Introduction

The exploration of exotic quantum phenomena and emergent electronic states in two-dimensional (2D) materials has fueled a vibrant and rapidly advancing field in condensed matter physics1. Among these, twisted bilayer moiré systems have attracted intense interest as fertile platforms for uncovering novel electronic behavior2,3,4,5. Twist-induced moiré patterns can dramatically alter electronic properties, giving rise to remarkable phenomena such as unconventional superconductivity in magic-angle twisted bilayer graphene (MATBG)6,7, and more recently, the observation of the fractional quantum anomalous Hall effect (FQAHE) in R-stacked twisted bilayer MoTe₂ (tbMoTe₂)8,9,10,11. The FQAHE—marked by the quantization of the anomalous Hall conductance at fractional values of the elementary charge—exemplifies a topologically nontrivial phase governed by strong electron correlations12,13,14,15. Understanding the underlying band structure of tbMoTe₂ is thus crucial for unraveling the mechanisms behind this exotic state and opens new avenues for both fundamental studies and potential technological applications.

In this study, we report a direct measurement of the electronic band structure of tbMoTe₂ with a 4° twist angle (the angle when FQAHE occurs) using angle-resolved photoemission spectroscopy with sub-micrometre spatial resolution (μ-ARPES). Over the past decade, μ-ARPES has emerged as a powerful technique for probing the electronic structures of 2D materials and their heterostructures16,17,18. However, most prior studies have focused on air-stable materials, such as graphene-based devices–including MATBG19,20,21,22 – and stable transition metal dichalcogenides (TMDs)23,24,25,26,27,28. In contrast, devices based on air-sensitive materials like tbMoTe₂ are typically encapsulated with inert, stable layers such as graphene to prevent degradation. While graphene encapsulation is compatible with μ-ARPES by allowing photoelectrons to escape with ~30% efficiency through a monolayer graphene capping 29, and has been successfully applied to few-layer WTe₂30,31, it remains incompatible with transport measurements and may introduce extrinsic effects such as strong dielectric screening and charge transfer, potentially obscuring the intrinsic electronic structures that give rise to the correlated topological states of the encapsulated material. Instead, here we employ monolayer hexagonal boron nitride (hBN) to encapsulate the tbMoTe₂ device. Owing to its wide band gap (~5.9 eV) and minimal thickness (~0.3 nm), monolayer hBN enables efficient photoelectron transmission in μ-ARPES measurements while preserving the intrinsic electronic structure of tbMoTe₂.

Result

Measurement schematic and sample geometry

A schematic of the μ-ARPES setup and device configuration is shown in Fig. 1a. The tbMoTe₂ device was fabricated entirely within an inert glovebox environment, with a partially overlapping graphene flake serving as an electrical ground (see “Methods” and Fig. S1 for fabrication details). The device is fully encapsulated between a monolayer hBN top layer and a ~12 nm thick hBN bottom layer (Fig. 1a). Consistent with the optical image of the device (Fig. 1b(i)), the μ-ARPES spectral intensity integrated around the Fermi level (EF) from real-space scanning (Fig. 1b(ii)) enables clear identification of regions with distinct conductivity, including gold contacts, the SiO₂/Si substrate, and hBN flakes. A higher-resolution scan of the sample area (Fig. 1b(iv); corresponding optical image in Fig. 1b(iii)) further employs the characteristic Te-4d level photoemission signal to precisely locate the tbMoTe₂ region. The band structures of monolayer MoTe₂ and tbMoTe₂, shown in Figs. 2 and 3, were acquired at the spatial locations labeled as P1 and P2 in Fig. 1b(iv), respectively.

