Dynamic twisting and imaging of moiré crystals

Abstract

Moiré superlattices in stacked two-dimensional crystals are powerful platforms for engineering correlated and topological quantum phases, with twisted graphene and transition metal dichalcogenides as prominent examples. Their angle-sensitive band structures enable rich tunability; however, conventional tear-and-stack methods fix the angle at assembly, limiting systematic exploration of angle-dependent phenomena. Here, we present a scanning probe–based manipulation scheme that enables in situ, continuous postfabrication twist control using nanostructured metal rotors. We demonstrate reproducible angle tuning and direct moiré imaging across three platforms: graphene, hexagonal boron nitride, and encapsulated, air-sensitive MoTe₂. Quantitative piezoresponse force microscopy analysis confirms subdegree precision with minimal induced heterostrain, preserving sample quality even in the marginally twisted regime. Crucially, the device architecture maintains open access to the active region, allowing optical, scanning probe, and transport measurements. This work enables single-device mapping of the angular phase diagram of moiré material including the minimally twisted regime.

A technique achieves high-resolution angular rotation and imaging of moiré superlattices formed by two atomically thin layers.

INTRODUCTION

The electronic structure of van der Waals moiré heterostructures is exceptionally sensitive to the relative crystallographic alignment of their constituent atomic layers. Small interlayer rotations generate long-wavelength moiré potentials that reshape band dispersion and topology, enabling interaction-driven ground states across a broad range of material platforms (1–7). In twisted bilayer graphene (TBG), narrow bands near the “magic angle” host correlated insulators, unconventional superconductivity, and quantum anomalous Hall states (3, 8–10). Beyond graphene, moiré phenomena have been observed in twisted transition metal dichalcogenides (tTMDs), whose strong spin-orbit coupling, broken inversion symmetry, and valley-contrasting physics support correlated and topological phases over a wide span of twist angles (11–15). More broadly, moiré periodicity provides a versatile design principle for applications ranging from photonic superlattices to angle-tunable electrochemical platforms (16–19). A central factor enabling such progress is the high tunability of moiré devices, whose displacement field, carrier density, and magnetic field can be adjusted postfabrication.

However, the structural parameters that most directly determine the underlying moiré Hamiltonian—such as the global twist angle, heterostrain, and disorder—are typically fixed at the time of fabrication. Conventional “tear-and-stack” fabrication permanently fixes the interlayer twist angle, forcing systematic exploration of angle space to rely on ensembles of nominally similar devices that inevitably differ in disorder, strain, and dielectric environment. These constraints consequently hinder experimental reproducibility and obscure the interpretation of intrinsic angle-dependent physics (20–23).

These practical limitations have motivated substantial experimental efforts to precisely read out and tune the geometric structure of moiré superlattices. There are two fundamental challenges that lie at the heart of any in situ twisting technology: (i) the challenge of uniform control: precisely rotating a single atomic layer relative to another in a uniform manner across the sample, and without introducing strain or other mesoscopic disorder, and (ii) the challenge of readout: high-resolution imaging of the superlattice structure in real space, which can directly resolve moiré lattice reconstruction, local twist angle variations, heterostrain fields, and domain wall networks at atomic to nanometer length scales (24–27). Because these microscopic effects greatly affect band structure, real-space superlattice characterization has been crucial for the development of accurate theoretical models of emergent phenomena in moiré systems (24–31).

Over the past 10 years, great strides have been made on the development of rotatable van der Waals structures (32–40), but at the cost of either uniformity or spatially resolved readout of the superlattice. For instance, nanomechanical bending was used to generate a twist angle gradient in TBG nanoribbons (38). While this indeed allowed mechanical reconfiguration, it was accompanied by large strains and twist angle disorder that strongly broke superlattice translation symmetry. A contrasting approach has achieved rotation of two independently contacted graphite or graphene devices against one another using an atomic force microscope (AFM) tip (32) or micropositoners (37). However, because the upper and lower layers are mounted onto thick substrates, the moiré superlattice at the interface cannot be directly imaged, hindering readout.

