Introduction

In a strongly correlated electronic system, Coulomb interactions among electrons dominate over kinetic energy. Recently, two-dimensional (2D) moiré superlattices of van der Waals materials have emerged as a promising platform to study correlated physics and exotic quantum phases in 2D, such as the correlated insulating states and superconductivity in graphene moiré superlattices1,2,3,4,5,6,7,8,9,10,11,12,13,14, the Mott insulator state at half band filling and various generalized Wigner crystal states at fractional fillings of the moiré superlattices based on transition metal dichalcogenides (TMDCs)15,16,17,18,19,20,21,22,23. The key to the strong correlation in these systems is the enhanced Coulomb interaction in 2D and greatly reduced kinetic energy in the flat moiré minibands. In TMDC-based moiré superlattices, the combination of large effective mass and strong moiré coupling renders the easier formation of flat bands and stronger electronic correlation, compared with graphene moiré superlattices. For example, the 0- or 60-degree angle-aligned WSe2/WS2 exhibits Mott insulating states with transition temperatures exceeding 150 K18,19, the highest among all 2D moiré systems studied so far. It also hosts various correlated insulating states at fractional fillings of the moiré lattice18,19, indicating strong and long-range electron interactions.

Meanwhile, the strong Coulomb interaction in 2D also leads to tightly bound excitons with large binding energy in TMDCs24,25,26,27. The moiré coupling in the TMDC moiré superlattices is expected to generate excitonic flat minibands28, beyond the single-particle electronic flat bands in the conduction and valence bands. Recently, the moiré excitons have been reported in the angle-aligned WSe2/WS2 heterojunction17,18, in which correlated insulating states also occur15,17,18,19. The excitonic flat band is promising for realizing topological exciton states and correlated exciton Hubbard model28,29, ushering in exciting opportunities for engineering correlated quantum states. However, there are key questions that remained to be addressed. For example, how is the moiré coupling’s extension in the out-of-plane direction? How could one systematically tune both the electronic flat bands and moiré exciton bands in the TMDCs moiré superlattice?

In this work, we investigate these questions utilizing the layer degree of freedom, inspired by the layer-layer coupling in TMDCs that leads to the abrupt direct-to-indirect bandgap transition from monolayer to bilayer TMDCs30,31. We demonstrate a general approach tuning both electronic and moiré exciton bands by increasing the layer number of WSe2 in the angle-aligned WSe2/WS2 heterojunction. As the layer number of WSe2 varies from monolayer (1 L) to bilayer (2 L) and trilayer (3 L), the optical spectra of the moiré exciton change systematically in a way that suggests the moiré coupling is highly interfacial, strongly confined at the WSe2/WS2 interface and barely affects the next neighboring WSe2 layer(s). However, the added WSe2 layer(s) could modify moiré excitons in the WSe2 layer interfacing WS2, resulting in a significant increase in the resonance energy separations between moiré excitons. This observation can be well described by a phenomenological model. Our work, to our best knowledge, reports the first sensitive tuning of moiré excitons via layer degree of freedom.

The correlated electronic structure is also sensitive to the number of layers in WSe2. The Mott insulator state at the filling of one hole per moiré unit cell (n = −1) is found to have a transition temperature decreased from 180 K in 1 L/1 L WSe2/WS2 to 120 K in 2 L/1 L WSe2/WS2 and 60 K in 3 L/1 L WSe2/WS2. The correlated states at fractional fillings (fractional charge per moiré supercell) are significantly quenched in the 3 L/1 L WSe2/WS2 heterojunction. The reduced Mott transition temperature, however, is still significantly higher than that of graphene moiré superlattices (~4 K1). Our study, therefore, also demonstrates a new knob to tune the strong electron correlation in TMDC moiré superlattices that can be further exploited for engineering new correlated quantum states.

