fig. 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_s 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_s-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 band^38,39, these ring structures surprisingly appear again and are located on the same XM domain under the larger negative V_s 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–f. 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_F should differ from the moiré flat band of tb-MoS₂ at the different energy levels above E_F.

Fig. 2. The spatially propagated behavior of V_s-modulated isotropic electronic stripes with multiple states.

a–f The 20×20 nm² raw dI/dV images (scale bar: 5.0 nm) at the same area are measured with the same set point V_s = −0.4 V, I = 200pA. (symbolically green dots indicate Wigner source and red circle indicates charge ring in (a)) The spatially propagated behavior of electronic stripes is observed under the different V_s modulation applied due to the local tip-induced charge/discharge event of the localized states on specific moiré sites. (See Supplementary Video 1 for details). g–l The enhanced dI/dV figures aligned with the schematic diagram corresponding to (a)–(f), indicating spatially propagated behavior of electronic stripes due to the charge/discharge event of the localized states at different energy levels. m The schematic diagram summarizes the spatially propagated behavior and the reappearing characteristics of electronic stripes from (g) to (l). The sequence of multiple localized states at different energy levels is named as the 1st, 2nd, and 3rd states, starting from the highest energy level, and is represented by the colors purple, red, and yellow, respectively. n The schematic diagram illustrates an array of moiré artificial atoms with three-electron landscapes per moiré unit cell. The three electrons in the moiré artificial atom are located around the center of the potential minimum. (unit: nA/V = nS).

Due to the semiconducting properties of tb-MoS₂, there exists an energy interval corresponding to its bandgap, where the density of states (DOS) from tb-MoS₂ is nearly absent (see Fig. 1h). Therefore, determining the conduction band minimum (CBM) of tb-MoS₂ helps identify the energy interval that corresponds to its bandgap. In this energy interval, the DOS from tb-MoS₂ 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_F, it is still insufficient to directly claim it as the energy level of the tb-MoS₂ CBM due to the vacuum tunneling decay discrepancy of different momentum electronic valley states under the constant height STS measurement^36,44. Thus, to further explore the CB valley band minimum of tb-MoS₂, 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-TMDs^45,46. By analyzing the emerged QPI period from the results of different energy levels, as shown in Supplementary Fig. 7, the tb-MoS₂ CBM is estimated to be around E-E_F$=$ −0.15 ~ −0.20 eV, which is roughly consistent with the STS results in Fig. 1g and supported by the MoS₂ and Bi interface behavior in previous work²¹. Therefore, the observed localized state with energy levels below E_F corresponds to the in-gap energy interval of tb-MoS₂, 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 geometry^14,15. 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 confinement^14,16, exhibiting flatter band dispersion properties and gradually becoming independent of momentum as localized behavior⁴⁷. Thus, the origin of localized states below the E_F 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_Bi) in this work from the large micrometer-scale topographic STM image in Supplementary Fig. 8).

Figure 3a–f, g–l show the raw dI/dV images (12 × 12 nm²) and corresponding enhanced image with the schematic diagram ranging from V_s = −0.20 V to −0.30 V within the voltage interval of 0.02 V, where the moiré period is ~7 nm at the present lattice-reconstructed tb-MoS₂ surface. Intriguingly, although the applied V_s values in Fig. 3 correspond to the results in Fig. 2, the V_s -modulated electronic patterns are observed but emerge with notable differences in their appearance. With the modulated V_s 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, f, 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–f, 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 Figs. 2 and 3, specifically comparing the isotropic ring structure with a single emerging point to the anisotropic pattern with a trimer emerging point.