Given the sensitivity of moiré systems to the microscopic details of the superlattice, it is of critical importance to meet both requirements of uniformity and readout in the same device. This is the key objective of the present work. Here we introduce a scanning probe–based manipulation platform that enables in situ twisting and imaging of the moiré superlattice in fully fabricated devices. This approach uses a lithographically patterned windowed metal rotor rigidly coupled to the top layer and actuated by programmed lateral forces from an AFM tip, producing precise subdegree rotation with global twist angle uniformity and minimal heterostrain. The rotor platform provides five key capabilities: (i) in situ postfabrication reconfigurability, enabling repeatable, stepwise tuning of the global twist angle within a single device; (ii) control of a single atomic layer within a heterostructure; (iii) access wide twist angle regime of moiré devices with low strain and angular disorder; (iv) microscopic structural verification, enabled by an open measurement window that permits high-resolution imaging and validation of the evolving superlattice geometry after each tuning step; and (v) broad material compatibility, including homobilayers, heterobilayers, and fully encapsulated homobilayers of air-sensitive tTMDs.

We demonstrate simultaneous in situ rotation and imaging in two moiré systems of notable interest: TBG and twisted MoTe₂ (tMoTe₂). Using piezoresponse force microscopy (PFM), we image the moiré lattice before and after each actuation step and quantitatively extract the local twist-angle distribution and heterostrain. These measurements confirm successive twist-angle control with minimal induced heterostrain and low angular disorder, establishing a route to systematically explore the twist angle dependence of moiré systems with simultaneous control and characterization of the lattice geometry and quality required for meaningful comparison between experiment and theory.

RESULTS

Experimental setup

Figure 1 provides a schematic illustration of the rotor geometry and manipulation process in the TBG system. First, a heterostructure of TBG is assembled by mechanical exfoliation and dry transfer with a hexagonal boron nitride (hBN) substrate (20, 22). Next, a lithographically defined metal rotor (roughly 5 μm by 10 μm) is patterned on the top monolayer (Fig. 1A), providing rigid coupling between the rotor and the active layer. Because adhesion to the rotor far exceeds interlayer friction and van der Waals forces between the two atomic layers, the rotor and top graphene layer translate and rotate together as a single body. The rotor acts as a mechanical handle that provides structural support and transmits controlled lateral force and clamps the top layer, so that once the applied force exceeds a threshold, the top graphene layer moves relative to the bottom layer. Before manipulation, standard contact-mode AFM cleaning is performed on the rotor surface (41, 42), which effectively removes most organic residues and reduces the friction for the rotation process. During the manipulation, the sample stage is heated, to further reduce interlayer friction.

Fig. 1. Mechanical manipulation of a moiré superlattice, enabling in situ control over the twist angle.

(A) Schematic illustration of a twisted bilayer graphene rotor device and dynamic manipulation of the twist angle using an AFM tip. The metal rotor is clamped onto the top graphene layer, so that when the AFM tip pushes the rotor, the top graphene moves relative to the bottom graphene. The orange arrow indicates the induced motion of the rotor under the applied AFM force. The circular opening in the middle of the rotor provides access to the moiré superlattice for, e.g., high-resolution imaging. (B) Cross-sectional view of the tip-induced mechanical manipulation of the rotor frame during a contact-mode AFM line scan. (C) Tapping-mode AFM overlay of the rotor device before and after rotation. The red arrow shows the direction of lateral force from the AFM tip, and the orange arrow is the resulting clockwise rotation. (D) Tapping-mode AFM overlay of the rotor before and after lateral translation of the top graphene relative to the bottom graphene. The red arrow indicates the AFM tip’s lateral force direction.

Manipulation is executed with the AFM in contact mode using programmed, line-scan paths targeted to a chosen location on the rotor (Fig. 1, A and B). The rotor geometry allows for two distinct manipulation modes: a rotation mode, which applies torque to adjust the twist angle between layers, and a lateral translation mode, which induces in-plane translation without rotation. In the rotation mode, the tip scan direction is oriented to apply a longitudinal push perpendicular to the lever arm, setting both the direction and magnitude of the induced rotation. Typical vertical forces applied on the tip for initiating in situ rotation in graphene rotor devices are 600 to 2000 nN. As illustrated in Fig. 1C, placing the contact point far from the geometric center of the rotor applies a torque that controllably rotates the rotor and the attached top layer graphene. As we quantify below, this rotation changes the moiré wavelength nearly isotropically, while the rotor provides mechanical support that minimizes stretching or tearing. The relative angle change of the rotor is shown by overlaying “before/after” tapping-mode AFM images of the full frame (Fig. 1C).