Results and discussion

The back-gated angle-aligned WSe2/WS2 heterojunction device is schematically shown in Fig. 1a, which includes three different regions in the same device: 1 L/1 L WSe2/WS2, 2 L/1 L WSe2/WS2, and 3 L/1 L WSe2/WS2. The device was constructed through a dry pickup method described previously13 (also see Methods), and the heterojunctions are encapsulated with flakes of boron nitride (BN) and gated through few-layer graphene flake working as the back gate electrode. WSe2 and WS2 have a lattice mismatch of ~4%, resulting in a moiré superlattice with a periodicity of ~8 nm32,33 when they are angle-aligned (0- or 60-degree twisted). Having the three regions (1 L/1 L WSe2/WS2, 2 L/1 L WSe2/WS2, and 3 L/1 L WSe2/WS2) in the same device is advantageous as these three regions have the same twist angle since the WSe2 for all these three regions are from the same flake. As a result, the moiré lattice constant in these three regions are about the same, and we can compare our measurements from these different regions directly.

Fig. 1: Angle-aligned multilayer WSe2/monolayer WS2 moiré superlattice.
figure 1

a Schematic of the multilayer WSe2/monolayer WS2 heterojunction devices, with the heterojunctions encapsulated with flakes of BN on both sides. The few-layer-graphene (FLG) works as the back gate electrode. b Differential reflectance spectra of different regions at zero gate voltage. c–e are the differential reflectance spectra as a function of the gate voltage (density of carriers) at the region of 1 L/1 L, 2 L/1 L, and 3 L/1 L WSe2/WS2. All data were taken at 4.5 K.

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The 1 L/1 L WSe2/WS2 heterojunction has a type-II band alignment, with the conduction band minimum located in the WS2 layer and the valance band maximum in the WSe2 layer15. Strong moiré coupling leads to a band folding in the mini-Brillouin zone and generates moiré exciton bands32, which will split the A exciton resonance of WSe2 into three moiré exciton peaks, as demonstrated in the previous experiments17,32. Here we measure the reflectance spectra in the three different regions of the WSe2/WS2 heterojunction as a function of the gate voltage, with results shown in Fig. 1c–e. There are two major differences between the moiré exciton spectra from the 1 L/1 L WSe2/WS2 and multilayer WSe2/monolayer WS2 (2 L/1 L WSe2/WS2 or 3 L/1 L WSe2/WS2) heterojunctions. First, it is evident that near the charge-neutral region (gate voltage ~0 V), there are three moiré exciton resonances in the 1 L/1 L WSe2/WS2 region (Fig. 1c) but four in both 2 L/1 L (Fig. 1d) and 3 L/1 L (Fig. 1e) WSe2/WS2 regions. Second, the moiré exciton energy difference between the lowest and highest energy moiré excitons increases significantly in both 2 L/1 L (Fig. 1d) and 3 L/1 L (Fig. 1e) WSe2/WS2 regions. These observations are better illustrated in Fig. 1b, which plots the differential reflectance spectra at the gate voltage of 0 V for the three different regions (line cuts at zero gate voltage in Fig. 1c–e. For the 1 L/1 L WSe2/WS2 region, we observe three moiré exciton peaks at ~1.662 eV (\({X}_{{{\rm{I}}}}^{1{{{{{\rm{L}}}}}}}\)), 1.715 eV (\({X}_{{{\rm{II}}}}^{1{{{{{\rm{L}}}}}}}\)), and 1.753 eV (\({X}_{{{\rm{III}}}}^{1{{{{{\rm{L}}}}}}}\)), consistent with the previous reports32. However, in the 2 L/1 L WSe2/WS2 region, one additional exciton resonance emerges, adding up to a total of four major excitons peaked at ~1.642 eV (\({X}_{{{\rm{I}}}}^{2{{{{{\rm{L}}}}}}}\)), ~1.693 eV (\({X}_{{{\rm{IV}}}}^{2{{{{{\rm{L}}}}}}}\)), 1.728 eV (\({X}_{{{\rm{II}}}}^{2{{{{{\rm{L}}}}}}}\)), and 1.793 eV (\({X}_{{{\rm{III}}}}^{2{{{{{\rm{L}}}}}}}\)). In the 3 L/1 L WSe2/WS2 region, there are also four major exciton resonances at ~1.645 eV (\({X}_{{{\rm{I}}}}^{3{{{{{\rm{L}}}}}}}\)), ~1.677 eV (\({X}_{{{\rm{IV}}}}^{3{{{{{\rm{L}}}}}}}\)), 1.730 eV (\({X}_{{{\rm{II}}}}^{3{{{{{\rm{L}}}}}}}\)), and 1.785 eV (\({X}_{{{\rm{III}}}}^{3{{{{{\rm{L}}}}}}}\)). The largest moiré exciton energy difference, defined as the energy difference between \({X}_{{{\rm{III}}}}\) and \({X}_{{{\rm{I}}}}\), is ~90 meV for the 1 L/1 L WSe2/WS2 region but ~150 meV for 1 L/2 L WSe2/WS2 region and ~140 meV for 1 L/3 L WSe2/WS2 region, an increase of more than 50%. Similar behaviors have been observed for all the devices we have studied (details in Supplementary Note 5).

