Lattice reconstruction and corresponding strain accumulation play a key role in defining the electronic structure of two-dimensional moir\'e superlattices, including those of transition metal dichalcogenides (TMDs). Imaging of TMD moir\'es 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 moir\'e layers in hBN further localizes and enhances these in-plane reconstruction pathways, 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 moir\'e potential.
@article{arxiv.2212.07006,
title = {Rotational and Dilational Reconstruction in Transition Metal Dichalcogenide Moir\'e Bilayers},
author = {Madeline Van Winkle and Isaac M. Craig and Stephen Carr and Medha Dandu and Karen C. Bustillo and Jim Ciston and Colin Ophus and Takashi Taniguchi and Kenji Watanabe and Archana Raja and Sinéad M. Griffin and D. Kwabena Bediako},
journal= {arXiv preprint arXiv:2212.07006},
year = {2023}
}