Figure 1D exhibits the lateral translation mode, where near-pure translation is achieved by aligning the push direction with the contact point and the center of mass of the rotor. While AFM cleaning and heated sample stage reduce friction, there is still sliding resistance arising from interlayer friction and device topography, which prevents pure translation but remains sufficiently small to maintain predominantly translational motion. Combining these two modes, this technique allows precise and controllable changes to the relative position and angle between the two graphene layers, allowing for in situ selection of the superlattice size.

In situ rotation of TBG

We demonstrate in situ dynamic rotation of a single monolayer graphene layer within a TBG heterostructure. Applying the rotation mode manipulation as above, we achieved a series of discrete changes in the superlattice periodicity, shown in Fig. 2 (A to D). The device was tuned to four distinct twist angles: 0.1°, 0.128°, 0.558°, and 1.054°, enabling microscopic studies from the domain wall network regime to the magic-angle regime within a single device. The smallest angle increment we demonstrate is Δθ = 0.028°, achieved by moving the rotor ∼30 nm at the AFM push point (Fig. 2, A and B). The resulting twist angles can be read out with high precision using PFM (details in Materials and Methods). While the initial twist angle does not impose a fundamental constraint on the manipulation, in practice, we initialize devices at small twist angles. In this regime, the moiré wavelength is sufficiently large to be reliably resolved by PFM, enabling accurate determination of the initial angle and providing a well-defined reference for subsequent tuning. Crucially, PFM images from the same location on the heterostructure (Fig. 2, A to D) demonstrate that the rotor produces an essentially isotropic rotation of one monolayer relative to the other. This, in turn, induces an isotropic change in the superlattice period with each successive twist, up to a small error quantified below.

Fig. 2. Nanoscale tuning of the moiré superlattice via in situ rotation of TBG.

(A to D) PFM images before and after sequential AFM-driven rotations: initial θ = 0.100°; first push Δθ₁ = 0.028° (θ = 0.128°); subsequent states at θ = 0.558° and θ = 1.054°. Insets: 100 nm by 100 nm PFM images. (E to H) Theory-experiment comparison: Hexagon-averaged PFM maps (E and G) and pseudomagnetic field textures computed from fitted lattice parameters (F and H) at θ = 0.100° and θ = 0.558°.

The superlattices produced by our in situ twisting method are highly uniform, as demonstrated via direct microscopy. To resolve fine sub–unit-cell features, we average the PFM signal over many moiré unit cells to produce a hexagonal moiré unit cell (see the Supplementary Materials for details). Figure 2E shows the averaged unit cell at 0.1°, where a triangular network of domain walls emerges clearly. This observation is consistent with theoretical predictions that, at minimal twist angles, lattice relaxation drives a reconstructed state characterized by a triangular domain wall network, giving rise to quasi–one-dimensional electronic phenomena (43–46). In contrast, at 0.558° (Fig. 2G), the signal is largest near the center of the unit cell, while the domain walls appear weaker and more spatially broadened. This evolution can be attributed to the energetic preference of graphene for local AB (Bernal) stacking over AA stacking by ∼10 meV/A² (47). During lattice relaxation, AB domains expand, but must be separated by AA stacking domain walls (which may be thought of as solitons in the atomic offset) with a characteristic width of ∼5 nm (47–50). Because this width remains roughly constant, the domain walls occupy a smaller fraction of the unit cell at smaller twist angles, making the network appear sharper. However, the domain wall width becomes comparable to the moiré wavelength at larger twist angles, leading to broadened features and a less sharply defined network.