Our observations suggest that the moiré potential is highly localized at the WSe2/WS2 interface and has a limited extension along the out-of-plane direction. As a result, the moiré coupling only significantly modifies the first WSe2 layer in contact with the monolayer WS2. The newly developed exciton resonances in the 2 L/1 L and 3 L/1 L WSe2/WS2 heterojunctions (\({X}_{{{\rm{IV}}}}^{2{{{{{\rm{L}}}}}}}\) and \({X}_{{{\rm{IV}}}}^{3{{{{{\rm{L}}}}}}}\)), therefore, arise from the barely modified intralayer A exciton in the upper WSe2 layers away from the interface (also see Supplementary Note 1). Our interpretation is supported by the fact that the energies of \({X}_{{{\rm{IV}}}}^{2{{{{{\rm{L}}}}}}}\) (1.693 eV) and \({X}_{{{\rm{IV}}}}^{3{{{{{\rm{L}}}}}}}\) (1.677 eV) are close to the intralayer A exciton energy of monolayer WSe2 (~1.70 eV), and it is further corroborated by the stronger reflectance intensity from the new moiré exciton in 3 L/1 L WSe2/WS2 (\({X}_{{{\rm{IV}}}}^{3{{{{{\rm{L}}}}}}}\)) compared with that in 2 L/1 L WSe2/WS2 (\({X}_{{{\rm{IV}}}}^{2{{{{{\rm{L}}}}}}}\)). Moreover, there is a redshift in the moiré exciton resonance \( {X}_{{{\rm{I}}}}\) and blueshifts in \({X}_{{{\rm{II}}}}\) and \({X}_{{{\rm{III}}}}\) in both 2 L/1 L and 3 L/1 L WSe2/WS2 compared with those in 1 L/1 L WSe2/WS2 (Fig. 1b). And the shift of \({X}_{{{\rm{II}}}}\) and \({X}_{{{\rm{III}}}}\) is more significant in magnitude than that of \({X}_{{{\rm{I}}}}\).

