Rotational and dilational reconstruction in transition metal dichalcogenide moire bilayers

Lattice reconstruction crucially influences the electronic properties of twisted van der Waals structures. Here, the authors report a quantitative characterization of the mechanical deformations occurring in small-angle twisted bilayers and heterobilayers of 2D semiconductors via interferometric 4D scanning transmission electron microscopy. Lattice reconstruction and corresponding strain accumulation plays a key role in defining the electronic structure of two-dimensional moire superlattices, including those of transition metal dichalcogenides (TMDs). Imaging of TMD moires has so far provided a qualitative understanding of this relaxation process in terms of interlayer stacking energy, while models of the underlying deformation mechanisms have relied on simulations. Here, we use interferometric four-dimensional scanning transmission electron microscopy to quantitatively map the mechanical deformations through which reconstruction occurs in small-angle twisted bilayer MoS2 and WSe2/MoS2 heterobilayers. We provide direct evidence that local rotations govern relaxation for twisted homobilayers, while local dilations are prominent in heterobilayers possessing a sufficiently large lattice mismatch. Encapsulation of the moire layers in hBN further localizes and enhances these in-plane reconstruction pathways by suppressing out-of-plane corrugation. We also find that extrinsic uniaxial heterostrain, which introduces a lattice constant difference in twisted homobilayers, leads to accumulation and redistribution of reconstruction strain, demonstrating another route to modify the moire potential.