Fig. 1: μ-ARPES measurement and twisted bilayer MoTe2 device geometries.
Fig. 1: μ-ARPES measurement and twisted bilayer MoTe2 device geometries.The alternative text for this image may have been generated using AI.
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a Schematic of the experiment setup. The twisted bilayer (tb) MoTe2 sample (4° twist) is fully encapsulated/protected by a monolayer hexagonal boron nitride (hBN), and electronically grounded through a graphene/gold electrode. hBN/graphite backgate is also incorporated in this device (but not activated in the current study). b Real-space information of the device. (i) Optical microscope image and (ii) corresponding ARPES spectral intensity map. The shape of encapsulation monolayer hBN, graphene electrode, and hBN/graphite backgate are indicated, respectively. (iii) Zoomed-in optical microscope image of the tbMoTe2 device. Top/bottom MoTe2 layers are highlighted with orange/yellow lines, and P1/ P2 indicates the spatial position of monolayer/twisted bilayer, where the μ-ARPES experiments were performed. (iv) Photoemission intensity map from Te-4d levels (Eb = 40.4 and 41.9 eV for Te-4d5/2 and Te-4d3/2, respectively), highlighting the tbMoTe2 sample. μ-ARPES: angle-resolved photoemission spectroscopy with sub-micrometre spatial resolution.

Fig. 2: General electronic structure of monolayer and twisted bilayer MoTe2.
Fig. 2: General electronic structure of monolayer and twisted bilayer MoTe2.The alternative text for this image may have been generated using AI.
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a Volume plot of photoemission intensity for monolayer (1 L) MoTe2 and twisted bilayer (tb) MoTe2. High symmetry points Γ and K in the Brillouin Zone (BZ) are labelled. EF energy of Fermi level. b Constant energy contours of the photoemission maps at binding energies of −0.6 eV, −1.2 eV, and −1.5 eV, for 1 L MoTe2 and tb MoTe2, respectively. The BZ and Γ, and K points are overlaid. c (i) ARPES band dispersion plot and (ii) corresponding second partial derivative plot, along M−Γ−K directions. d Zoomed-in details of the band parameters (left column) and its comparison with theoretical calculation (right column). The intensity as a function of energy at both Γ (blue curve) and K (red curve) points are plotted on the side, with the band positions marked by the arrows.

Fig. 3: Direct band gap in monolayer and twisted bilayer MoTe2.
Fig. 3: Direct band gap in monolayer and twisted bilayer MoTe2.The alternative text for this image may have been generated using AI.
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a Illustration of in-situ potassium surface dosing, which introduces additional electron carriers into the sample. b Slices plot of constant energy contours of tbMoTe2 after potassium surface dosing, showing the positions of conduction bands (CB) and valence bands (VB). c (i) ARPES band dispersion plot and (ii) corresponding second partial derivative plot, along Γ−K direction of monolayer (top row) and tbMoTe2 (bottom row), after potassium surface dosing. The intensity as a function of energy is plotted on the side in (ii), where the band positions are marked by arrows. d Schematic of photoluminescence (PL) measurement and the generation of exciton. \({{{\rm{E}}}}_{g}\) band gap size, \({{{\rm{E}}}}_{b}\) exciton binding energy. However, the observed \({{{\rm{E}}}}_{g}\) in ARPES is suppressed, likely due to the free-carrier screening effect, making it comparable with the exciton energy. e PL intensity as a function of carrier density n, taken on (i) monolayer MoTe2 and (ii) tbMoTe2 devices (3.6° twist).

Genearal electronic band structure

Remarkably, photoelectrons from the underlying MoTe₂ sample can also penetrate the monolayer hBN encapsulation layer efficiently, enabling high-quality ARPES measurements. Figure 2 displays well-resolved band dispersions for both monolayer MoTe₂ and tbMoTe₂. The 3D spectral plot (Fig. 2a) and constant energy contour (Fig. 2b) reveal the overall band structure within the first Brillouin zone (BZ), with the most prominent differences observed near the Γ point. To highlight the distinctions between monolayer and twisted bilayer MoTe₂, detailed band dispersions along the M–Γ–K high-symmetry directions in the BZ are presented in Fig. 2c. At the Γ point, monolayer MoTe₂ exhibits a characteristic flat valence band top (Fig. 2c, top row). In contrast, tbMoTe₂ shows a pronounced upward shift of the valence band due to strong interlayer coupling, resulting in a dome-shaped valence band maximum (Fig. 2c, bottom row). At the K point, however, the band structures of both systems remain mostly similar, indicating small twist-induced modifications in that region of momentum space.