Our results can be understood with a phenomenological model (details in Supplementary Note 2), considering the moiré excitons in the first WSe2 layer interacting with a exciton state in the added WSe2 layer (s) that has the resonance energy between \({X}_{{{\rm{I}}}}\) and \({X}_{{{\rm{II}}}}\). The resulting level repulsion naturally explains the redshift of \({X}_{{{\rm{I}}}}\) and blue shift of \({X}_{{{\rm{II}}}}\) and \({X}_{{{\rm{III}}}}\) in the 2 L/1 L (3 L/1 L) WSe2/WS2 compared with 1 L/1 L WSe2/WS2. To understand the phenomenological model, we propose a possible microscopic mechanism by considering the hybridization between moiré excitons and interlayer-like hybrid exciton (\({iX}\)) in multilayer WSe2/1 L WS2 (details in Supplementary Information Note 2). The hybridization can increase the energy separation between moiré excitons and is enabled by the moiré-potential-induced Umklapp scattering34,35,36. The interlayer-like hybrid exciton arises from the interlayer tunneling in multilayer WSe2 that hybridizes the valence bands in different layers37. However, it has much weaker oscillator strength than the intralayer-like hybrid exciton and cannot be resolved in the experiment. In the absence of hybridization between different excitonic states, the energy dispersion of bare intralayer A excitons in 1 L WSe2 and moiré excitons in 1 L/1 L WSe2/WS2 are shown in Fig. 2a, b, respectively. Here we fold the energy bands of A excitons into the mini-Brillouin zone to compare directly with that of moiré excitons. The bright A exciton state at the mini-Brillouin zone center (which is denoted as \(\gamma\) point as shown in the inset of Fig. 2a) is marked as \({X}_{A}\) in Fig. 2a, and the bright moiré exciton states are marked as \({X}_{{{{{{\rm{I}}}}}}}^{1{{{{{\rm{L}}}}}}}\), \({X}_{{{{{{\rm{II}}}}}}}^{1{{{{{\rm{L}}}}}}}\), and \({X}_{{{{{{\rm{III}}}}}}}^{1{{{{{\rm{L}}}}}}}\) in Fig. 2b. The optical absorption spectrum of moiré excitons in 1 L/1 L WSe2/WS2 is shown in Fig. 2c, with the three resonances corresponding to the three bright moiré exciton states. For the absorption spectrum of 2 L/1 L WSe2/Ws2 in Fig. 2d, we introduce the hybridization between moiré excitons and interlayer-like hybrid excitons (see Supplementary Information Note 2). The hybridization induces a redshift in \({X}_{{{{{{\rm{I}}}}}}}^{2{{{{{\rm{L}}}}}}}\) and blueshifts in \({X}_{{{{{{\rm{II}}}}}}}^{2{{{{{\rm{L}}}}}}}\) and \({X}_{{{{{{\rm{III}}}}}}}^{2{{{{{\rm{L}}}}}}}\) compared with those of 1 L/1 L WSe2/Ws2 in Fig. 2c. The larger shift in the magnitude of \({X}_{{{{{{\rm{II}}}}}}}^{2{{{{{\rm{L}}}}}}}\) and \({X}_{{{{{{\rm{III}}}}}}}^{2{{{{{\rm{L}}}}}}}\) indicates stronger hybridization with the interlayer-like hybrid exciton, which is consistent with the proposed mechanism (see Supplementary Information Note 2).

Fig. 2: Theoretical simulation of moiré excitons.
figure 2

a, b are the energy bands of bare intralayer A excitons in 1 L WSe2 and moiré excitons in 1 L/1 L WSe2/WS2, respectively. a The A exciton bands are folded into the mini-Brillouin zone of the moiré superlattice to compare directly with that of moiré excitons in b. Inset of a shows the schematic of the mini-Brillouin zone and the label of high symmetry points. The WSe2 bright intralayer A exciton state is marked by \({X}_{{{{{{\rm{A}}}}}}}\) in a. The three bright Moiré exciton states are marked by \({X}_{{{{{{\rm{I}}}}}}}^{1{{{{{\rm{L}}}}}}}\), \({X}_{{{{{{\rm{II}}}}}}}^{1{{{{{\rm{L}}}}}}}\), and \({X}_{{{{{{\rm{III}}}}}}}^{1{{{{{\rm{L}}}}}}}\) in b. Here, we set the energy \({E}_{{{{{{\rm{A}}}}}}}\) of \({X}_{{{{{{\rm{A}}}}}}}\) as the energy reference. c–e Optical absorption spectra in 1 L/1 L, 2 L/1 L, and 3 L/1 L WSe2/WS2. The interlayer hybridization between moiré exciton and intralayer A exciton is considered in d and e, with details elaborated in Supplementary Information Note 2.