To quantitatively validate this interpretation, we compare the PFM images with lattice relaxation theory. We model the displacement of the atomic positions using a displacement vector field, r → r′ = r + u(r′), determined by standard elastic theory (47, 49, 51, 52). At a given twist angle (and heterostrain, discussed below), we solve the Euler-Lagrange equations to find u(r′), as described in the Supplementary Materials. To compare with the PFM maps, which are sensitive to the high-strain regions of the sample, we compute the strain-sensitive pseudomagnetic field $\mathcal{B}=\hat{z}\cdot \nabla \times \mathcal{A}$ with $\mathcal{A}\propto (u_{\mathit{xx}}-u_{\mathit{yy}},-2u_{\mathit{xy}})$, where $u_{\mathrm{\alpha \beta }}=({\mathrm{\partial }}_{\mathrm{\alpha }}{u}_{\mathrm{\beta }}+{\mathrm{\partial }}_{\mathrm{\beta }}{u}_{\mathrm{\alpha }})$ is the usual strain tensor. In the marginally twisted device θ = 0.100°, the domain wall features are pronounced and closely match the calculated pseudomagnetic field texture (Fig. 2, E and F). At the larger twist angle of 0.558°, the calculated real space pattern similarly reproduces the dominant features observed experimentally (Fig. 2, G and H), including the domain wall texture and the chiral asymmetric high-amplitude features inside each domain. However, some discrepancies remain between theory and experiment, including the finer features surrounding each AA site. These differences may arise from deviations between $\mathcal{B}$ and the true piezo response, suggesting the presence of additional electro-mechanical mechanism. These results demonstrate continuous, single-device access to the relaxation-driven structural crossover in TBG, with direct microscopic and quantitative verification of lattice reconstruction across the small-angle regime.

Analysis of superlattice quality: Mapping twist angle disorder and heterostrain

Figure 3 analyzes the superlattice quality across the in situ twist-angle evolution from 0.100° to 1.054° using a series of PFM images (spanning many unit cells), which provide a direct measure of superlattice quality as the twist angle is tuned. Crucially, this provides a sequence of spatially resolved “snapshots” of the heterostrain profile and twist angle disorder in the evolving superlattice—key microscopic structural quantities that determine the resulting electronic band structure. To extract these quantities, we identify each AA stacking center in the PFM data and reconstruct each moiré unit cell (Fig. 3, A and E). From the geometry of each triangle, we extract (see the Supplementary Materials) the local twist angles θ_T, shown in Fig. 3 (B and F). Beyond the twist angle, we also extract the local uniaxial heterostrain ϵ in Fig. 3 (C and G). Heterostrain is substantial because, after the twist angle, it has the largest effect on the band structure near the magic angle (53–55). For instance, the bandwidth of the narrow (“flat”) bands near the magic angle increases fivefold under a heterostrain of only ϵ ≈ 0.3% (Fig. 3, D and H).

Fig. 3. Local disorder and geometry analysis of the graphene moiré superlattice.

(A to C and E to G) Local twist angle and heterostrain maps extracted from PFM images of the moiré superlattice. (A) and (E) are PFM images of the graphene moiré superlattice at θ = 0.128° and θ = 0.558°, respectively. AA stacking sites (white dots) are used to define triangular units (grid lines), from which spatial maps of the local twist angle θ_T (B and F) and heterostrain ϵ (C and G) are extracted. (D and H) Calculated band structures near charge neutrality for θ = 1.054°, with ϵ = 0% and ϵ = 0.288%, respectively. Heterostrain lifts degeneracies and modifies the bandwidth. (I and J) Histograms of θ_T and ϵ across all four twist angle stages. The narrow spreads in both θ_T and ϵ confirm that successive manipulation preserve lattice quality with minimal added disorder. The corresponding statistics are summarized in the Supplementary Materials (table S2).

Overall, the maps and histograms in Fig. 3 show high uniformity of both θ_T and ϵ, confirming that successive manipulation preserves lattice quality with minimal added disorder. Across three successive rotations spanning the marginal-twist regime to the magic-angle regime, from θ ≈ 0.1° initially to θ ≈ 1.05° at the final stage, the twist-angle disorder remains suppressed to σ_θ < 0.033° throughout. Furthermore, as summarized in Fig. 3J, the mean heterostrain is at most ϵ ≈ 0.32% at all angles, even in the marginally twisted regime where superlattice regularity is more difficult to achieve. Notably, these disorder and strain values are approximately at the same level with devices fabricated using tear-and-stack method (26, 29–31). These quantitative results highlight the unique advantages of the rotor platform, which combines postfabrication twist angle tunability at the atomic layer level with direct access to real-space imaging for structural characterization and verification of superlattice and quality. This validation indicates that our multistep rotation protocol reliably tunes the twist angle while keeping heterostrain, twist angle disorder, and other forms of mesoscopic disorder low enough to enable superlattice physics at a chosen twist angle.

