Relaxation effects in transition metal dichalcogenide bilayer heterostructures

While moiré structures in twisted bilayer transition metal dichalcogenides (TMDCs) have been studied for over a decade, the importance of lattice relaxation effects was pointed out only in 2021 by DiAngelo and MacDonald1, who reported the emergence of a Dirac cone upon relaxation. TMDCs of group 6 transition metals MX2 (M = Mo, W, X = S, Se) share layered structures with pronounced interlayer interactions, exhibiting a direct band gap when exfoliated to a two-dimensional (2D) monolayer. As their heterolayers are incommensurable, moiré structures are present in the bilayers even if stacked without a twist angle. This study addresses the challenge of accurately modeling and understanding the structural relaxation in twisted TMDC heterobilayers. We show that the typical experimental situation of finite-size flakes stacked upon larger flakes can reliably be modeled by fully periodic commensurate models. Our findings reveal significant lattice reconstruction in TMDC heterobilayers, which strongly depend on the twist angle. We can categorize the results in two principal cases: at or near the untwisted configurations of 0° and 60°, domains with matching lattice constants form and the two constituting layers exhibit significant in-phase corrugation—their out-of-plane displacements are oriented towards the same direction in all local stackings—while at large twist angles—deviating from the 0° and 60°—the two layers show an out-of-phase corrugation. In particular, we reveal that the lattice reconstruction results from the competition between the strain energy cost and the van der Waals energy gain. Additionally, our systematical study highlights structural disparities between heterostructures composed of different or identical chalcogen atoms. Our research not only confirms the reliability of using periodic commensurate models to predict heterostructure behavior but also enriches the understanding of TMDC bilayer heterostructures.