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Moreover, the intralayer-like hybrid exciton in the second WSe2 layer leads to another resonance \({X}_{{{\rm{IV}}}}^{2{{{{{\rm{L}}}}}}}\) between \({X}_{{{\rm{I}}}}^{2{{{{{\rm{L}}}}}}}\) and \({X}_{{{\rm{II}}}}^{2{{{{{\rm{L}}}}}}}\), as shown in Fig. 2d, which is consistent with our experimental observation (Fig. 1b, d). In 3 L/1 L WSe2/WS2, additional hybrid excitons can be induced by the interlayer tunneling between valence bands in the 2nd and 3rd WSe2 layers. In this case, the additional hybrid excitons away from the WSe2/WS2 interface do not affect the moiré excitons. Therefore, the moiré excitons in 3 L/1 L WSe2/WS2 are nearly identical to those in 2 L/1 L WSe2/WS2 (Fig. 2d), also consistent with our experimental results (Fig. 1b). On the other hand, the additional hybrid excitons from upper WSe2 layers will contribute to the resonant peak \({X}_{{{{{{\rm{IV}}}}}}}^{3{{{{{\rm{L}}}}}}}\) which should be consisted of two sub-resonances. This is also consistent with our experimental data, as \({X}_{{{\rm{IV}}}}^{3{{{{{\rm{L}}}}}}}\) (Fig. 1e) is broader than \({X}_{{{\rm{IV}}}}^{2{{{{{\rm{L}}}}}}}\) (Fig. 1d). Interestingly, although these two resonances in \({X}_{{{\rm{IV}}}}^{3{{{{{\rm{L}}}}}}}\) cannot be resolved at the charge-neutral region, likely due to linewidth broadening, they can be revealed in the p-doping region (Fig. 1e). The exact mechanism will be investigated in the future.

The moiré excitons in the three regions show distinct gate dependence, which also confirms the interfacial nature of the moiré coupling in the WSe2/WS2 superlattice. Our theoretical model, which considers the interfacial nature of the moiré coupling, shows that the valence bands due to the added layers are higher in energy than the moiré electronic flat band from the WSe2/WS2 interface, as shown in Fig. 3a–c (detailed calculations in Supplementary Information Note 3). When carriers are added to the 1 L/1 L WSe2/WS2 heterostructure, they will fill the first moiré valence band in the WSe2 layer and the first moiré conduction band in the WS2 layer. The first flat moiré miniband has a strong electron correlation due to their narrow bandwidth, and at the half-filling states (one electron/hole per moiré unit cell, n = +1 or −1), Mott insulator states will occur, as demonstrated in several recent experiments15,16,17,18,19,20. The optical reflectance spectra are expected to be modulated by these correlated states. In the 1 L/1 L WSe2/WS2 region, all three excitons are modulated, with \({X}_{{{\rm{I}}}}^{1{{{{{\rm{L}}}}}}}\) being the most obvious one (Fig. 1c). In the 2 L/1 L and 3 L/1 L WSe2/WS2 regions, the excitons at the lowest energy (\({X}_{{{\rm{I}}}}^{2{{{{{\rm{L}}}}}}}\) and \({X}_{{{\rm{I}}}}^{3{{{{{\rm{L}}}}}}}\)) are also strongly modulated (Fig. 1d, e). Figure 3d–f plots the gate voltage dependence of the lowest energy moiré exciton for the three different regions (\({X}_{{{\rm{I}}}}^{1{{{{{\rm{L}}}}}}}\), \({X}_{{{\rm{I}}}}^{2{{{{{\rm{L}}}}}}}\) and \({X}_{{{\rm{I}}}}^{3{{{{{\rm{L}}}}}}}\)), which clearly shows intensity modulations at n = −1 and +1. On the other hand, the additional excitons in 2 L/1 L (\({X}_{{{\rm{IV}}}}^{2{{{{{\rm{L}}}}}}}\)) and 3 L/1 L (\({X}_{{{\rm{IV}}}}^{3{{{{{\rm{L}}}}}}}\)) WSe2/WS2 regions are barely affected by the formation of the Mott states at n = ±1 (Fig. 1d, e). These behaviors can also be explained by the interfacial nature of the moiré coupling, which confines the correlated electrons at the interface of WSe2/WS2. The modulation of the moiré excitons at the n = ±1 is likely due to the dielectric constant change and gap opening associated with the Mott insulator states. Due to the small radius of the strongly bound exciton24, only the moiré excitons in the first WSe2 layer immediately interfacing with the WS2 monolayer can sensitively detect the dielectric constant change at the interface. In the 2 L/1 L and 3 L/1 L regions, the additional excitons originated from intralayer excitons localized in the added layers, are thus barely affected.