To assess reproducibility, we applied the same protocol to a second TBG device, which exhibited similar rotation-induced changes in the moiré superlattice (see fig. S6). The same device architecture and manipulation technique also operate in twisted hBN/hBN bilayers, where we demonstrate tunable ferroelectric domain structures. Representative devices and results are provided in the Supplementary Materials (see figs. S8 and S9).

In situ twisting of MoTe₂

The same in situ twisting method is easily adapted to manipulate single atomic layers in homobilayer systems beyond graphene, including air-sensitive TMDs. To demonstrate this, we realized a fully twistable, hBN-encapsulated MoTe₂ homobilayer rotor device. To protect the MoTe₂ from oxidation while preserving the rotatable structure, we introduce hBN encapsulation layers with central openings, enabling both structural protection and direct imaging of the twisted region. The detailed fabrication procedures are provided in the Supplementary Materials.

Using the same AFM-based manipulation technique developed for graphene rotors, we achieve multiple in situ twist-angle adjustments in a MoTe₂ rotor. Figure 4 (A to D) shows PFM images that track the evolution of the moiré superlattice through three rotations, during which the twist angle is step-wisely tuned from −0.559° to 0.596°. Figure 4E shows the schematics of the twisted MoTe₂ rotor. The metal rotor rigidly clamps the encapsulated top stack (hBN/MoTe₂/hBN) (fig. S12A), causing it to move as a single unit during manipulation, so that the twist is localized at the MoTe₂/MoTe₂ interface within the imaging window. Applying the same analysis methods as in the graphene case, we extract the local twist angle and uniaxial heterostrain from each PFM image (spatial maps shown fig. S11). Any hBN/MoTe₂ moiré would have a much smaller wavelength (less than 1 nm), below the spatial resolution of PFM, and thus cannot explain the observed superlattice. Histogram analysis reveals that the manipulation process introduces minimal additional twist-angle disorder (Fig. 4F), with the standard deviation slightly decreasing from 0.036° in the initial state to 0.027° after the third rotation. Similarly, heterostrain histograms across the four rotation stages show no obvious increase in strain throughout the rotation process (Fig. 4G), from 0.239% to −0.143%, indicating that the system remains structurally stable throughout the manipulation process. Our heterostrain falls within, but toward the lower bound of, the range reported in prior STM characterizations of twisted MoTe₂ devices (56, 57). To demonstrate reproducibility and the range of accessible angles, we implemented the same manipulation procedure on two additional devices, tuning each over a broad span of twist angles. Representative AFM and PFM datasets collected at each step are presented in the Supplementary Materials (figs. S12 and S13).

Fig. 4. Local disorder and geometry analysis of the MoTe₂ moiré superlattice under in situ rotation.

(A to D) PFM images of the MoTe₂ moiré superlattice before and after three successive in situ AFM manipulations. Colored overlays highlight the domain walls of the moiré unit cell. (E) Three-dimensional schematics of the MoTe₂ rotor. The encapsulation hBN protects the MoTe₂ from air, while an etched window in the middle hBN allows the two MoTe₂ layers to directly touch and form the moiré superlattice. (F and G) Histograms of the local twist angle and heterostrain across all four twist angle stages. The corresponding statistics are summarized in the Supplementary Materials (table S3).

DISCUSSION

We have presented a robust route to dynamically tune and image moiré superlattices by rotating one atomic layer relative to another in situ using a commercial AFM. This approach achieves subdegree angular control while minimizing induced heterostrain, preserving optical, transport, and scanning probe access, and enabling measurements at multiple twist angles within a single device. We demonstrate this workflow in graphene and extend it to air-sensitive TMDs, establishing a broadly applicable platform for the systematic study of angle-dependent phenomena. The current rotor geometry already provides direct access to the superlattice for optical and scanning-probe measurements. Extending this platform to transport measurements will require the integration of a rotatable top gate and compatible contact geometries, such as a Corbino configuration. We discuss these potential implementations in more detail in the Supplementary Materials (see figs. S15 and S16).

Crucially, this capability grants access to the marginal twist regime—a domain often challenging for fixed-angle assemblies. In minimally twisted graphene, lattice reconstruction and soliton networks strongly govern both local electronic structure and macroscopic response (46, 58, 59). However, heterostrain and spatial inhomogeneity often obscure flat-band physics at these small angles (26, 60). By decoupling twist angle from initial assembly and enabling iterative angle verification via real-space moiré imaging, our approach provides a concrete experimental path toward low-strain, marginally twisted devices and the controlled exploration of reconstruction-driven transport networks (24, 46).

