Dynamic twisting and imaging of moiré crystals

Abstract

Moiré superlattices in stacked 2D crystals are powerful platforms for engineering correlated and topological quantum phases, with twisted graphene and transition metal dichalcogenides (TMDs) 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 post-fabrication twist control using nanostructured metal rotors. We demonstrate reproducible angle tuning and direct moiré imaging across three platforms: graphene, hBN, and encapsulated, air-sensitive MoTe2. Quantitative piezoresponse force microscopy (PFM) analysis confirms sub-degree 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 materials, including the twisted TMD homobilayers.

Figures (17)

• Figure 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, then 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.
• Figure 2: Nanoscale tuning of the moiré superlattice via in situ rotation of TBG.(A–D) PFM images before and after sequential AFM-driven rotations: initial $\theta=0.100^\circ$; first push $\Delta\theta_1=0.028^\circ$ ($\theta=0.128^\circ$); subsequent states at $\theta=0.558^\circ$ and $\theta=1.054^\circ$. Insets: $100nm\times100nm$ PFM images. (E–H) Theory–experiment comparison: Hexagon-averaged PFM maps (E,G) and Pseudomagnetic field textures computed from fitted lattice parameters (F,H) at $\theta=0.100^\circ$ and $\theta=0.558^\circ$.
• Figure 3: Local disorder and geometry analysis of the graphene moiré superlattice(A-F) Local twist angle and heterostrain maps extracted from PFM images of the moiré superlattice. Panel (A,D) are PFM images of the graphene moiré superlattice at $\theta=0.128\degree$ and $\theta=0.558\degree$, respectively. AA stacking sites (white dots) are used to define triangular units (grid lines), from which spatial maps of the local twist angle $\theta_T$ (B,E) and heterostrain $\epsilon$ (C,F) are extracted. (G-H) Histograms of $\theta_T$ and $\epsilon$ across all four twist angle stages. The narrow spreads in both $\theta_T$ and $\epsilon$ confirm that successive manipulation preserve lattice quality with minimal added disorder. (I-J) Calculated band structures near charge neutrality for $\theta=1.054\degree$, with $\epsilon=0\%$ and $\epsilon=0.288\%$ respectively. Heterostrain lifts degeneracies and modifies the bandwidth.
• Figure 4: (A-D) PFM images of the $\mathrm{MoTe_2}$ 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 $\mathrm{MoTe_2}$ rotor. The encapsulation hBN protects the $\mathrm{MoTe_2}$ from air, while an etched window in the middle hBN allows the two $\mathrm{MoTe_2}$ layers to directly touch and form the moiré superlattice. (F-G) Histograms of the local twist angle and heterostrain across all four twist angle stages.
• Figure S1: Lattice relaxation in TBG. (a) Displacement field $\boldsymbol{v}(x)$. Blue arrows are the moiré lattice vectors in the presence of heterostrain and gray are their unstrained counterparts. (b) Magnitude of the displacement field $|\boldsymbol{v}(\boldsymbol{x})|$. (c) Resulting psuedomagnetic field.