Moiré superlattices arise when two crystal surfaces are overlaid with a slight mismatch in angle or lattice period. At small twist angles, flexible two-dimensional layers rearrange to form regions with energetically favorable stacking, separated by dislocations. Such rearrangement alters optical, electronic, and mechanical properties. However, so far it has been observed mainly in suspended bilayers or on surfaces using scanning tunneling microscopy, atomic force microscopy, and other surface-sensitive techniques. For thick multilayer systems, where the interface is hidden inside the bulk, no direct experimental data on the rearrangement existed. This work fills that gap by using multislice electron ptychography to reconstruct the three-dimensional atomic structure of a buried interface.
Samples were prepared by mechanical transfer of MoS2 and WS2 crystals, 12–18 atomic layers thick, with a designed twist angle of about 1–2 degrees. To minimize contamination, silicon nitride cantilevers with lithographically patterned windows were used. Ptychography data were acquired on a transmission electron microscope at an accelerating voltage of 80 kV, scanning a defocused convergent beam across the sample and recording diffraction patterns at each point. An iterative multislice ptychography algorithm, ePIE, was then applied with a slice thickness corresponding to two or three MoS2 layers (1.23–1.84 nm). This allowed reconstruction of phase slices at different depths and tracking the positions of more than 40,000 atomic columns with a precision of 3 pm. For comparison, a theoretical model was built that accounts for adhesion energy between layers and elastic strain energy.
At the interface between two MoS2 crystals twisted by 1.23°, a pronounced rearrangement was observed: extended domains with ideal MX' and XM' stacking formed, separated by partial dislocations. Away from the interface, the lattice remained nearly ideal hexagonal. Analysis of atomic displacements showed that the rearrangement decays with distance: the root-mean-square displacement was greater than 6 pm at a distance of two layers from the interface and dropped to the noise level of about 3 pm at a distance of four layers. The depth resolution of the method reached 0.94±0.11 nm, allowing separation of contributions from adjacent layers. Experimental data agree well with the theoretical model, but the strength of the rearrangement was higher than predictions based on bilayer parameters. This is explained by the suppression of bending by outer layers, which forces inner layers to rearrange more strongly in-plane. Additionally, the strain tensor across a partial dislocation was measured, confirming its screw character.
This work demonstrates for the first time that multislice electron ptychography can reconstruct the three-dimensional atomic structure of buried interfaces with picometer precision. This is a fundamentally new tool for studying hidden interfaces in multilayer van der Waals heterostructures. Unlike related studies that relied on surface methods or projection images, here a layer-by-layer picture of the rearrangement and its decay in the bulk was obtained. The data show that the rearrangement in thick crystals is stronger than expected, requiring a revision of theoretical models. This opens the way to deliberate design of multilayer systems with tailored mechanical and electronic properties.
The multislice ptychography method can be extended to other materials and interfaces, including heterostructures with different bonding types, ferroelectric vortices, color centers in semiconductors, and dislocation networks. As computational resources grow and algorithms improve, ptychography will become a standard tool for non-destructive reconstruction of volumetric atomic data. In the future, structural data can be correlated with local transport, optical, and tribological measurements, linking atomic rearrangement to macroscopic properties.
The results will impact the physics of moiré systems, tribology, electronics based on sliding ferroelectricity, and neuromorphic computing, where precise information about the structure of buried interfaces is crucial.
Immediate next steps include correlating structural data with vertical transport and local friction measurements, as well as applying the method to a broader class of materials and interfaces.
For condensed matter physics, an open question remains how lattice rearrangement at buried interfaces affects electronic correlations, superconductivity, and topological properties in multilayer moiré systems. This work provides the first direct experimental access to the atomic structure of such interfaces, which is necessary for testing theoretical predictions.
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What the work does
This work reconstructs the three-dimensional atomic structure of a buried interface between thick MoS2 and MoS2/WS2 crystals using multislice electron ptychography. The authors find that the moiré reconstruction penetrates several layers deep and is stronger than predicted by bilayer models.
Where its strength is
The method allows direct visualization of atomic displacements at buried interfaces with picometer precision, opening new avenues for studying the bulk properties of twisted systems.
Where it could go next
Worth trying
Nearby works in our archive
The archive is sparse around this work: the closest review is only 0.54, against a usual 0.64. It looks like few have drilled nearby.
The precision of atomic position determination in this experiment was about 3 picometers, which is 30 times smaller than the diameter of a hydrogen atom.
The idea of controlling material properties by twisting layers resembles the concept of 'twisted' worlds in science fiction, where small changes in geometry lead to radically different physical laws, as in Greg Egan's novel 'Schild's Ladder'.