Fig. 3. The spatially propagated behavior of V_s-modulated anisotropic electronic stripes with multiple states.

a–f The 12 × 12 nm² raw dI/dV images (scale bar: 3.0 nm) at the same area are measured with the same set point V_s = −0.5 V, I = 400pA. (symbolically green dots indicate Wigner source and red circles indicate charge ring in (a)) The spatially propagated behavior of electronic stripes is observed under the different V_s modulation applied due to the local tip-induced charge/discharge event of the localized states on specific moiré sites. (See Supplementary Video 2 for details). g–l The enhanced dI/dV figures aligned with the schematic diagram corresponding to (a)–(f), indicating spatially propagated behavior of electronic stripes due to the charge/discharge event of the localized states at different energy levels. m The schematic diagram summarizes the spatially propagated behavior and the reappearing characteristics of electronic stripes from (g) to (l). The sequence of multiple localized states at different energy levels is named as the 1st, 2nd, and 3rd states, starting from the highest energy level, and is represented by the colors purple, red, and yellow, respectively. n The schematic diagram illustrates an array of moiré artificial atoms with three-electron landscapes per moiré unit cell. The three electrons in the moiré artificial atoms are spatially distributed farther apart from each other and from the center of the potential minimum. (unit: nA/V = nS).

Wigner moiré artificial atoms

Recent theoretical calculations have predicted that multiple electrons within a moiré unit cell constitute the Wigner moiré atom^4,48–50, 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 energy^4,49. 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 electrons^4,13. The multiple electrons with weaker or stronger localized behavior can be positioned closer together or further apart on the moiré site^4,48, respectively. (See the three-electron landscapes in Figs. 2n and 3n) Since this work focuses on the 2D vdW heterostructure of tb-MoS₂ 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 MoS₂/Bi interface. These states exhibit vertically quantum electronic states constrained by MoS₂’s moiré potential. These states are evaluated in conjunction with kinetic energy (E_k), Coulombic repulsion (U_Coulomb), and the moiré potential energy (U_moiré) at the MoS₂/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 Figs. 2 and 3, respectively, is expected to be dominated by their intrinsic localized behavior, which determined by dimensionless parameter $\lambda \propto L^{\frac{1}{2}}{\times m}_{eff}^{\frac{3}{4}}$ (see Supplementary Note 9 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 Figs. 2 and 3, the corresponding spatial band alignment analysis is presented in Fig. 4b, e for further examination. These intensity-normalized band alignments are constructed from the same area as in Figs. 2 and 3, corresponding to the results along the arrows presented in Fig. 4a, d, 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 Figs. 2 and 3 (see the detailed indications of reappearing behavior and the raw band alignments in Supplementary Fig. 12). Figure 4c, f 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 Figs. 2 and 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_F 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_Bi with the ΔE of discrete quantized states at the M point of Bi(111) 1st BZ^14,16, this analysis provides a possible approach to qualitatively compare the relative tendency of the effective Bi thickness (N_Bi) underlying the tb-MoS₂ 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 (e$\mathrm{\Delta }{V}_{\mathrm{sample}}$) does not directly reflect the intrinsic QWS energy spacing, because part of the applied tip bias is screened by tip-induced band bending (TIBB) in the MoS₂ overlayer. After correcting for this effect, the intrinsic spacing follows ΔE_LIQ = αe$\mathrm{\Delta }{V}_{sample}$ with α < 1²⁰, 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 Supplementary Fig. 8. Overall, these consistencies strengthen our interpretation that the STS multi-peak features arise from thickness-dependent QWS localized at the MoS₂/Bi(111) interface.

Fig. 4. The spatial band alignment analysis and the concept of engineering potential-integrated quantum confinement to design artificial solid.

a, d The 18$\times$18 nm² dI/dV images (scale bar: 5.0 nm) at the same area in Figs. 2 and 3, respectively. The triangular pointers indicate the positions of localized states, with the color corresponding to the sequence of the emerging localized states discussed in the main text. b, e The spatial band alignments along the white arrow in (a) and (d), revealing the spatially propagated behavior of multiple electronic strips. The triangular pointers indicate the emergence of localized states, corresponding to the same labels in (a) and (d). c, f The representative dI/dV curves from spatial band alignment in (b) and (e) with the corresponding position, revealing the multiple peaks with the nearly equal energy interval $\mathrm{\Delta }$E. These prominent peaks in each dI/dV curve correspond to the multiple electronic strips and are labeled with the same color in the band alignments (b) and (e). g Illustration of the concept for potential-integrated engineering. The artificial hybrid nano-confined environment synergistically combines two different nano-confined systems: the in-plane 2D moiré potential from tb-MoS₂ and the out-of-plane quantum size effect from Bi(111) nanofilm. h, i Illustration of the multiple energy quantized arrays of moiré artificial atoms with three electrons landscape. h The manipulation of thinner Bi(111) nanofilms results in the charge configuration of moiré artificial atoms being centered on the potential minimum due to reduced localized properties. i The manipulation of thicker Bi(111) nanofilms leads to the charge configuration of moiré artificial atoms being positioned further apart from the potential minimum due to increased localized properties. (unit: nA/V = nS).