Fig. 3: Layer dependence of the electronic flat miniband for WSe2/WS2 moiré superlattices.
figure 3

a–c are calculated electronic bandstructure of the valence band in 1 L/1 L WSe2/WS2, 2 L/1 L WSe2/WS2, 3 L/1 L WSe2/WS2, respectively (details in Supplementary Information Note 3), with the moiré flat band from the 1st layer WSe2 labeled in red. d–f are differential reflectance intensity of the lowest energy moiré exciton (\({X}_{{{\rm{I}}}}\)) as a function of the back gate voltage (carrier density) in Fig. 1c–e, respectively (vertical dashed line cuts), with the 2D color plots showing the enhanced reflectance spectra near the moiré excitons \({X}_{{{\rm{II}}}}\) and \({X}_{{{\rm{III}}}}\).

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To better investigate the tuning of the electron correlation by the layer degree of freedom, we perform microwave impedance microscopy (MIM) measurements to study the correlated insulating states in the three different heterostructure regions (Fig. 4a). MIM probes the local conductivity of the sample and has been successfully employed to reveal a rich structure of correlated insulating states in the angle-aligned 1 L/1 L WSe2/WS2 device8. In the multilayer WSe2/1 L WS2 device, we primarily focus on the features on the hole side, as the holes reside in the WSe2 layer due to the type-II alignment, and we introduce the layer degree of freedom by modulating the layer number of WSe2. At temperature T = 10 K, the MIM spectra in both 1 L/1 L and 2 L/1 L WSe2/WS2 regions show similar pronounced features at various fillings, including the Mott insulator states at n = −1, the generalized Wigner crystal states at fractional fillings of n = −1/3 & −2/3, −1/2, −1/4 & −3/4, etc. The 3 L/1 L WSe2/WS2 data show fewer and less pronounced dips: other than the Mott insulator state at n = −1, only two fractional fillings n = −1/3 and −1/2 can be resolved. There is also a small difference in the twist angle in the 3 L/1 L WSe2/WS2 region (~1.3°) compared to that in the 1 L/1 L and 2 L/1 L regions (~0.9°), which results in different gate voltage positions for these insulating states in the 3 L/1 L WSe2/WS2 region (details in method). Since the formation of the correlated insulating states at fractional fillings depends on long-range Coulomb interaction among electrons in neighboring moiré unit cells, our results suggest that the inter-site electron interaction strength is weaker in 3 L/1 L than in 1 L/1 L or 2 L/1 L WSe2/WS2. The difference in the on-site interaction, corresponding to the Mott insulator state at n = −1, can be further revealed in its temperature dependence. As shown in Fig. 4b–d, as the temperature is raised, the features at fractional fillings disappear at ~30 K in both 1 L/1 L and 2 L/1 L WSe2/WS2 regions and at ~15 K in the 3 L/1 L WSe2/WS2 region. The Mott insulator state at n = −1 survives at much higher temperatures in 1 L/1 L WSe2/WS2, persisting to above 180 K, the highest Mott transition temperature reported in all 2D moiré superlattice structures so far. In the 2 L/1 L WSe2/WS2 region, the Mott transition temperature is ~120 K, while it is much lower, ~60 K, in the 3 L/1 L region. As the correlation strength is determined by the ratio of the Coulomb interaction to the kinetic energy, the reduction of electron correlation strength from 1 L/1 L or 2 L/1 L WSe2/WS2 is likely due to the increased dielectric screening from the added WSe2, which reduces the Coulomb interaction at the interface. However, the further reduced correlation strength in the 3 L/1 L WSe2/WS2 is facilitated by the additional increase of kinetic energy, which arises from the increased bandwidth of the flat band, according to our calculation shown in Supplementary Information Fig. 2. We emphasize here that even the reduced electron correlation in the 2 L/1 L and 3 L/1 L WSe2/WS2 is still significantly stronger than that in graphene moiré systems, which has a Mott transition temperature ~4 K1. As a result, the layer degree of freedom can be utilized for engineering new correlated states.