In TMD moiré systems, continuous twist control directly targets a regime rich in strong correlations and topology. Twisted MoTe₂ bilayers, for example, exhibit electrically tunable correlated magnetism (61) and signatures of integer and fractional quantum anomalous Hall states (13, 14, 62). Given the critical role of polarization and stacking in shaping band topology (63), our platform is uniquely suited for mapping phase boundaries. It allows for the rigorous disentanglement of twist, strain, and electrostatic control within a single device, facilitating precise sweeps through the low-angle MoTe₂ parameter space (13, 61).

Looking ahead, this method extends beyond the active moiré homobilayer. In graphene-based systems, the alignment between graphene and encapsulating hBN generates minibands and fractal quantum anomalous Hall physics and generates Chern bands resulting from quantum anomalous Hall physics (5, 7), while in rhombohedral graphene, hBN alignment dictates ferroelectric and topological behaviors (64, 65). Rotating an encapsulating hBN layer in situ offers a versatile knob to tune moiré potentials and examine the evolution of ferroelectric textures under continuously adjustable orientation (64, 66). By leveraging standard nanofabrication and widely available AFM instrumentation, this technique accelerates high-precision mapping of the moiré phase space with unprecedented control over twist angle and disorder.

MATERIALS AND METHODS

Fabrication of graphene and hBN rotors

Graphene and hBN flakes were mechanically exfoliated onto Si/SiO₂ substrates with a 285-nm thermal oxide using the Scotch tape method. Candidate flakes were identified by optical contrast. Heterostructures were assembled by a dry-transfer process using a polycarbonate/polypropylene carbonate film on a polydimethylsiloxane stamp. Flakes were cut using an AFM tip and then sequentially picked up and released onto target substrates. After release, polymer residue was removed by chloroform soak followed by light contact-mode AFM cleaning with a soft cantilever (spring constant ∼2 N/m) at ∼10 nN normal load. Edges of thin hBN were avoided to prevent tearing. The AFM image that we obtain during the cleaning step is also used for rotor frame design, making sure that the rotor is clamped to the desired layer.

Rotor frames (10 nm Ti + 150 nm Au) were patterned by electron-beam lithography (EBL) on ∼500 nm polymethyl methacrylate (950K A6) E-beam resist. Metals were deposited by e-beam evaporation at a base pressure ∼3 × 10⁻⁷ torr. The rotor geometry is patterned to span most of the top-layer perimeter, providing strong mechanical clamping and robust adhesion. There is a trench of approximately 300 nm in the metal rotor arm, which was introduced to improve lift-off yield after metal deposition. Less than 800 nm is left between the rotor frame and the flake edge to prevent metal deposition onto the bottom layer, which could otherwise pin and immobilize the top layer. Surrounding the bottom layer flake, metal is deposited along the edges to pin down the bottom layer flake. A final light contact-mode AFM clean removes lithography residuals. This architecture was used for graphene and for double-layer hBN rotor devices.

Fabrication of MoTe₂ rotors

High-purity MoTe₂ (from HQ Graphene) was exfoliated onto Si/SiO₂ (285 nm oxide). Monolayers were identified by optical contrast. All MoTe₂ handling and assembly were performed in a nitrogen glovebox (O₂, H₂O < 0.1 parts per million). Where needed, AFM tip cutting was used to define paired MoTe₂ regions for stacking.

A three-dimensional schematic illustration of the rotor device structure is presented in Fig. 4E, which is composed of three parts. The bottom part consists of a graphite flake overlaid with a boron nitride flake that serves as both the structural foundation and an electrostatic gate. The middle part is a TMD monolayer flake, encapsulated by a boron nitride layer that has a 5 × 5 μm square-shaped opening created by reactive ion etching. The top part of the device comprises another TMD monolayer flake, which is encapsulated by two boron nitride flakes from the bottom and top. For this top part, there is a 3 μm by 3 μm opening on the bottom boron nitride flake, which enables effective contact between the central areas of the top and bottom TMD flakes through the aligned apertures. During the manipulation process, friction occurs between two hBN layers with etched windows. As reported in previous studies, the friction coefficient between angle-stacked hBN layers is predicted to be extremely low (67, 68), which facilitates the rotation of the entire top structure. Assembly of the device involves two sequential dry transfer steps. In the first step, the graphite back gate and the hBN base structure are transferred and deposited on a silicon substrate. Extensive AFM contact-mode cleaning is performed on this bottom part to ensure a clean and smooth surface for rotation. Following this, the rest of the structure is stacked, aligned, and deposited onto the base structure. After the heterostructure is made, a Ti/Au metal frame is deposited on top of the heterostructure using EBL. This metal frame is in contact with both hBN flakes that encapsulate the top TMD flake, which secures the relative positions of the top three layers and provides rigid structural support, allowing the hBN/TMD/hBN heterostructure to rotate as an integrated unit while minimizing strain induced by external force (labeled using dashed box in fig. S12A).