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 Figs. 2 and 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 Figs. 2 and 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 MoS₂/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.

Van der Waals heterostructures exhibit unique physical properties that render them valuable for investigating quantum confinement effects and charge quantization phenomena. In this study, scanning tunneling microscopy (STM) serves as a crucial investigative tool to control the tunability of Wigner configurations by the presence of vertically confined Bi(111) interfacial quantum well states (QWS) occur at the MoS₂/Bi(111) interface¹². Our results reveal that the tb-MoS₂/Bi(111) heterostructure hosts robust Wigner physics with interfacial QWS and electron effective mass tunable by Bi thickness. Through this interfacial potential engineering, we demonstrate strategic tunability of functional Wigner moiré atoms in phase (charge configuration), space (moiré period), and energy (quantized energy spacing). The capacity to probe interfacial electronic states and visualize quantum coupling in real space potentially contributes to advancing future quantum device technologies or van der Waals-based charge qubit architectures.

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 (Al₂O₃) substrate using MoO₃ and S powder precursors. The growth process was conducted at 900 °C under an Ar gas flow at 20 Torr for 20 min. (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 Al₂O₃ using electron beam evaporation, forming a top-down Bi/MoS₂/Al₂O₃ structure. (3) Layer transfer with PVA membrane: A polyvinyl alcohol (PVA) membrane was applied onto the Bi/MoS₂/Al₂O₃ stack and bonded using a commercial wafer bonding system (EV Group) at 110 °C under high vacuum (10^-4Torr), and then peeled PVA/Bi/MoS₂ from Al₂O₃ by pure mechanical force⁵¹. (4) Formation of tb-MoS₂: after pick-up PVA/Bi/MoS₂, then it was bond onto another CVD-grown monolayer MoS₂ to form PVA/Bi/tb-MoS₂. (5) Final Transfer to HOPG: The PVA/Bi/tb-MoS₂ 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-MoS₂/Bi nanofilm/PVA/HOPG sample. (6) The crystalline quality of Bi(111) films and the atomic sharpness of MoS₂/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 Figs. 2–4 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) MoS₂ 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 MoS₂/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-MoS₂ 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-MoS₂ and Bi(111). Specifically, a 7 × 7 BL-MoS₂ supercell was matched with a 5 × 5 Bi(111) supercell for the 0° model, while a 5 × 5 BL-MoS₂ supercell was aligned with a 2$\sqrt{2}$ × 2$\sqrt{2}$ Bi(111) supercell for the 30° model. The unfolded band structures of the BL-MoS₂/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.

Author contributions

Y.-P.C. conceived and supervised the research. H.-Y.C. and H.-C.H. discussed the experimental design. H.-Y.C., H.-C.H., J.-Y.L., and J.-Y.H. performed STM/S measurements of the tb-MoS₂ on Bi(111) nanofilm sample. H.-Y.C., H.-C.H., and H.-C.L. performed data analysis. The first-principle calculations were carried out by L.-S.L., J.-P.C. and C.-M.W. H.-Y.C., H.-C.H., Y.-F.C., Y.-R.L. and Y.-W.C. discussed the experimental results. M.-Y.L. and I.R. fabricated the tb-MoS₂, Bi(111) nanofilm, and transferred it onto the HOPG substrate. H.-Y.C. wrote the initial draft of the manuscript. All authors discussed the experimental results and provided constructive comments on the manuscript.

Peer review

Peer review information

Nature Communications thanks the anonymous reviewers for their contribution to the peer review of this work. A peer review file is available.

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.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s41467-026-70614-w.