Fig. 4: MIM measurements of correlated states in different moiré superlattices.
figure 4

a MIM spectra as a function of gate voltage for the moiré superlattice of 1 L/1 L WSe2/WS2 (green), 2 L/1 L WSe2/WS2 (orange), and 3 L/1 L WSe2/WS2 (brown) at 10 K. b–d are the temperature-dependent MIM spectra for the moiré superlattice of 1 L/1 L, 2 L/1 L, and 3 L/1 L WSe2/WS2, respectively.

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In summary, we have demonstrated a new moiré superlattice system based on multilayer TMDC heterojunctions. The added layers host additional intralayer excitons that interact with the moiré excitons residing at the moiré interface, and they can further modify the correlation strength of the correlated states. Considering the layer-valley-spin locking in TMDC38, these new TMDCs moiré superlattices provide an exciting platform to investigate emerging correlated valley and spin physics.

Methods

Heterostructure device fabrication

We use a dry pickup method20,39 to fabricate the WSe2/WS2 heterostructures. We exfoliate monolayer WS2, multilayer WSe2, graphite, and BN layers on silicon substrate with a 285 nm thermal oxide layer. For angle-aligned heterostructures, we choose exfoliated WS2 and WSe2 layers with sharp edges, whose crystal axes are further confirmed by second harmonic generation measurements. We then mount the SiO2/Si substrate on a rotational stage and clamp the glass slide with thin flakes to another three-dimensional (3D) stage. We adjust the 3D stage to control the distance between substrates and thin flakes, and we sequentially pickup different layers onto the pre-patterned Au electrodes on SiO2/Si substrates. We fine adjust the angle of the rotational stage (accuracy of 0.02°) under a microscope objective to stack the WSe2/WS2 heterojunction, ensuring a near-zero twist angle between the two flakes. The final constructed device is annealed at 130 °C for 12 hours in a vacuum chamber. The pre-patterned Au contact electrodes are fabricated through standard electron-beam lithography and e-beam evaporation processes (see Supplementary Information Fig. 3 for the optical microscope image of the device used in the main text). More sample characterization details can be found in Supplementary Note 4.

Optical spectroscopy measurements

To perform differential reflectance contrast measurement, the samples were mounted in a helium flow-controlled cryostat with a quartz optical window and electrical feedthroughs. A super-continuum laser (YSL Photonics) was used as the white light source. The laser was focused onto the sample with a ×50 objective (the typical laser spot size is ~2 μm). The reflected light was directed into a spectrograph and collected with a CCD camera (Princeton Instruments). The differential reflectance is calculated as \(\frac{\triangle R}{R}=\frac{R-{R}_{0}}{{R}_{0}}\) by using the reflectance spectrum at the highest p-doping region as the reference \({R}_{0}\).

Microwave impedance microscopy measurements

The MIM measurement is performed on a homebuilt cryogenic scanning probe microscope platform. A small microwave excitation of about 0.1 μW at a fixed frequency ~10 GHz is delivered to a chemically etched tungsten tip mounted on a quartz tuning fork. The reflected signal is analyzed to extract the demodulated output channels, MIM-Im and MIM-Re, which are proportional to the imaginary and real parts of the admittance between the tip and sample, respectively. To enhance the MIM signal quality, the tip on the tuning fork is excited to oscillate at a frequency of around 32 kHz with an amplitude of ~8 nm. The resulting oscillation amplitudes of MIM-Im and MIM-Re are then extracted using a lock-in amplifier to yield d(MIM-Im)/dz and d(MIM-Re)/dz, respectively. The d(MIM)/dz signals are free of fluctuating backgrounds, and their behavior is very similar to that of the standard MIM signals. In this paper, we simply refer to d(MIM)/dz as the MIM signal.

Estimating the twist angle

Twist angles of the moiré superlattices can be estimated by the carrier density corresponding to the correlated insulating state at n = ±1, with a bottom hBN of thickness ~52 nm and dielectric constant 3.5. The 1 L/1 L WSe2/WS2 and 2 L/1 L WSe2/WS2 regions have a similar moiré periodicity of 7.4 nm and twist angle of 0.9°. For the 3 L/1 L WSe2/WS2 region, the moiré periodicity is 6.0 nm and the twist angle is 1.3°. This difference is likely caused by a small distortion or wrinkle between WSe2 and WS2 layers.