The different behavior at Γ and K points can be understood based on the orbital components of the bands at these two points (Fig. S2), respectively: In each constituent MoTe2 layer, the K-valley bands are contributed by orbitals with in-plane spatial extensions (Mo dxy, dx2−y2 and smaller contributions from Te px, py orbitals), which are weakly coupled between layers due to the small interlayer overlap of their wave functions; while for Γ valley, the bands are formed by Mo dz2 and Te pz orbitals, which naturally have more out-of-plane extentions and larger overlap (thus stronger interlayer coupling), similar to the situation in twisted bilayer WSe2 system23.

The high-resolution measurements further enable the extraction of key band structure parameters. As shown in Fig. 2d, the valence band maximum (VBM) is located at the K point in both monolayer and tbMoTe₂ (see Fig. S3 for its robustness). Compared to monolayer MoTe₂ (Fig. 2d, top row), the valence band near the Γ point in tbMoTe₂ (Fig. 2d, bottom row) is significantly elevated due to interlayer coupling, bringing it closer in energy to the VBM at K. The identification of the VBM at the K point is the first step towards determining the magnitude and location of the band gap in tbMoTe₂.

Probing conduction band via in-situ dosing

To locate the conduction band minimum (CBM) of both MoTe2 and tbMoTe2, we need to probe the unoccupied bands above the EF. The electrostatic-gating ARPES measurement remains technically challenging in these air-sensitive and semiconducting 2H-phase TMDs systems, mainly due to the insufficiency of one-side gating and the high metal-semiconductor contact resistance. Alternatively, we adopted the widely used in-situ alkali metal dosing in ARPES measurement, which is both more convenient and effective in visualizing the unoccupied states17. Remarkably, this method is effective even in our monolayer hBN-encapsulated device (Fig. 3a), and we observed the CBM emerging at the K point (Fig. 3b, c), with an estimated direct band gap of ~1.1 eV for both MoTe2 and tbMoTe2. On the other side, the photoluminescence (PL) experiment on a tbMoTe2 device (with top gate) also illustrates prominent signals from both exciton and trion excitations (Fig. 3d, e). These evidences unambiguously confirm the direct band gap nature of tbMoTe₂, making it a rare case in moiré system based on 2H-TMDs. This is crucial for realizing exotic emergent phenomena, such as FQAHE, related to K-valley moiré physics32,33. It is worth noting that the observed band gap in ARPES is comparable to the exciton energy in PL, but slightly less - this phenomenon can be attributed to the renormalization of the quasiparticle band gap, which has been observed in both alkali metal doping and electrostatic-gating ARPES experiments34,35. In a semiconductor, this effect is expected to occur due to the free-carrier screening effect36.

Theoretical calculation of band structure

To gain a more comprehensive understanding of the electronic structure of tbMoTe₂, we performed first-principles calculations within the framework of Kohn-Sham density functional theory (DFT). The calculated band structures for monolayer MoTe₂, R-stacked bilayer MoTe₂, and tbMoTe₂ are presented and compared in Fig. 4. For monolayer MoTe₂, the calculations reveals a direct band gap at the K point of the Brillouin zone (Fig. 4a(i)), in excellent agreement with our experimental results (Figs. 2c and 3c, and ref. 37. For both R-stacked bilayer and tbMoTe₂ (Fig. 4a(ii, iii)), the valence band maximum at the Γ point is significantly elevated, consistent with the experimental data (Figs. 2c and 3c). However, the CBM in both bilayer configurations is predicted to shift away from the K point to an off-symmetry location (denoted as Q; Fig. 4a(ii, iii)), in clear contrast to our ARPES measurements, which reveal the CBM to reside at the K point (Fig. 3c).