PFM imaging

Contact-resonance PFM (CR-PFM) was used for imaging the superlattice. The tip-sample contact resonance was identified at around 300 kHz and an AC drive (∼1.5 V) was applied at resonance. Because the hBN/MoTe₂ moiré period is <1 nm (below CR-PFM resolution), the observed contrast originates from the twisted MoTe₂ superlattice. Imaging of MoTe₂ rotors is performed in an ambient environment. In practice, imaging was typically performed near the center of the rotor window, where the superlattice is generally homogeneous. By contrast, regions closer to the metal frame often exhibit larger strain and reduced homogeneity, which we attribute to strain introduced during metal deposition and to the boundary condition imposed by the rotor frame (see fig. S14). The extent of this homogeneous central region depends on the rotor geometry and the lateral size of the top stack.

Method for in situ rotation and translation

Manipulation was performed with the AFM in contact mode using programmed, high–aspect ratio (often single-line) scan paths targeted to a selected lever-arm location on the rotor. The scan direction was oriented to apply a longitudinal push approximately perpendicular to the lever arm, which sets both the sign and magnitude of the induced rotation. The push distance can be finely controlled by pausing the tip mid-line scan. For the manipulation, we used high spring constant ∼45 N/m tapping-mode tips to access higher lateral force. Typical normal loads for in situ rotation in graphene rotor devices were ∼600 to 2000 nN, with device- and tip-dependent variations. Loads up to 3500 nN were used for MoTe₂ stacks under encapsulation. At each manipulation step, tapping-mode z-height scans were used to verify movement of the rotor frame, locate the etched window where PFM measurements of twisted MoTe₂ are performed, and confirm that no flake tearing or cracking occurred. Contact resonance PFM images were then collected to quantify the twist from the moiré wavelength and its local variations. The commanded scan path and push-point radius set the coarse Δθ. The PFM-derived periodicity provided the precise Δθ used in analysis. The balance between rotation and translation is set by the push-point position: Near-pure translation was achieved by aligning the contact point with the rotor’s center of mass (Fig. 1D). To achieve the sequence of rotations featured in Fig. 2 (A to D), the sample stage was heated to 190°C, an empirically chosen operating condition used to reduce the effective actuation threshold and improve the probability of controlled interlayer sliding in our setup. This choice is motivated by prior studies showing that elevated temperature can promote thermally activated sliding and reduce effective pinning in related layered and atomic-scale friction systems (69–71). Longitudinal forces ranging from 1000 to 1500 nN were applied to the rotor frame. The smallest twist step we demonstrate is Δθ = 0.028°, achieved with a ∼30-nm push at the rotor arm (Fig. 2, A and B). The discrepancy between the projected rotation angle (Δα = 0.1°) and the twist angle change (Δθ = 0.028°) extracted from PFM images might be attributed to the deformation of the edge of the frame at the contact point, which introduces an offset to the actual travel distance of the tip. An AFM image of the rotor device used for these measurements is provided in fig. S5.

In practice, device robustness is influenced by interfacial quality and the actuation threshold required to initiate sliding. We observe occasional failure modes including rotor delamination, surface damage from repeated actuation, and tearing of the two-dimensional crystal, with cleaner interfaces enabling more reproducible manipulation over multiple cycles. These observations suggest that device performance can be further improved through optimized fabrication (e.g., surface cleaning procedures) and materials engineering (e.g., alternative metals for the rotor frame).

Supplementary Materials

This PDF file includes:

Supplementary Text

Figs. S1 to S16

Tables S1 to S3

References