Fig. 4: DFT calculated band structure.
Fig. 4: DFT calculated band structure.The alternative text for this image may have been generated using AI.
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a Calculated band structure along M−Γ−K directions for (i) monolayer, (ii) R-bilayer, and (iii) twisted(3.89°)-R-bilayer MoTe2. b Calculated band structure with a biaxial strain of 1%.

The DFT calculated energy positions of K and Q valleys are sensitive to many factors, such as the choice of lattice constant and the pseudopotential used38,39, making the calculation unreliable in determining the actual band alignment. This is why the experimental result, such as the ARPES data presented above, is crucial. Nevertheless, to address this discrepancy between calculation and experiment, and also to showcase the influence of lattice parameter, we investigated the effect of potential in-plane strain on the band alignment. As illustrated in Fig. 4b, the local CBM at the Q point shifts upward relative to the K point with a biaxial strain of 1%. This behavior can be understood by considering the orbital components contributing to the conduction band. At the K point, the conduction band states are dominated by dz2, whereas at the Q valley, they have a more mixed orbital character, including dxy, dx2-y2, and some chalcogen p orbitals. As a result, the K valley is less sensitive to in-plane lattice expansion, but the Q valley shifts upwards more significantly. We found that with 1% of biaxial strain, we can align the CBM at the K point. It is worth noting, the real situation is more complex. Factors such as local strain, lattice distortion, and corrugation will need careful investigation in future works.

Discussion

The successful extraction of the electronic band structure of tbMoTe₂ within a functional device with key band parameters derived from both our μ-ARPES measurements (Fig. S4) and DFT calculations (see Table 1), represents a significant step forward in elucidating the detailed electronic structure of this system. A clear signature of moiré or flat bands at both the Γ and K points is still beyond the reach of our current resolution. Compared with the twisted bilayer WSe2 system, where the signature of moiré bands at the Γ point is evidenced in ARPES measurements23,40, spectroscopic investigation on the moiré effect of tbMoTe₂ presents more challenges. This is likely due to the higher instability of telluride compared to selenide, which not only reduces intrinsic sample/device quality but also necessitates the use of a top encapsulation layer. This results in an overall reduction of the statistics and energy resolution of the current ARPES measurement.

Table 1 Band parameters of monolayer MoTe2 and tbMoTe2, extracted from experimental results and theoretical calculations
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Looking ahead, we anticipate that future spectroscopic investigations—featuring higher energy and momentum resolution, improved statistical accuracy, and optimized device quality—will provide deeper insights into this moiré-engineered quantum system. Feasible improvements include the use of conventional high-resolution ARPES systems on larger samples to gain higher measurement throughput and better energy/momentum resolution; in situ sample fabrication method in vacuum18 to avoid both the use of encapsulation layer and air-exposure/vacuum-annealing process; the use of single crystal with improved crystal quality41, etc. Future investigation is expected to not only delineate detailed moiré band structure on a single particle level, but also the complex interplay among lattice, topology, and strong correlations, where the exotic emergent phenomena such as FQAHE originate.

In addition, this work demonstrates the technical feasibility of performing high-resolution μ-ARPES on hBN-encapsulated tbMoTe₂ devices, establishing a robust and non-invasive approach for probing the electronic structure of air-sensitive two-dimensional materials. Furthermore, the successful implementation of in-situ potassium dosing through the top hBN layer showcases a versatile and effective strategy for tuning the EF and engineering the band structure in operando, particularly in situations where electrostatic gating is either impractical or insufficient. We anticipate that the distinctive capabilities of μ-ARPES will find widespread use in investigating the microscopic mechanisms of exotic quantum phenomena in moiré systems.

Note added

During the preparation of this manuscript, we became aware of a related ARPES study on twisted MoTe242.

Methods

Sample fabrication

To fabricate the device, hBN and graphite flakes were first exfoliated onto SiO2/Si substrates and characterized using contrast-enhanced optical microscopy and atomic force microscopy (AFM). Then the bottom gate structure was fabricated using a standard poly-(bisphenol A) carbonate (PC)-based dry transfer process. A hBN flake as the bottom gate dielectric was picked up, successively followed by a graphite bottom gate electrode and melted down onto a 285 nm SiO2/Si substrate with pre-patterned Cr/Au (7/70 nm) electrodes via standard electron beam lithography. Next, MoTe2 flakes were exfoliated onto a 285 nm SiO2/Si inside a glovebox with O2 and H2O levels less than 0.1 ppm. A monolayer MoTe2 flake was cut in half using an AFM tip before the transfer to minimize strain. The tbMoTe2 heterostructure was created by picking up part of the monolayer MoTe2 with the monolayer hBN encapsulation layer, rotating the transfer stage by a desired angle, and picking up the remaining flake. A graphene flake is also picked up, partially overlapped with tbMoTe2 as a grounding electrode. The stack was then placed down on the prepared and cleaned backgate, such that the grounding graphene flake was electrically connected to the deposited contacts. The heterostructure geometry allows for full hBN encapsulation of the air-sensitive MoTe2. The stamp polymer was dissolved in anhydrous chloroform for 5 min and washed by anhydrous isopropyl alcohol inside a glovebox. The sample surface was further cleaned by an AFM (Bruker Edge) in contact mode.

Spatial- and angle-resolved photoemission spectroscopy (μ-ARPES)

Synchrotron-based μ-ARPES measurements were performed at Beamline 7.0.2 (MAESTRO) of the Advanced Light Source (ALS), USA. The samples were annealed in ultra-high vacuum at 220 °C for 3 h (stability of the twist angle see SI Fig. S5) and measured under ultra-high vacuum below 3 × 10-11 Torr. The photon energy of the incident beam is 95 eV (Fig. 2) and 70 eV (Fig. 3), and the measurement was performed at a temperature of 20 K. Data was collected using a R4000 analyser upgraded with deflectors. The incoming photon beam was focused down to 2 μm spot size by using a capillary mirror. The total energy and angle resolutions were 20 meV and 0.1°, respectively.

Optical measurement

Photoluminescence measurements were performed in reflection geometry in a home-built confocal optical microscope system. The sample was mounted in an exchange-gas cooled cryostat (attoDRY 2100) with a 9T superconducting magnet in Faraday geometry. A 632.8 nm HeNe laser was used as excitation for the photoluminescence measurements. The FWHM of the diffraction-limited excitation beam spot was ~1 µm. Photoluminescence signals were dispersed with a 600 grooves/mm diffraction grating blazed at 1 µm and detected using an LN-cooled InGaAs photodiode array (Princeton Instruments PyLoN-IR 1.7). A long pass filter was used to remove the excitation laser from the photoluminescence signal before entrance into the spectrometer.

Theoretical calculation

The lattice relaxations of the moiré superlattice were performed using the neural network (NN) potential. The NN potential was parameterized using the deep potential molecular dynamics (DPMD) method43,44. The training datasets were generated from 5000-step ab initio molecular dynamics simulations (AIMD) at 500 K for a \({6}^{\circ }\) tbMoTe2 using the VASP package45. The van der Waals corrections were included using the D2 formalism46. More details of NN potential parameterization can be found in ref. 47 The experimental lattice constant of 3.492 Å was used for the unstrained monolayer, bilayer, and twisted bilayer MoTe248. The band structures were calculated within the SIESTA package49. Optimized norm-conserving Vanderbilt pseudopotentials50, Perdew–Burke–Ernzerhof functional51, and double-zeta plus polarization basis were used. The unfolding of moiré minibands into the extended Brillouin zone is performed following the method outlined in ref. 52. To simulate ARPES spectra, a Gaussian smearing is applied to the calculated band structure presented in Fig. 4.